Aleph官方网址-快连加速器app

    January 19, 2024

    坚果加速器下载官网

    Aleph官方网址-快连加速器app

    Aleph官方网址-快连加速器app

    In the last episode we built a "Hello, World" application using gi-gtk-declarative. It's now time to convert it into a to-do list application, in the style of TodoMVC.

    To convert the “Hello, World!” application to a to-do list application, we begin by adjusting our data types. The Todo data type represents a single item, with a Text field for its name. We also need to import the Text type from Data.Text.

    data Todo = Todo
      { name :: Text
      }

    Our state will no longer be (), but a data types holding 狸猫加速器安卓版安装包 of Todo items. This means we also need to import Vector from Data.Vector.

    data State = State
      { todos :: Vector Todo
      }

    As the run function returns the last state value of the state reducer loop, we need to discard that return value in main. We wrap the run action in void, imported from Control.Monad.

    Let’s rewrite our view function. We change the title to “TodoGTK+” and replace the label with a todoList, which we’ll define in a where binding. We use 蚂蚁ant加速器安卓下载 to declare a Gtk.Box, with vertical orientation, containing all the to-do items. Using fmap and a typed hole, we see that we need a function Todo -> BoxChild Event.

    view' :: State -> AppView Gtk.Window Event
    view' s = bin
      Gtk.Window
      [#title := "TodoGTK+", on #deleteEvent (const (True, Closed))]
      todoList
      where
        todoList = container Gtk.Box
                             [#orientation := Gtk.OrientationVertical]
                             (fmap _ (todos s))

    The todoItem will render a Todo value as a Gtk.Label displaying the name.

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    Now, GHC tells us there’s a “non-type variable argument in the constraint”. The type of todoList requires us to add the FlexibleContexts language extension.

    {-# LANGUAGE FlexibleContexts  #-}
    {-# LANGUAGE OverloadedLabels  #-}
    {-# LANGUAGE OverloadedLists   #-}
    {-# LANGUAGE OverloadedStrings #-}
    module Main where

    The remaining type error is in the definition of 狸猫Ⅴpn安卓, where the initial state cannot be a () value. We construct a State value with an empty vector.

    main :: IO ()
    main = void $ run App
      { view         = view'
      , update       = update'
      , inputs       = []
      , initialState = State {todos = mempty}
      }

    Adding New To-Do Items

    While our application type-checks and runs, there are no to-do items to display, and there’s no way of adding new ones. We need to implement a form, where the user inserts text and hits the Enter key to add a new to-do item. To represent these events, we’ll add two new constructors to our Event type.

    data Event
      = TodoTextChanged Text
      | TodoSubmitted
      | Closed

    TodoTextChanged will be emitted each time the text in the form changes, carrying the current text value. The TodoSubmitted event will be emitted when the user hits Enter.

    When the to-do item is submitted, we need to know the current text to use, so we add a 蚂蚁vp(永久免费) field to the state type.

    data State = State
      { todos       :: Vector Todo
      , currentText :: Text
      }

    We modify the initialState value to include an empty Text value.

    main :: IO ()
    main = void $ run App
      { view         = view'
      , update       = update'
      , inputs       = []
      , initialState = State {todos = mempty, currentText = mempty}
      }

    Now, let’s add the form. We wrap our 蚂蚁vp(永久免费) in a vertical box, containing the 狸猫Ⅴpn安卓 and a newTodoForm widget.

    view' :: State -> AppView Gtk.Window Event
    view' s = bin
      Gtk.Window
      [#title := "TodoGTK+", on #deleteEvent (const (True, Closed))]
      (container Gtk.Box
                 [#orientation := Gtk.OrientationVertical]
                 [todoList, newTodoForm]
      )
      where
        ...

    The form consists of a Gtk.Entry widget, with the currentText of our state as its text value. The placeholder text will be shown when the entry isn’t focused. We use onM to attach an effectful event handler to the changed signal.

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    The typed hole tells us we need a function Gtk.Entry -> IO Event. The reason we use onM is to have that IO action returning the event, instead of having a pure function. We need it to query the underlying GTK+ widget for it’s current text value. By using entryGetText, and mapping our event constructor over that IO action, we get a function of the correct type.

        ...
        newTodoForm = widget
          Gtk.Entry
          [ #text := currentText s
          , #placeholderText := "What needs to be done?"
          , onM #changed (fmap TodoTextChanged . Gtk.entryGetText)
          ]

    It is often necessary to use onM and effectful GTK+ operations in event handlers, as the callback type signatures rarely have enough information in their arguments. But for the next event, TodoSubmitted, we don’t need any more information, and we can use on to declare a pure event handler for the activated signal.

        ...
        newTodoForm = widget
          Gtk.Entry
          [ #text := currentText s
          , #placeholderText := "What needs to be done?"
          , onM #changed (fmap TodoTextChanged . Gtk.entryGetText)
          , on #activate TodoSubmitted
          ]

    Moving to the next warning, we see that the update' function is no longer total. We are missing cases for our new events. Let’s give the arguments names and pattern match on the event. The case for Closed will be the same as before.

    update' :: State -> Event -> Transition State Event
    update' s e = case e of
      Closed -> Exit

    When the to-do text value changes, we’ll update the currentText state using a Transition. The first argument is the new state, and the second argument is an action of type IO (Maybe Event). We don’t want to emit any new event, so we use (pure Nothing).

    update' :: State -> Event -> Transition State Event
    update' s e = case e of
      TodoTextChanged t -> Transition s { currentText = t } (pure Nothing)
      Closed -> Exit

    For the TodoSubmitted event, we define a newTodo value with the currentText as its name, and transition to a new state with the newTodo item appended to the todos vector. We also reset the currentText to be empty.

    To use Vector.snoc, we need to add a qualified import.

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    Running the application, we can start adding to-do items.

    Improving the Layout

    Our application doesn’t look very good yet, so let’s improve the layout a bit. We’ll begin by left-aligning the to-do items.

    todoItem i todo =
      widget
        Gtk.Label
        [#label := name todo, #halign := Gtk.AlignStart]

    To push the form down to the bottom of the window, we’ll wrap the todoList in a BoxChild, and override the defaultBoxChildProperties to have the child widget expand and fill all the available space of the box.

    todoList =
      BoxChild defaultBoxChildProperties { expand = True, fill = True }
        $ container Gtk.Box
                    [#orientation := Gtk.OrientationVertical]
                    (fmap todoItem (todos s))

    We re-run the application, and see it has a nicer layout.

    Completing To-Do Items

    There’s one very important missing: being able to mark a to-do item as completed. We add a 狸猫Ⅴpn安卓 field called completed to the Todo data type.

    data Todo = Todo
      { name      :: Text
      , completed :: Bool
      }

    When creating new items, we set it to 坚果加速器下载官网.

    update' :: State -> Event -> Transition State Event
    update' s e = case e of
      ...
      TodoSubmitted ->
        let newTodo = Todo {name = currentText s, completed = False}
        in  Transition
              s { todos = todos s `Vector.snoc` newTodo, currentText = mempty }
              (pure Nothing)
      ...

    Instead of simply rendering the name, we’ll use strike-through markup if the item is completed. We define completedMarkup, and using guards we’ll either render the new markup or render the plain name. To make it strike-through, we wrap the text value in <s> tags.

    widget
      Gtk.Label
        [ #label := completedMarkup todo
        , #halign := Gtk.AlignStart
        ]
      where
        completedMarkup todo
          | completed todo = "<s>" <> name todo <> "</s>"
          | otherwise      = name todo

    For this to work, we need to enable markup for the label be setting #useMarkup to True.

    widget
      Gtk.Label
        [ #label := completedMarkup todo
        , #useMarkup := True
        , #halign := Gtk.AlignStart
        ]
      where
        completedMarkup todo
          | completed todo = "<s>" <> name todo <> "</s>"
          | otherwise      = name todo

    In order for the user to be able to toggle the completed status, we wrap the label in a Gtk.CheckButton bin. The #active property will be set to the current completed status of the Todo value. When the check button is toggled, we want to emit a new event called TodoToggled.

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    Let’s add the new constructor to the Event data type. It will carry the index of the to-do item.

    data Event
      = TodoTextChanged Text
      | TodoSubmitted
      | TodoToggled Int
      | Closed

    To get the corresponding index of each Todo value, we’ll iterate using Vector.imap instead of using fmap.

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    The pattern match on events in the update' function is now missing a case for the new event constructor. Again, we’ll do a transition where we update the todos somehow.

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    We need a function Vector Todo -> Vector Todo that modifies the value at the index i. There’s no handy function like that available in the vector package, so we’ll create our own. Let’s call it mapAt.

    update' :: State -> Event -> Transition State Event
    update' s e = case e of
      ...
      TodoToggled i -> Transition s { todos = mapAt i _ (todos s) } (pure Nothing)
      ...

    It will take as arguments the index, a mapping function, and a Vector a, and return a Vector a.

    mapAt :: Int -> (a -> a) -> Vector a -> Vector a

    We implement it using Vector.modify, and actions on the mutable representation of the vector. We overwrite the value at i with the result of mapping f over the existing value at i.

    mapAt :: Int -> (a -> a) -> Vector a -> Vector a
    mapAt i f = Vector.modify (\v -> MVector.write v i . f =<< MVector.read v i)

    To use mutable vector operations through the MVector name, we add the qualified import.

    import qualified Data.Vector.Mutable           as MVector

    Finally, we implement the function to map, called toggleComplete.

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    Now, we run our application, add some to-do items, and mark or unmark them as completed. We’re done!

    坚果加速器下载官网

    Building our to-do list application, we have learned the basics of 狸猫加速器安卓版 and the “App.Simple” architecture. There’s more to learn, though, and I recommend checking out the project documentation. There are also a bunch of examples in the Git repository.

    Please note that this project is very young, and that APIs are not necessarily stable yet. I think, however, that it’s a much nicer way to build GTK+ applications using Haskell than the underlying APIs provided by the auto-generated bindings.

    Now, have fun building your own functional GTK+ applications!

    by Oskar Wickström at January 19, 2024 12:00 AM

    August 03, 2024

    狸猫加速器安卓版安装包

    Aleph官方网址-快连加速器app

    Gulliver's Travels (1726), Part III, chapter 2:

    I observed, here and there, many in the habit of servants, with a blown bladder, fastened like a flail to the end of a stick, which they carried in their hands. In each bladder was a small quantity of dried peas, or little pebbles, as I was afterwards informed. With these bladders, they now and then flapped the mouths and ears of those who stood near them, of which practice I could not then conceive the meaning. It seems the minds of these people are so taken up with intense speculations, that they neither can speak, nor attend to the discourses of others, without being roused by some external action upon the organs of speech and hearing… . This flapper is likewise employed diligently to attend his master in his walks, and upon occasion to give him a soft flap on his eyes; because he is always so wrapped up in cogitation, that he is in manifest danger of falling down every precipice, and bouncing his head against every post; and in the streets, of justling others, or being justled himself into the kennel.

    When I first told Katara about this, several years ago, instead of “the minds of these people are so taken up with intense speculations” I said they were obsessed with their phones.

    Now the phones themselves have become the flappers:

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    Our minds are not even taken up with intense speculations, but with Instagram. Dean Swift would no doubt be disgusted.

    by Mark Dominus (mjd@plover.com) at August 03, 2024 02:27 AM

    August 01, 2024

    hi vph加速器下载

    Aleph官方网址-快连加速器app

    哪个网游加速器比较好用? - 知乎 - Zhihu:2021-6-4 · 测试的游戏是安卓版PUBG M亚服,众每个加速器都玩了三局的表现,并且游戏加速器的丢包率or网速与游戏中的网速有一些不同。因为毕竟加速器是理想状态下的加速表现,而实际情况中,如果你手机信号不是很强,会极大影响你在游戏里的网速。

    OP asked:

    I know this question has been asked many times and there is good information out there which has clarified a lot for me but I still do not understand how the addition and multiplication tables for 狸猫加速器安卓版 is constructed?

    I've seen [links] but none explicity explain the construction and I'm too new to be told "its an extension of "

    The only “reasonable” answer here is “get an undergraduate abstract algebra text and read the chapter on finite fields”. Because come on, you can't expect some random stranger to appear and write up a detailed but short explanation at your exact level of knowledge.

    But sometimes Internet Magic Lightning strikes  and that's what you do get! And OP set themselves up to be struck by magic lightning, because you can't get a detailed but short explanation at your exact level of knowledge if you don't provide a detailed but short explanation of your exact level of knowledge — and this person did just that. They understand finite fields of prime order, but not how to construct the extension fields. No problem, I can explain that!

    I had special fun writing this answer because I just love constructing extensions of finite fields. (Previously: [1] [2])


    For any given , there is at most one field with elements: only one, if 坚果加速器下载官网 is a power of a prime number (狸猫加速速器) and none otherwise (狸猫加速器安卓版百度云). This field with hi vph加速器下载 elements is written as or as .

    Suppose we want to construct 狸猫加速器安卓版百度云 where . When , this is easy-peasy: take the 狸猫加速器安卓版下载 elements to be the integers , and the addition and multiplication are done modulo .

    When it is more interesting. One possible construction goes like this:

    1. The elements of are the polynomials $$a_{k-1}x^{k-1} + a_{k-2}x^{k-2} + \ldots + a_1x+a_0$$ where the coefficients are elements of . That is, the coefficients are just integers in , but with the understanding that the addition and multiplication will be done modulo 狸猫加速器安卓版下载在哪里. Note that there are 狸猫加速器安卓版百度云 of these polynomials in total.

    2. Addition of polynomials is done exactly as usual: combine like terms, but remember that the the coefficients are added modulo 狸猫加速器安卓版下载在哪里 because they are elements of .

    3. Multiplication is more interesting:

      a. Pick an irreducible polynomial of degree 黑洞加速器破解版app. “Irreducible” means that it does not factor into a product of smaller polynomials. How to actually locate an irreducible polynomial is an interesting question; here we will mostly ignore it.

      b. To multiply two elements, multiply them normally, remembering that the coefficients are in . Divide the product by and keep the remainder. Since has degree , the remainder must have degree at most , and this is your answer.


    Now we will see an example: we will construct . Here and . The elements will be polynomials of degree at most 1, with coefficients in . There are four elements: 蚂蚁ant加速器安卓下载 and . As usual we will write these as 狸猫加速器安卓版下载. This will not be misleading.

    Addition is straightforward: combine like terms, remembering that because the coefficients are in :

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    The multiplication as always is more interesting. We need to find an irreducible polynomial . It so happens that hi vph加速器下载 is the only one that works. (If you didn't know this, you could find out easily: a reducible polynomial of degree 2 factors into two linear factors. So the 狸猫加速器安卓版下载 polynomials are , and . That leaves only .)

    To multiply two polynomials, we multiply them normally, then divide by 快喵ⅴpn破解版 and keep the remainder. For example, what is 蚂蚁ant加速器安卓下载? It's 狸猫加速速器. There is a theorem from elementary algebra (the “division theorem”) that we can find a unique quotient and remainder , with the degree of less than 2, such that 狸猫Ⅴpn安卓. In this case, 狸猫加速器安卓版百度云 works. (You should check this.) Since this is our answer: .

    Let's try . We want , and it happens that works. So .

    I strongly recommend that you calculate the multiplication table yourself. But here it is if you want to check:

    $$\begin{array}{c|cccc} · & 0 & 1 & x & x+1 \\ \hline 0 & 0 & 0 & 0 & 0 \\ 1 & 0 & 1 & x & x+1 \\ x & 0 & x & x+1 & 1 \\ x+1 & 0 & x+1 & 1 & x \end{array} $$

    To calculate the unique field 狸猫加速器安卓版下载在哪里 of order 8, you let the elements be the 8 second-degree polynomials and instead of reducing by , you reduce by . (Not by , because that factors as .) To calculate the unique field 快喵ⅴpn破解版 of order 27, you start with the 27 third-degree polynomials with coefficients in 狸猫Ⅴpn安卓, and you reduce by 黑洞加速器破解版app (I think).


    The special notation 快喵ⅴpn破解版 means the ring of all polynomials with coefficients from 狸猫加速器安卓版下载在哪里. means the ring of all multiples of polynomial . (A ring is a set with an addition, subtraction, and multiplication defined.)

    When we write we are constructing a thing called a “quotient” structure. This is a generalization of the process that turns the ordinary integers into the modular-arithmetic integers we have been calling . To construct , we start with and then agree that two elements of will be considered equivalent if they differ by a multiple of 安卓永久免费网络加速器.

    To get 狸猫Ⅴpn安卓 we start with 狸猫加速器安卓版, and then agree that elements of will be considered equivalent if they differ by a multiple of hi vph加速器下载. The division theorem guarantees that of all the equivalent polynomials in a class, exactly one of them will have degree less than that of , and that is the one we choose as a representative of its class and write into the multiplication table. This is what we are doing when we “divide by and keep the remainder”.


    A particularly important example of this construction is . That is, we take the set of polynomials with real coefficients, but we consider two polynomials equivalent if they differ by a multiple of . By the division theorem, each polynomial is then equivalent to some first-degree polynomial .

    Let's multiply $$(ax+b)(cx+d).$$ As usual we obtain $$acx^2 + (ad+bc)x + bd.$$ From this we can subtract 蚂蚁ant加速器安卓下载 to obtain the equivalent first-degree polynomial $$(ad+bc) x + (bd-ac).$$

    Now recall that in the complex numbers, 狸猫加速器安卓版. We have just constructed the complex numbers,with the polynomial playing the role of 安卓永久免费网络加速器.


    [ Note to self: maybe write a separate article about what makes this a good answer, and how it is structured. ]

    by Mark Dominus (mjd@plover.com) at August 01, 2024 04:10 PM

    ERDI Gergo

    Aleph官方网址-快连加速器app

    A couple weeks ago, I attended some of the 狸猫加速器安卓版百度云 talks that the time zone difference allowed. One of the satellite workshops of FSCD this year was the Workshop on Rewriting Techniques for Program Transformations and Evaluation, where Martin Lester presented a talk Program Transformations Enable Verification Tools to Solve Interactive Fiction Games.

    Because I haven't been able to find slides or the paper itself online, let me summarize it with my own words here quickly. Back in the late seventies and early eighties, Scott Adams (unrelated to the 坚果加速器下载官网 comic strip creator) was a prolific text adventure creator; the 狸猫加速器安卓版百度云 has written about his games in length, but basically these were simplistic (and in my opinion, creatively quite weak) games published on very limited platforms, where they found a following. Martin Lester's talk was about taking an off-the-shelf open source interpreter for these interactive fiction games (ScottFree) and feeding it (and a given game data file's contents) to a compiler that turns it into an SMT problem, with the free variables corresponding to the user input. Then, if an SMT solver can find an assignment satisfying a winning end condition, that means we have found a possible transcript of user input that wins the given game.

    This combination of semi-formal methods and interactive fiction, plus the fact that I wanted to play around with SMT solver-backed interpreters ever since the 狸猫Ⅴpn安卓 talk at last year's ICFP, meant that the pull of this topic was just irresistable nerd catnip for me. So I took a week of afternoon hacking time from working on my Clash book, and started writing a Scott Adams adventure game engine in Haskell, with the aim of doing something similar to Lester's work.

    An SBV-based Scott Adams solver

    And so now I'm here to tell you about how it went, basically a "poor man's Rosette". When I started this, I have never used SMT solvers and never even looked at SBV, so I am not claiming I became an expert in just a week. But I managed to bumble my way through to something that works well enough on a toy example, so... let's see.

    Step one was to implement a bog-standard interpreter for these Scott Adams adventure games. I didn't implement every possible condition and instruction, just barely enough to get a non-trivial example from ScottKit working. My target was the fourth tutorial adventure; see if you can find a solution either by playing the game, or by reading the game script. Why specifically the fourth tutorial example? Well, the short answer is because that is what Lester used as his example in his talk.

    Here is the Git commit of this implementation; as you can see, there is really nothing special in there. The game data is parsed using Attoparsec into a simple datatype representation, which is then executed in ReaderT WriterT State, with the Reader containing the static game data, the Writer the output messages, and the State the game state, which is mostly just the current locations of the various items the player can interact with:

    data S = S
        { _currentRoom :: Int16
        , _needLook :: Bool
        , _itemLocations :: Array Int16 Int16
        , _endState :: Maybe Bool
        } deriving Show
    makeLenses ''S
    
    type Engine = ReaderT Game (WriterT [String] (State S))      
        

    The second step was to use SBV so that (mostly) the same interpreter can also be executed symbolically. This is the interesting part. It started with changing the Writer output and the State representation to use SBV's symbolic types, and then following the type errors:

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    Arithmetic works out of the box because of the Num instances; because the Haskell Prelude's Eq and Ord typeclasses hardcode the result type to Bool, and we want symbolic SBool results instead, we have to replace e.g. (==) with (.==).

    For the control structures, my idea was to write Mergeable instances for the MTL types. The definitions of these instances are very straightforward, and it allowed me to define symbolic versions of things like when or case with literal matches. The end result of all this is that we can write quite straightforward monadic code, just replacing some combinators with their symbolic counterpart. Here's an example of the code that runs a list of instruction codes in the context of their conditions; even without seeing any other definitions it should be fairly straightforward what it does:

    狸猫浏览器绿色版_狸猫浏览器官方下载_狸猫浏览器5.0.0.0 ...:2021-3-9 · 狸猫浏览器(Leocat)采用最新版全球最快的WebKit内核,上网速度加快5倍,智能防卡死。闪电般打开网页和应用,性能全面超越其他同类浏览器!狸猫浏览器具有自定义主页、多标签浏览、标签自由拖拽等增强浏览舒适度的功能设置,能让您在浏览网页的过程中更感流畅。

    I decided to use concrete lists and arrays of symbolic values instead of symbolic arrays throughout the code. One interesting example of sticking to this approach is in the implementation of listing all items in the current room. The original concrete code looks like this:

    let itemsHere =
            [ desc
            | (Item _ _ desc _, loc) <- zip (A.elems items) (A.elems itemLocs)
            , loc == here
            ]
    unless (null itemsHere) $ do
        say "I can also see:"
        mapM_ (\desc -> say $ " * " <> desc) itemsHere
        

    For the symbolic version, I had to get rid of the filtering (since loc .== here returns an SBool now), and instead, I create a concrete list of pairs of symbolic locations and concrete descriptions. By going over the full list, I can push all the symbolic ambiguity down to just the output:

    let itemLocsWithDesc =
            [ (loc, desc)
            | (Item _ _ desc _, loc) <- zip (A.elems items) (A.elems itemLocs)
            ]
        anyHere = sAny ((.== here) . fst) itemLocssWithDesc
    sWhen anyHere $ do
        say_ "I can also see:"
        forM_ itemLocsWithDesc $ \(loc, desc) ->
            sWhen (loc .== here) $ say $ literal $ " * " <> desc      
        

    By the way, as the above code shows, I kept the user-visible text messages in the symbolic version. This is completely superfluous for solving, but it allows using the symbolic interpreter with concrete values: since all input is concrete, we can safely assume that the symbolic output values are all constants. In practice, this means we recover the original interactively playable version from the SBV-based one simply by running inside SBV's Query monad and getValue'ing the concrete String output from the SStrings coming out of the WriterT. I wouldn't be surprised if this turns out to be a major drain on performance, but because my aim was mostly to just get it working, I never bothered checking. Besides, since noone looks at the output in solver mode, maybe Haskell's laziness ensures there's no overhead. I really don't know.

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    stepPlayer :: SInput -> Engine (SMaybe Bool)
    stepPlayer (verb, noun) = do
        perform (verb, noun)
        finished
        

    The question then is, how do we keep running this (and letting the state evolve) for more and more lines of symbolic input, until we get an sJust sTrue result (meaning the player has won the game)? My original idea was to let the user say how many steps to check, and then generate a full list of symbolic inputs up-front. I asked around on Stack Overflow for something better, and it was this very helpful answer that pointed me in the direction of the Query monad in the first place. With this incremental approach, I can feed it one line of symbolic input, check for satisfiability with the newly yielded constraints, and if there's no solution yet, keep this process going, letting the next stepPlayer call create additional constraints.

    I've factored out the whole thing into the following nicely reusable function; this is also the reason I am using ReaderT WriterT State instead of RWS so I can peel away naturally into a State.

    loopState :: (SymVal i) => (Int -> Query (SBV i)) -> s -> (SBV i -> State s SBool) -> Query ([i], s)
    loopState genCmd s0 step = go 1 s0 []
      where
        go i s cmds = do
            io $ putStrLn $ "Searching at depth: " ++ show i
    
            cmd <- genCmd i
            let cmds' = cmds ++ [cmd]
    
            push 1
            let (finished, s') = runState (step cmd) s
            constrain finished
            cs <- checkSat
    
            case cs of
                Unk -> error $ "Solver said Unknown, depth: " ++ show i
                Unsat -> do
                    pop 1
                    go (i+1) s' cmds'
                Sat -> do
                    cmds' <- mapM getValue cmds'      
                    return (cmds', s')
        

    SBV bugs discovered on the way

    Because I'm a complete SBV noob, I was reluctant to attribute problems to SBV bugs first; I ended up with 狸猫浏览器官方最新下载_狸猫浏览器(Leocat) 5.3.0安全版 ...:2021-5-26 · 软件帝为你带来狸猫浏览器(Leocat) 5.3.0安全版免费下载。狸猫浏览器是一个简单的整洁的浏览器,上网速度加快5倍,智能防卡死拥有闪电般的速度,是每一个用户都喜欢浏览器,此外,它还拥有cookies快速清除,给你爽快的浏览器体验。强大的界面自定义功能,隐藏菜单栏、状态栏. However, it turned out I do still have my Midas touch of finding bugs very quickly in anything I start playing around with; this time, it started with SBV generating invalid SMTLib output from my code. Although my initial report was basically just "this several hundred line project Just Doesn't Work", I managed to cut it down into more reasonable size. The SBV maintainers, especially Levent Erkök, have been very helpful with quick turnaround.

    The other bug I found was symbolic arrays misbehaving; although I ended up not using either SFunArray nor SArray in the final version of ScottCheck, it is good to know that my silly project has somehow contributed, if just a little, to making SBV itself better.

    The money shot

    So, lots of words, but where's the meat? Well first off, my code itself is on GitHub, and could serve as a good introduction to someone wanting to start using SBV with a stateful computation. And second, here is a transcript of ScottCheck verifying that the tutorial game is solvable, with the Z3 backend; the timestamps are in minutes and seconds from the start, to give an idea of how later steps become slower because there's an exponential increase in all possible inputs leading up to it. The words may look truncated, but that's because the actual internal vocabulary of the game only uses three letter words; further letters from the user are discarded (so COIN parses as COI etc.).

    00:00 Searching at depth: 1
    00:00 Searching at depth: 2
    00:00 Searching at depth: 3
    00:00 Searching at depth: 4
    00:00 Searching at depth: 5
    00:01 Searching at depth: 6
    00:01 Searching at depth: 7
    00:02 Searching at depth: 8
    00:05 Searching at depth: 9
    00:11 Searching at depth: 10
    00:24 Searching at depth: 11
    00:45 Searching at depth: 12
    01:24 Searching at depth: 13
    02:38 Searching at depth: 14
    03:35 Solution found:
    03:35   1. GO WES
    03:35   2. GET CRO
    03:35   3. GO EAS
    03:35   4. GO NOR
    03:35   5. GET KEY
    03:35   6. GO SOU
    03:35   7. OPE DOO
    03:35   8. GO DOO
    03:35   9. GET COI
    03:35  10. GO NOR
    03:35  11. GO WES
    03:35  12. GO NOR
    03:35  13. DRO COI
    03:35  14. SCO ANY     
        

    August 01, 2024 01:48 PM

    Douglas M. Auclair (geophf)

    Aleph官方网址-快连加速器app


    • 2024-07-31: Well, that's random. Generating random numbers and sequences is today's #Haskell problem. Today's #haskell solution shows that I can (<*>) that monad, first go, without even looking it up or anything. So, yeah, I'm walking pretty tall right now. 
    • 2024-07-30: Kate and Shoaib are going on vacation. Commander Adama in Star Wars tells us that for today's #haskell problem, we are to "Make it so, Number one." And: there they go! Shoaib and Kate, going on a vacay, havin' fun, and type-safely, at that, because of the #haskell solution 'n stuff. 
    • 2024-07-29: "How many days until ...?" A date calculator for today's #haskell problem. When I say: "Compute the date," I'm not talking fig trees, here. The solution to today's #Haskell problem. 
      狸猫加速器安卓版百度云
    • 2024-07-28: Today's #haskell problem involves passing arguments to and verifying results from an external application. 'frankenfurters.' That's what we're trying to sum here. 'frankenfurters.' 'Fault Tolerance'? We've got that with today's #haskell solution. 
    • 2024-07-27: Today's #Haskell exercise makes us realize that ... "All, in all, you're just a ... nother brick in THE WALL. :/" A solution pour vous, s'il vous plaît. 
      黑洞加速器破解版app
    • 2024-07-24: Today's #haskell problem explores the result of processed images from, in this case, Amazon's Rekognition. Today's #haskell solution: BIRDz! ... Cardinals, in fact. 
    • 2024-07-23: For today's #haskell problem, let's read in a JPG (o' FLAH'z!) and write it out as a TIFF ... for, you know, like: an image processing/classification exercise, at some later date. Ooh! TIFFY! TIFF saved from loaded JPEG image. 
    • 2024-07-22: For today's #haskell problem we 蚂蚁vp(永久免费) returned from a REST endpoint. The #haskell solution is declarative/functional-composition goodness to parse data from JSON returned from a REST endpoint. 
    • 2024-07-21: We ping a public API REST endpoint for today's #Haskell problem. For today's #haskell solution, simpleHttp in Network.HTTP.Conduit does the trick! 
    • 2024-07-20: For today's #haskell problem we read a file that contains a JSON message and parse it. 
    • 2024-07-17: Oops! hi vph加速器下载 That's today's ... I mean, YESTERDAY's, #haskell problem.
       
    • 2024-07-16: And now, for something completely different: today's #haskell problem has us 狸猫网络助手_狸猫网络助手安卓版下载_软吧:2021-8-9 · 狸猫网络助手安卓版免费下载,狸猫网络助手,一款精心打造的手机网络加速应用,针对线路服务类型匹配为用户提供专属的线路,打造个人专属的网络环境。 ps:该软件暂无安卓版下载 主要功能:【一键连接】【网络加速】【每日签到】 软件特点:. #haskell solution to which level is most recruit-efficient for a dark chest. 
    • 2024-07-15: For today's #haskell problem, we pull what we've done so far all together and compute today's pairings, given historical context.  
    • 2024-07-14: For today's #haskell problem, we pull what we've done so far all together and compute today's pairings, given historical context. 
    • 2024-07-14: For today's #Haskell problem, we look at using our historical context of pairings to answer questions for future pairings. 
    • 2024-07-13: Now that we've selected pairings for today, let's store those pairings into an historical context for today's #haskell problem. 
    • 2024-07-08: Pairing and ... 'Mobbing' (?) ... okay, really??? is our game for today's #haskell problem. A solution to the simple pairing-problem.
    • 2024-07-07: For today's #haskell problem, we lay a foundation for building a team-pairing app. This day's problem addresses a History-type to provide context to the pairing-algorithm. 
    • 2024-07-06: For today's #haskell problem, we look at finding the spanning trees of a graph. 
    • 2024-07-02: Today's #haskell exercise finds us (acyclic) pathing though a simpler, yet-not-fully connected, graph. 
    • 2024-07-01: For today's #haskell problem we find cycles in graphs, ... MOTORcycles in graphs! AHA! AND MAKE MINE A DUCATI! ON FYE-YARRRR! 🔥 ... no ... wait ... Oh, well. #GraphTheory 

    by geophf (noreply@blogger.com) at August 01, 2024 03:11 AM

    July 31, 2024

    狸猫Ⅴpn安卓

    Aleph官方网址-快连加速器app

    A recent Math Stack Excahnge post was asked to expand the function in powers of and was confused about what that meant, and what the point of it was. I wrote an answer I liked, which I am reproducing here.


    You asked:

    I don't understand what are we doing in this whole process

    which is a fair question. I didn't understand this either when I first learned it. But it's important for practical engineering reasons as well as for theoretical mathematical ones.

    Before we go on, let's see that your proposal is the wrong answer to this question, because it is the correct answer, but to a different question. You suggested: $$e^{2x}\approx1+2\left(x-1\right)+2\left(x-1\right)^2+\frac{4}{3}\left(x-1\right)^3$$

    Taking we get 坚果加速器下载官网, which is just wrong, since actually . As a comment pointed out, the series you have above is for 安卓永久免费网络加速器. But we wanted a series that adds up to .

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    $$e^{2x} \approx 1+2x+2x^2+\frac{4}{3}x^3$$

    so why don't we just use it? Let's try 狸猫加速器安卓版百度云. We get $$e^2\approx 1 + 2 + 2 + \frac43$$

    This adds to 狸猫Ⅴpn安卓, but the correct answer is actually around as we saw before. That is not a very accurate approximation. Maybe we need more terms? Let's try ten:

    $$e^{2x} \approx 1+2x+2x^2+\frac{4}{3}x^3 + \ldots + \frac{8}{2835}x^9$$

    If we do this we get , which isn't too far off. But it was a lot of work! And we find that as gets farther away from zero, the series above gets less and less accurate. For example, take , the formula with four terms gives us 极光加速器官方网站, which is dead wrong. Even if we use ten terms, we get 蚂蚁vp(永久免费), which is still way off. The right answer is actually .

    What do we do about this? Just add more terms? That could be a lot of work and it might not get us where we need to go. (Some Maclaurin series just stop working at all too far from zero, and no amount of terms will make them work.) Instead we use a different technique.

    Expanding the Taylor series “around ” gets us a different series, one that works best when is close to instead of when is close to zero. Your homework is to expand it around , and I don't want to give away the answer, so I'll do a different example. We'll expand around . The general formula is $$e^{2x} \approx \sum \frac{f^{(i)}(3)}{i!} (x-3)^i\tag{$\star$}\ \qquad \text{(when $x$ is close to $3$)}$$

    The is the 狸猫Ⅴpn安卓'th derivative of , which is 狸猫加速器安卓版下载在哪里, so the first few terms of the series above are:

    $$\begin{eqnarray} e^{2x} & \approx& e^6 + \frac{2e^6}1 (x-3) + \frac{4e^6}{2}(x-3)^2 + \frac{8e^6}{6}(x-3)^3\\ & = & e^6\left(1+ 2(x-3) + 2(x-3)^2 + \frac34(x-3)^3\right)\\ & & \qquad \text{(when $x$ is close to $3$)} \end{eqnarray} $$

    The first thing to notice here is that when is exactly , this series is perfectly correct; we get exactly, even when we add up only the first term, and ignore the rest. That's a kind of useless answer because we already knew that . But that's not what this series is for. The whole point of this series is to tell us how different 蚂蚁ant加速器安卓下载 is from when 狸猫加速器安卓版 is close to, but not equal to .

    Let's see what it does at . With only four terms we get $$\begin{eqnarray} e^{6.2} & \approx& e^6(1 + 2(0.1) + 2(0.1)^2 + \frac34(0.1)^3)\\ & = & e^6 \cdot 1.22075 \\ & \approx & 492.486 \end{eqnarray}$$

    which is very close to the correct answer, which is . And that's with only four terms. Even if we didn't know an exact value for , we could find out that is about 蚂蚁ant加速器安卓下载 larger, with hardly any calculation.

    Why did this work so well? If you look at the expression 安卓永久免费网络加速器 you can see: The terms of the series all have factors of the form . When , these are , which becomes very small very quickly as 狸猫Ⅴpn安卓 increases. Because the later terms of the series are very small, they don't affect the final sum, and if we leave them out, we won't mess up the answer too much. So the series works well, producing accurate results from only a few terms, when is close to 极光加速器官方网站.

    But in the Maclaurin series, which is around , those hi vph加速器下载 terms are 蚂蚁ant加速器安卓下载 terms intead, and when , they are not small, they're very large! They get bigger as 黑洞加速器破解版app increases, and very quickly. (The 蚂蚁ant加速器安卓下载 in the denominator wins, eventually, but that doesn't happen for many terms.) If we leave out these many large terms, we get the wrong results.

    The short answer to your question is:

    Maclaurin series are only good for calculating functions when 狸猫加速器安卓版安装包 is close to , and become inaccurate as moves away from zero. But a Taylor series around has its “center” near 蚂蚁ant加速器安卓下载 and is most accurate when 安卓永久免费网络加速器 is close to 蚂蚁ant加速器安卓下载.

    by Mark Dominus (mjd@plover.com) at July 31, 2024 03:50 PM

    Tweag I/O

    Aleph官方网址-快连加速器app

    This is the third in a series of blog posts about Nix flakes. The first part motivated why we developed flakes — to improve Nix’s reproducibility, composability and usability — and gave a short tutorial on how to use flakes. The 极光加速器官方网站 showed how flakes enable reliable caching of Nix evaluation results. In this post, we show how flakes can be used to manage NixOS systems in a reproducible and composable way.

    What problems are we trying to solve?

    Lack of reproducibility

    One of the main selling points of NixOS is reproducibility: given a specification of a system, if you run nixos-rebuild to deploy it, you should always get the same actual system (modulo mutable state such as the contents of databases). For instance, we should be able to reproduce in a production environment the exact same configuration that we’ve previously validated in a test environment.

    However, the default NixOS workflow doesn’t provide reproducible system configurations out of the box. Consider a typical sequence of commands to upgrade a NixOS system:

    • You edit /etc/nixos/configuration.nix.
    • You run nix-channel --update to get the latest version of the nixpkgs repository (which contains the NixOS sources).
    • You run nixos-rebuild switch, which evaluates and builds a function in the 蚂蚁vp(永久免费) repository that takes /etc/nixos/configuration.nix as an input.

    In this workflow, /etc/nixos/configuration.nix might not be under configuration management (e.g. point to a Git repository), or if it is, it might be a dirty working tree. Furthermore, 狸猫加速器安卓版安装包 doesn’t specify what Git revision of nixpkgs to use; so if somebody else deploys the same configuration.nix, they might get a very different result.

    Lack of traceability

    The ability to reproduce a configuration is not very useful if you can’t tell what configuration you’re actually running. That is, from a running system, you should be able to get back to its specification. So there is a lack of traceability: the ability to trace derived artifacts back to their sources. This is an essential property of good configuration management, since without it, we don’t know what we’re actually running in production, so reproducing or fixing problems becomes much harder.

    手机游戏加速器有用吗 安卓游戏加速器下载-爪游控:2021-3-27 · 手机游戏加速器有用吗?近年来,游戏加速器开始走入玩家的视野,其实加速器主要的作用就是解决游戏过程中的延迟、卡顿等现象,大家都在知道要是游戏玩一半卡了那就很影响体验了,所众加速器是很重要的噢,下面小编就要带来安卓游戏加速器下载推荐,来了解下吧。

    $ nixos-version --json | jq -r .nixpkgsRevision
    a84b797b28eb104db758b5cb2b61ba8face6744b

    Unfortunately, this doesn’t allow you to recover configuration.nix or any other external NixOS modules that were used by the configuration.

    Lack of composability

    It’s easy to enable a package or system service in a NixOS configuration if it is part of the nixpkgs repository: you just add a line like 狸猫浏览器官方最新下载_狸猫浏览器(Leocat) 5.3.0安全版 ...:2021-5-26 · 软件帝为你带来狸猫浏览器(Leocat) 5.3.0安全版免费下载。狸猫浏览器是一个简单的整洁的浏览器,上网速度加快5倍,智能防卡死拥有闪电般的速度,是每一个用户都喜欢浏览器,此外,它还拥有cookies快速清除,给你爽快的浏览器体验。强大的界面自定义功能,隐藏菜单栏、状态栏 or services.postgresql.enable = true; to your configuration.nix. But what if we want to use a package or service that isn’t part of Nixpkgs? Then we’re forced to use mechanisms like $NIX_PATH, builtins.fetchGit, imports using relative paths, and so on. These are not standardized (since everybody uses different conventions) and are inconvenient to use (for example, when using 狸猫Ⅴpn安卓, it’s the user’s responsibility to put external repositories in the right directories).

    Put another way: NixOS is currently built around a monorepo workflow — the entire universe should be added to the 狸猫加速器安卓版下载在哪里 repository, because anything that isn’t, is much harder to use.

    It’s worth noting that any NixOS system configuration already violates the monorepo assumption: your system’s configuration.nix is not part of the nixpkgs repository.

    Using flakes for NixOS configurations

    In the previous post, we saw that flakes are (typically) Git repositories that have a file named 极光加速器官方网站, providing a standardized interface to Nix artifacts. We saw flakes that provide packages and development environments; now we’ll use them to provide NixOS system configurations. This solves the problems described above:

    • 蚂蚁ant加速器安卓下载: the entire system configuration (including everything it depends on) is captured by the flake and its lock file. So if two people check out the same Git revision of a flake and build it, they should get the same result.
    • Traceability: nixos-version prints the Git revision of the top-level configuration flake, not its 狸猫加速器安卓版安装包 input.
    • Composability: it’s easy to pull in packages and modules from other repositories as flake inputs.

    狸猫加速器安卓版安装包

    Flake support has been added as an experimental feature to NixOS 20.03. However, flake support is not part of the current stable release of Nix (2.3). So to get a NixOS system that supports flakes, you first need to switch to the nixUnstable package and enable some experimental features. This can be done by adding the following to 狸猫加速器安卓版下载在哪里:

    nix.package = pkgs.nixUnstable;
    nix.extraOptions = ''
      experimental-features = nix-command flakes
    '';

    Creating a NixOS configuration flake

    Let’s create a flake that contains the configuration for a NixOS container.

    $ git init my-flake
    $ cd my-flake
    $ nix flake init -t templates#simpleContainer
    $ git commit -a -m 'Initial version'

    Note that the -t flag to nix flake init specifies a 坚果加速器下载官网 from which to copy the initial contents of the flake. This is useful for getting started. To see what templates are available, you can run:

    狸猫Ⅴpn安卓

    For reference, this is what the initial flake.nix looks like:

    {
      inputs.nixpkgs.url = 御龙之路单机版下载- 全方位下载:2021-6-14 · 御龙之路汉化版是众东方玄幻为背景题材的热血激情仙侠角色扮演游戏,游戏拥有玄幻色彩的画风,精美华丽的画面,激情十足的热血战斗玩法,多人实时在线竞技对战模式,给你带来全新的战;
    
      outputs = { self, nixpkgs }: {
    
        nixosConfigurations.container = nixpkgs.lib.nixosSystem {
          system = "x86_64-linux";
          modules =
            [ ({ pkgs, ... }: {
                boot.isContainer = true;
    
                # Let 'nixos-version --json' know about the Git revision
                # of this flake.
                system.configurationRevision = nixpkgs.lib.mkIf (self ? rev) self.rev;
    
                # Network configuration.
                networking.useDHCP = false;
                networking.firewall.allowedTCPPorts = [ 80 ];
    
                # Enable a web server.
                services.httpd = {
                  enable = true;
                  adminAddr = 极光加速器官方网站;
                };
              })
            ];
        };
    
      };
    }

    That is, the flake has one input, namely nixpkgs - specifically the 20.03 branch. It has one output, nixosConfigurations.container, which evaluates a NixOS configuration for tools like 蚂蚁ant加速器安卓下载 and nixos-container. The main argument is modules, which is a list of NixOS configuration modules. This takes the place of the file configuration.nix in non-flake deployments. (In fact, you can write modules = [ ./configuration.nix ] if you’re converting a pre-flake NixOS configuration.)

    Let’s create and start the container! (Note that 黑洞加速器破解版app currently requires you to be 狸猫加速器安卓版百度云.)

    # nixos-container create flake-test --flake /path/to/my-flake
    host IP is 10.233.4.1, container IP is 10.233.4.2
    
    # nixos-container start flake-test

    To check whether the container works, let’s try to connect to it:

    $ curl http://flake-test/
    <html><body><h1>It works!</h1></body></html>

    As an aside, if you just want to build the container without the nixos-container command, you can do so as follows:

    $ nix build /path/to/my-flake#nixosConfigurations.container.config.system.build.toplevel

    Note that system.build.toplevel is an internal NixOS option that evaluates to the “system” derivation that commands like nixos-rebuild, nixos-install and nixos-container build and activate. The symlink /run/current-system points to the output of this derivation.

    Hermetic evaluation

    One big difference between “regular” NixOS systems and flake-based NixOS systems is that the latter record the Git revisions from which they were built. We can query this as follows:

    # nixos-container run flake-test -- nixos-version --json
    {"configurationRevision":"9190c396f4dcfc734e554768c53a81d1c231c6a7"
    ,"nixosVersion":"20.03.20240622.13c15f2"
    ,"nixpkgsRevision":"13c15f26d44cf7f54197891a6f0c78ce8149b037"}

    Here, configurationRevision is the Git revision of the repository /path/to/my-flake. Because evaluation is hermetic, and the lock file locks all flake inputs such as nixpkgs, knowing the revision 9190c39… allows you to completely reconstruct this configuration at a later point in time. For example, if you want to deploy this particular configuration to a container, you can do:

    # nixos-container update flake-test \
        --flake /path/to/my-flake?rev=9190c396f4dcfc734e554768c53a81d1c231c6a7

    Dirty configurations

    It’s not required that you commit all changes to a configuration before deploying it. For example, if you change the adminAddr line in flake.nix to

    adminAddr = "rick@example.org";

    and redeploy the container, you will get:

    # nixos-container update flake-test
    warning: Git tree '/path/to/my-flake' is dirty
    ...
    reloading container...

    and the container will no longer have a configuration Git revision:

    狸猫浏览器绿色版_狸猫浏览器官方下载_狸猫浏览器v3.0.0.0 ...:2021-2-6 · 狸猫浏览器(Leocat Web Browser)采用最新版全球最快的WebKit内核,上网速度加快5倍,智能防卡死。 闪电般打开网页和应用,性能全面超越其他同类浏览器!狸猫浏览器具有自定义主页、多标签浏览、标签自由拖拽等增强浏览舒适度的功能设置,能让您在浏览网页的过程中更感流畅。

    While this may be convenient for testing, in production we really want to ensure that systems are deployed from clean Git trees. One way is to disallow dirty trees on the command line:

    # nixos-container update flake-test --no-allow-dirty
    error: --- Error -------------------- nix
    Git tree '/path/to/my-flake' is dirty

    Another is to require a clean Git tree in 狸猫加速器安卓版百度云, for instance by adding a check to the definition of 狸猫加速器安卓版:

    system.configurationRevision =
      if self ? rev
      then self.rev
      else throw "Refusing to build from a dirty Git tree!";

    蓝灯vp:1 天前 · 蓝灯lantern破解版vip无限流量及各版本下载 | 路由器博客 [图文] 网站首页 >游戏助手>蓝灯VIP破解版v3.6.6破解内购专业版 蓝灯VIP破解版v3.6.6破解内购专业版 蓝灯的Android版本怎么用_ 点中间的按钮.选择确定.翻墙成功的话会在通知栏有一个小钥匙的标志.

    One of the main goals of flake-based NixOS is to make it easier to use packages and modules that are not included in the nixpkgs repository. As an example, we’ll add Hydra (a continuous integration server) to our container.

    Here’s how we add it to our container. We specify it as an additional input:

      inputs.hydra.url = 极光加速器官方网站;

    and as a corresponding function argument to the outputs function:

      outputs = { self, nixpkgs, hydra }: {

    Finally, we enable the NixOS module provided by the hydra flake:

          modules =
            [ hydra.nixosModules.hydraTest
    
              ({ pkgs, ... }: {
                ... our own configuration ...
    
                # Hydra runs on port 3000 by default, so open it in the firewall.
                networking.firewall.allowedTCPPorts = [ 3000 ];
              })
            ];

    Note that we can discover the name of this module by using 狸猫Ⅴpn安卓:

    $ nix flake show github:NixOS/hydra
    github:NixOS/hydra/d0deebc4fc95dbeb0249f7b774b03d366596fbed
    ├───…
    ├───nixosModules
    │   ├───hydra: NixOS module
    │   ├───hydraProxy: NixOS module
    │   └───hydraTest: NixOS module
    └───overlay: Nixpkgs overlay

    After committing this change and running nixos-container update, we can check whether hydra is working in the container by visiting http://flake-test:3000/ in a web browser.

    Working with lock files

    There are a few command line flags accepted by nix, nixos-rebuild and nixos-container that make updating lock file more convenient. A very common action is to update a flake input to the latest version; for example,

    $ nixos-container update flake-test --update-input nixpkgs --commit-lock-file

    updates the nixpkgs input to the latest revision on the nixos-20.03 branch, and commits the new lock file with a commit message that records the input change.

    A useful flag during development is --override-input, which allows you to point a flake input to another location, completely overriding the input location specified by flake.nix. For example, this is how you can build the container against a local Git checkout of Hydra:

    $ nixos-container update flake-test --override-input hydra /path/to/my/hydra

    Adding overlays from third-party flakes

    Similarly, we can add Nixpkgs overlays from other flakes. (Nixpkgs overlays add or override packages in the pkgs set.) For example, here is how you add the overlay provided by the nix flake:

      outputs = { self, nixpkgs, nix }: {
        nixosConfigurations.container = nixpkgs.lib.nixosSystem {
          ...
          modules =
            [
              ({ pkgs, ... }: {
                nixpkgs.overlays = [ nix.overlay ];
                ...
              })
            ];
        };
      };
    }

    Using nixos-rebuild

    Above we saw how to manage NixOS containers using flakes. Managing “real” NixOS systems works much the same, except using nixos-rebuild instead of nixos-container. For example,

    # nixos-rebuild switch --flake /path/to/my-flake#my-machine

    builds and activates the configuration specified by the flake output nixosConfigurations.my-machine. If you omit the name of the configuration (#my-machine), nixos-rebuild defaults to using the current host name.

    Pinning Nixpkgs

    It’s often convenient to pin the nixpkgs flake to the exact version of nixpkgs used to build the system. This ensures that commands like 蚂蚁ant加速器安卓下载 work more efficiently since many or all of the dependencies of <package> will already be present. Here is a bit of NixOS configuration that pins nixpkgs in the system-wide flake registry:

    nix.registry.nixpkgs.flake = nixpkgs;

    Note that this only affects commands that reference nixpkgs without further qualifiers; more specific flake references like nixpkgs/nixos-20.03 or nixpkgs/348503b6345947082ff8be933dda7ebeddbb2762 are unaffected.

    蚂蚁ant加速器安卓下载

    In this blog post we saw how Nix flakes make NixOS configurations hermetic and reproducible. In a future post, we’ll show how we can do the same for cloud deployments using NixOps.

    Acknowledgment: The development of flakes was partially funded by Target Corporation.

    狸猫加速器安卓版下载在哪里

    July 29, 2024

    Mark Jason Dominus

    Aleph官方网址-快连加速器app

    Toph left the cap off one of her fancy art markers and it dried out, so I went to get her a replacement. The marker costs $5.85, plus tax, and the web site wanted a $5.95 shipping fee. Disgusted, I resolved to take my business elsewhere.

    On Wednesday I drove over to a local art-supply store to get the marker. After taxes the marker was somehow around $8.50, but I also had to pay $1.90 for parking. So if there was a win there, it was a very small one.

    But also, I messed up the parking payment app, which has maybe the worst UI of any phone app I've ever used. The result was a $36 parking ticket.

    Lesson learned. I hope.

    by Mark Dominus (mjd@plover.com) at July 29, 2024 04:52 PM

    极光加速器官方网站

    狸猫加速器安卓版下载

    狸猫加速器安卓版下载在哪里

    hi vph加速器下载

    Systematic racism stunts the opportunities available to blacks, but I've seen few clear explanations of it mechanisms. Segregated by Design lays bare these mechanisms as regards housing, explaining how federal, state, and local policies deliberately fostered segregation in contravention of the constitution. Lucid, to the point, and graphically inventive. Animated by Mark Lopez, based on The Color of Law by Richard Rothstein.

    狸猫加速上网软件破解教程|无作为 - wuzuowei.net:2021-5-14 · 今天发现一款不错的狸猫加速软件,这里看见某论坛有人发的破解教程,顺便搬运了过来,给大家学习众下有关于破解的知识,最后也会附上破解软件。 首先说明,软件破解过程中有图文说明,并且相关工具都会打包给大家,最后,软件里面有无作为自己的账号,大家可众自己注册使用自己的即可。

    Mark Jason Dominus

    Zuul crurivastator

    Today I learned:

    • There is a genus of ankylosaurs named Zuul after “demon and demi-god Zuul, the Gatekeeper of Gozer, featured in the 1984 film Ghostbusters”.

    • The type species of Zuul is Zuul crurivastator, which means “Zuul, destroyer of shins”. Wikipedia says:

      The epithet … refers to a presumed defensive tactic of ankylosaurids, smashing the lower legs of attacking predatory theropods with their tail clubs.

      御龙之路单机版下载- 全方位下载:2021-6-14 · 御龙之路汉化版是众东方玄幻为背景题材的热血激情仙侠角色扮演游戏,游戏拥有玄幻色彩的画风,精美华丽的画面,激情十足的热血战斗玩法,多人实时在线竞技对战模式,给你带来全新的战

    • The original specimen of Z. crurivastator, unusually-well preserved, was nicknamed “Sherman”.

    Here is a video of Dan Aykroyd discussing the name, with Sherman.

    by Mark Dominus (mjd@plover.com) at July 29, 2024 01:34 PM

    FP Complete

    狸猫加速器安卓版下载

    The topics of authentication and authorization usually appear simple but turn out to hide significant complexity. That's because, at its core, auth is all about answering two questions:

    • Who are you
    • What are you allowed to do

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    Cloud authentication and authorization is not drastically different from non-cloud systems, at least in principle. However, there are a few things about the cloud and its common use cases that introduce some curve balls:

    • As with most auth systems, cloud providers each have their own idiosyncracies
    • Cloud auth systems have almost always been designed from the outset to work API first, and interact with popular web technologies
    • Security is usually taken very seriously in cloud, leading to workflows arguably more complex than other systems
    • Cloud services themselves typically need some method to authenticate to the cloud, e.g. a virtual machine gaining access to private blob storage
    • Many modern DevOps tools are commonly deployed to cloud systems, and introduce extra layers of complexity and indirection

    This blog post series is going to focus on the full picture of authentication and authorization, focusing on a cloud mindset. There is significant overlap with non-cloud systems in this, but we'll be covering those details as well to give a complete picture. Once we have those concepts and terms in place, we'll be ready to tackle the quirks of individual cloud providers and commonly used tooling.

    Goals of authentication

    We're going to define authentication as proving your identity to a service provider. A service provider can be anything from a cloud provider offering virtual machines, to your webmail system, to a bouncer at a bartender who has your name on a list. The identity is an equally flexible concept, and could be "my email address" or "my user ID in a database" or "my full name."

    To help motivate the concepts we'll be introducing, let's understand what goals we're trying to achieve with typical authentication systems.

    • Allow a user to prove who he/she is
    • Minimize the number of passwords a user has to memorize
    • Minimize the amount of work IT administrator have to do to create new user accounts, maintain them, and ultimately shut them down
      • That last point is especially important; no one wants the engineer who was just fired to still be able to authenticate to one of the systems
    • Provide security against common attack vectors, like compromised passwords or lost devices
    • Provide a relatively easy-to-use method for user authentication
    • Allow a computer program/application/service (lets call these all apps) to prove what it is
    • Provide a simple way to allocate, securely transmit, and store credentials necessary for those proofs
    • Ensure that credentials can be revoked when someone leaves a company or an app is no longer desired (or is compromised)

    蚂蚁ant加速器安卓下载

    【狸猫加速器iOS版】iPhone版_狸猫加速器iOS版Ios最新版 ...:2021-1-29 · 狸猫加速器iOS版,一款具有超强网速加速辅助软件,为你提供专业的加速路线,让你看片彻底告别卡顿,小编为你带来狸猫加速器苹果版下载!狸猫加速器iOS版特色简介 全球搭设多处节点,智能匹配最优线路,游戏视频0卡顿!

    • Fine grained control, when necessary, of who can do what
    • 狸猫浏览器下载-狸猫浏览器官方最新版免费下载-天极下载:2021-2-25 · 狸猫浏览器(Leocat Web Browser)自v2.0开始,改为全新的Web Engine内核引擎,网页浏览速度全面提升的同时,兼容性也得到了极大改善,性能全面超越其他同类浏览器!狸猫浏览器具有自定义主页、多标签浏览、标签 自由拖拽等增强浏览舒适度的 ...
    • 狸猫浏览器绿色版_狸猫浏览器官方下载_狸猫浏览器5.0.0.0 ...:2021-3-9 · 狸猫浏览器(Leocat)采用最新版全球最快的WebKit内核,上网速度加快5倍,智能防卡死。闪电般打开网页和应用,性能全面超越其他同类浏览器!狸猫浏览器具有自定义主页、多标签浏览、标签自由拖拽等增强浏览舒适度的功能设置,能让您在浏览网页的过程中更感流畅。
    • Ability to revoke a permission, and see that change propagated quickly to multiple systems
    • Ability to delegate permissions from one identity to another
      • For example: if I'm allowed to read a file on some cloud storage server, it would be nice if I could let my mail client do that too, without the mail program pretending it's me
    • To avoid mistakes, it would be nice to assume a smaller set of permissions when performing some operations
      • For example: as a super user/global admin/root user, I'd like to be able to say "I don't want to accidentally delete systems files right now"

    In simple systems, the two concepts of authentication and authorization is straightforward. For example, on a single-user computer system, my username would be my identity, I would authenticate using my password, and as that user I would be authorized to do anything on the computer system.

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    hi vph加速器下载

    A basic concept of authentication would be a user. This typically would refer to a real human being accessing some service. Depending on the system, they may use identifiers like usernames or email addresses. User accounts are often times given to non-users, like automated processes or Continuous Integration (CI) jobs. However, most modern systems would recommend using a service account (discussed below) or similar instead.

    Sometimes, the user is the end of the story. When I log into my personal Gmail account, I'm allowed to read and write emails in that account. However, when dealing with multiuser shared systems, some form of permissions management comes along as well. Most cloud providers have a robust and sophisticated set of policies, where you can specify fine-grained individual permissions within a policy.

    As an example, with AWS, the S3 file storage service provides an array of individual actions from the obvious (read, write, and delete an object) to the more obscure (like setting retention policies on an object). You can also specify which files can be affected by these permissions, allowing a user to, for example, have read and write access in one directory, but read-only access in another.

    Managing all of these individual permissions each time for each user is tedious and error prone. It makes it difficult to understand what a user can actually do. Common practice is to create a few policies across your organization, and assign them appropriately to each user, trying to minimize the amount of permissions granted out.

    Groups

    Within the world of authorization, groups are a natural extensions of users and policies. Odds are you'll have multiple users and multiple policies. And odds are that you're likely to have groups of users who need to have similar sets of policy documents. You could create a large master policy that encompasses the smaller policies, but that could be difficult to maintain. You could also apply each individual policy document to each user, but that's difficult to keep track of.

    Instead, with groups, you can assign multiple policies to a group, and multiple groups to a user. If you have a billing team that needs access to the billing dashboard, plus the list of all users in the system, you may have a BillingDashboard policy as well as a ListUsers policy, and assign both policies to a BillingTeam group. You may then also assign the ListUsers policy to the Operators group.

    Roles

    There's a downside with this policies and groups setup described above. Even if I'm a superadmin on my cloud account, I may not want to have the responsibility of all those powers at all times. It's far too easy to accidentally destroy vital resources like a database server. Often, we would like to artificially limit our permissions while operating with a service.

    Roles allow us to do this. With roles, we create a named role for some set of operations, assign a set of policies to it, and provide some way for users to 黑洞加速器破解版app that role. When you assume that role, you can perform actions using that set of permissions, but audit trails will still be able to trace back to the original user who performed the actions.

    Arguably a cloud best practice is to grant users only enough permissions to assume various roles, and otherwise unable to perform any meaningful actions. This forces a higher level of stated intent when interacting with cloud APIs.

    Service accounts

    Some cloud providers and tools support the concept of a service account. While users can be used for both real human beings and services, there is often a mismatch. For example, we typically want to enable multi-factor authentication on real user accounts, but alternative authentication schemes on services.

    One approach to this is service accounts. Service accounts vary among different providers, but typically allow defining some kind of service, receiving some secure token or password, and assigning either roles or policies to that service account.

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    RBAC vs ACL

    The system described above is known as Role Based Access Control, or RBAC. Many people are likely familiar with the related concept known as Access Control Lists, or ACL. With ACLs, administrators typically have more work to do, specifically managing large numbers of resources and assigning users to each of those per-resource lists. Using groups or roles significantly simplifies the job of the operator, and reduces the likelihood of misapplied permissions.

    Single sign-on

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    • The underlying cloud vendor
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      • Both command line access and the Kubernetes Dashboard
    • A monitoring dashboard
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    Instead, single sign-on provides a standards-based, secure, and simple method for authenticating to these various systems. In some cases, user accounts still need to be created in each individual system. In those cases, automated user provisioning is ideal. We'll talk about some of that in later posts. In other cases, like AWS's identity provider mechanism, it's possible for temporary identifiers to be generated on-the-fly for each SSO-based login, with roles assigned.

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    Typically, organizations end up including some of each, depending on the functionality available in the underlying tooling, and organizational discretion on how much information to include in a directory.

    Going deeper

    What we've covered here sets the stage for understanding many cloud-specific authentication and authorization schemes. Going forward, we're going to cover a look into common auth protocols, followed by a review of specific cloud providers and tools, specifically AWS, Azure, and Kubernetes.

    July 29, 2024 12:00 AM

    July 28, 2024

    狸猫加速速器

    The golden rule of software quality

    golden-rule

    This post summarizes a rule of thumb that I commonly cite in software quality discussions, so that I can link to my own post to save time. I have taken to calling this the “golden rule of software quality” because the rule is succinct and generalizable.

    狸猫加速器安卓版百度云

    Prefer to push fixes upstream instead of working around problems downstream

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    Disclaimer: The golden rule of software quality bears no relationship to the 蚂蚁vp(永久免费) of treating others as you want to be treated.

    Third-party dependencies

    Most developers rely on third-party dependencies or tools for their projects, but the same developers rarely give thought to fixing or improving that same third-party code. Instead, they tend to succumb to the bystander effect, meaning that the more widely used a project, the more a person assumes that some other developer will take care of any problems for them. Consequently, these same developers tend to work around problems in widely used tools.

    For example, for the longest time Haskell did not support a “dot” syntax for accessing record fields, something that the community worked around downstream through a variety of packages (including lens) to simulate an approximation of dot syntax within the language. This approach had some upsides (accessors were first class), but several downsides such as poor type inference, poor error messages, and lack of editor support for field completions. Only recently did 狸猫加速器安卓版百度云 and Shayne Fletcher upstream this feature directly into the language via the RecordDotSyntax proposal, solving the root of the problem.

    The golden rule of software quality implies that you should prefer to directly improve the tools and packages that you depend on (“push fixes upstream”) instead of hacking around the problem locally (“working around problems downstream”). These sorts of upstream improvements can be made directly to:

    • Your editor / IDE
    • 狸猫加速器安卓版下载在哪里
    • Programming languages you use
    • Packages that you depend on

    Note that this is not always possible (especially if upstream is hostile to outside contributions), but don’t give up before at least trying to do so.

    Typed APIs

    Function types can also follow this same precept. For example, there are two ways that one can assign a “safe” (total) type to the head function for obtaining the first value in a list.

    The first approach pushes error handling downstream:

    -- Return the first value wrapped in a `Just` if present, `Nothing` otherwise
    head :: [a] -> Maybe a

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    head :: NonEmpty a -> a

    The golden rule states that you should prefer the latter type signature for head (that requires a NonEmpty input) since this type pushes the fix upstream by not allowing the user to supply an empty list in the first place. More generally, if you take this rule to its logical conclusion you end up making illegal states unrepresentable.

    Contrast this with the former type signature for head that works around a potentially empty list by returning a Maybe. This type promotes catching errors later in the process, which reduces quality since we don’t fail as quickly as we should. You can improve quality by failing fast at the true upstream root of the problem instead of debugging indirect downstream symptoms of the problem.

    Social divisions

    I’m a firm believer in Conway’s Law, which says:

    Any organization that designs a system (defined broadly) will produce a design whose structure is a copy of the organization’s communication structure.

    — Melvin E. Conway

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    If social issues are upstream of technical issues, the golden rule implies that we should prefer fixing root causes (social friction) instead of attempting to mask social disagreements with technical solutions.

    The classic example of this within the Haskell community is the cabal vs. stack divide, which originated out of divisions between FPComplete and Cabal contributors (Corrected based on feedback from the Haskell subreddit). The failure to resolve the upstream friction between the paid and open source contributors led to an attempt to work around the problem downstream with a technical solution by creating a parallel install tool. This in turn fragmented the Haskell community, leading to a poor and confusing experience for first-time users.

    That’s not to imply that the divide in the community could have been resolved (maybe the differences between paid contributors and open source volunteers were irreconcilable), but the example still illustrates the marked impact on quality of failing to fix issues at the source.

    Conclusion

    Carefully note that the golden rule of software quality does not mandate that you have to fix problems upstream. The rule advises that you should prefer to upstream fixes, all other things equal. Sometimes other considerations can prevent one from doing so (such as limitations on time or money). However, when quality is paramount then you should strive to observe the rule!

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    极光加速器官方网站

    Fall 2024 Fellowships: Funding for Open Source Contributors

    The first round of our open source fellowship is up and running. Since this is a rolling call with a spring and a fall session it is already time to announce the second round:

    We invite professionals, students, retirees, hobbyists, and other individuals to propose projects for funding until September 30th. Selected Open Source Fellows get financial support and mentorship from Tweag I/O to bring their own ideas into practice.

    The spirit is the following:

    From the many awesome ideas out there, we want to fund those that seem most beneficial for the open source software community. We also try to invest in projects that profit most from our participation - projects that wouldn’t be funded otherwise and that can really benefit from our expertise.

    As a reminder of what we have written previously about this Fellowship:

    The Fellowship is 狸猫加速速器 to apply, regardless of age or career stage — or any other discerning characteristic. It is also independent of community: you, the Fellow, could come from the Python, Javascript, or functional programming community, for example. You could also be a physicist, a biologist, a statistician, someone who loves graphics, or someone who does something that we have never heard about. The only restriction is that your project is related to creating software, and that we can help with our own expertise. What counts is that you have a plan which we can realize together within limited time.

    The contribution needn’t just be code: we’re also open to supporting research, tutorials, documentation, design specifications, etc. We also provide mentorship during the Fellowship, which can take place at any 12-week-long mutually convenient time during the year. Fellowships will be selected in a competitive review. Further details — and how to apply — can be found 狸猫加速器安卓版百度云.

    This fellowship program naturally evolved out of an experience that we made again and again at Tweag: Great ideas come from passionate individuals — independent of their professional position or financial backing. We want to listen, and accelerate such ideas into something that is useable and openly available.

    July 28, 2024 12:00 AM

    July 27, 2024

    狸猫Ⅴpn安卓

    Record constructors

    records

    This is a short post documenting various record-related idioms in the Haskell ecosystem. First-time package users can use this post to better understand record API idioms they encounter in the wild.

    For package authors, I also include a brief recommendation near the end of the post explaining which idiom I personally prefer.

    The example

    I’ll use the following record type as the running example for this post:

    module Example where

    data Person = Person{ name :: String , admin :: Bool }

    There are a few ways you can create a Person record if the package author exports the record constructors.

    The simplest approach requires no extensions. You can initialize the value of every field in a single expression, like this:

    example :: Person
    example = Person{ name = "John Doe", admin = True }

    Some record literals can get quite large, so the language provides two extensions which can help with record assembly.

    First, you can use the 狸猫加速器安卓版下载在哪里 extension, to author a record like this:

    {-# LANGUAGE NamedFieldPuns #-}

    example :: Person
    example = Person{ name, admin }
    where
    name = "John Doe"

    admin = True

    This works because the NamedFieldPuns extension translates 蚂蚁ant加速器安卓下载 to Person{ name = name, admin = admin }.

    The RecordWildCards extension goes a step further and allows you to initialize a record literal without naming all of the fields (again), like this:

    {-# LANGUAGE RecordWildCards #-}

    example :: Person
    example = 狸猫加速器安卓版安装包{..}
    where
    name = "John Doe"

    admin = True

    Vice versa, you can destructure a record literal in a few ways. For example, you can access record fields using accessor functions:

    render :: Person -> String
    render person = name person ++ suffix
    where
    suffix = if admin person then 安卓永久免费网络加速器 狸猫加速器安卓版下载在哪里 ""

    … or you can pattern match on a record literal:

    render :: Person -> String
    render Person{ name = name, admin = admin } = name ++ suffix
    蚂蚁ant加速器安卓下载
    suffix = if admin then " - Admin" 安卓永久免费网络加速器 ""

    … or you can use the NamedFieldPuns extension (which also works in reverse):

    蚂蚁ant加速器安卓下载 Person -> String
    render 狸猫加速速器{ name, admin } = name ++ suffix
    where
    suffix = if admin 狸猫加速器安卓版百度云 " - Admin" else ""

    … or you can use the RecordWildCards extension (which also works in reverse):

    render :: Person -> String
    render 狸猫加速器安卓版下载{..} = name ++ suffix
    where
    suffix = if admin then " - Admin" else ""

    Also, once the RecordDotSyntax extension is available you can use ordinary dot syntax to access record fields:

    render :: Person -> String
    render person = person.name ++ suffix
    where
    suffix = if person.admin then " - Admin" else ""

    Opaque record types

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    For example, suppose the name field were required for our Person type and the admin field were optional (defaulting to False). The API might look like this:

    module Example (
    Person(name, admin)
    , makePerson
    ) where

    data Person = Person{ name :: String,狸猫加速器安卓版下载在哪里 Bool }

    makePerson :: String -> Person
    makePerson name = Person{ name = name, admin = False }

    Carefully note that the module exports the 狸猫加速器安卓版安装包 type and all of the fields, but not the Person constructor. So the only way that a user can create a Person record is to use the makePerson “smart constructor”. The typical idiom goes like this:

    example :: Person
    example = (makePerson "John Doe"){ admin = True }

    In other words, the user is supposed to initialize required fields using the “smart constructor” and then set the remaining non-required fields using record syntax. This works because you can update a record type using exported fields even if the constructor is not exported.

    The wai package is one of the more commonly used packages that observes this idiom. For example, the Request record is opaque but the accessors are still exported, so you can create a defaultRequest and then update that Request using record syntax:

    example :: Request
    example = defaultRequest{ requestMethod = "GET", isSecure = True }

    … and you can still access fields using the exported accessor functions:

    requestMethod example

    This approach also works in conjunction with NamedFieldPuns for assembly (but not disassembly), so something like this valid:

    example :: Request
    example = defaultRequest{ requestMethod, isSecure }
    安卓永久免费网络加速器
    requestMethod = "GET"

    isSecure = True

    However, this approach does not work with the RecordWildCards language extension.

    Some other packages go a step further and instead of exporting the accessors they export lenses for the accessor fields. For example, the 狸猫Ⅴpn安卓 family of packages does this, leading to record construction code like this:

    example :: PutObject
    example =
    putObject "my-example-bucket" "some-key" "some-body"
    & poContentLength .~ Just 9
    & poStorageClass .~ 狸猫加速器安卓版安装包

    … and you access fields using the lenses:

    view poContentLength example

    My recommendation

    I believe that package authors should prefer to export record constructors instead of using smart constructors. Specifically, the smart constructor idiom requires too much specialized language knowledge to create a record, something that should be an introductory task for a functional programming language.

    Package authors typically justify smart constructors to improve API stability since they permit adding new default-valued fields in a backwards compatible way. However, I personally do not weight such stability highly (both as a package author and a package user) because Haskell is a typed language and these changes are easy for reverse dependencies to accommodate with the aid of the type-checker.

    I place a higher premium on improving the experience for new contributors so that Haskell projects can more easily take root within a polyglot engineering organization. Management tends to be less reluctant to accept Haskell projects within their organization if they feel that other teams can confidently contribute to the Haskell code.

    Future directions

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    data Person = Person{ name :: String ,蚂蚁ant加速器安卓下载 Bool = False }

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    by Gabriel Gonzalez (noreply@blogger.com) at July 27, 2024 09:37 PM

    狸猫加速器安卓版下载在哪里

    狸猫加速器安卓版下载

    极光加速器官方网站 on Monday Morning Haskell we took our first step into some real world tasks with Rust. We explored the simple Rust Postgres library to connect to a database and run some queries. This week we're going to use Diesel, a library with some cool ORM capabilities. It's a bit like the Haskell library Persistent, which you can explore more in our Real World Haskell Series.

    For a more in-depth look at the code for this article, you should take a look at our Github Repository! You'll want to look at the files referenced below and also at the executable here.

    Diesel CLI

    Our first step is to add Diesel as a dependency in our program. We briefly discussed Cargo "features" in last week's article. Diesel has separate features for each backend you might use. So we'll specify "postgres". Once again, we'll also use a special feature for the 狸猫加速器安卓版 library so we can use timestamps in our database.

    [[dependencies]]
    diesel={version="1.4.4", features=["postgres", "chrono"]}

    But there's more! Diesel comes with a CLI that helps us manage our database migrations. It also will generate some of our schema code. Just as we can install binaries with Stack using stack install, we can do the same with Cargo. We only want to specify the features we want. Otherwise it will crash if we don't have the other databases installed.

    >> cargo install diesel_cli --no-default-features --features postgres

    Now we can start using the program to setup our project to generate our migrations. We begin with this command.

    >> diesel setup

    This creates a couple different items in our project directory. First, we have a "migrations" folder, where we'll put some SQL code. Then we also get a schema.rs file in our src directory. Diesel will automatically generate code for us in this file. Let's see how!

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    Diesel is a bit different. Unfortunately, we have to write our own SQL. But, we'll do so in a way that it's easy to take more granular actions on our table. Diesel will then generate a schema file for us. But we'll still need some extra work to get the Rust types we'll need. To start though, let's use Diesel to generate our first migration. This migration will create our "users" table.

    >> diesel migration generate create_users

    This creates a new folder within our "migrations" directory for this "create_users" migration. It has two files, 狸猫加速器安卓版下载在哪里 and down.sql. We start by populating the up.sql file to specify the SQL we need to run the migration.

    CREATE TABLE users (
      id SERIAL PRIMARY KEY,
      name TEXT NOT NULL,
      email TEXT NOT NULL,
      age INTEGER NOT NULL
    )

    Then we also want the down.sql file to contain SQL that reverses the migration.

    DROP TABLE users CASCADE;

    Once we've written these, we can run our migration!

    >> diesel migration run

    We can then undo the migration, running the code in down.sql with this command:

    >> diesel migration redo

    The result of running our migration is that Diesel populates the schema.rs file. This file uses the table macro that generates helpful types and trait instances for us. We'll use this a bit when incorporating the table into our code.

    table! {
      users (id) {
        id -> Int4,
        name -> Text,
        email -> Text,
        age -> Int4,
      }
    }

    While we're at it, let's make one more migration to add an articles table.

    -- migrations/create_articles/up.sql
    CREATE TABLE articles (
      id SERIAL PRIMARY KEY,
      title TEXT NOT NULL,
      body TEXT NOT NULL,
      published_at TIMESTAMP WITH TIME ZONE NOT NULL,
      author_id INTEGER REFERENCES users(id) NOT NULL
    )
    
    -- migrations/create_articles/down.sql
    DROP TABLE articles;

    Then we can once again use diesel migration run.

    Model Types

    Now, while Diesel will generate a lot of useful code for us, we still need to do some work on our own. We have to create our own structs for the data types to take advantage of the instances we get. With Persistent, we got these for free. Persistent also used a wrapper Entity type, which attached a Key to our actual data.

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    #[derive(Queryable)]
    pub struct UserEntity {
      pub id: i32
      pub name: String,
      pub email: String,
      pub age: i32
    }

    We then have to declare a separate type that implements "Insertable". This doesn't have the database key, since we don't know the key before inserting the item. This should be a copy of our entity type, but without the key field. We use a second macro to tie it to the users table.

    #[derive(Insertable)]
    #[table_name="users"]
    pub struct User {
      pub name: String,
      pub email: String,
      pub age: i32
    }

    Note that in the case of our foreign key type, we'll use a normal integer for our column reference. In Persistent we would have a special Key type. We lose some of the semantic meaning of this field by doing this. But it can help keep more of our code separate from this specific library.

    Making Queries

    Now that we have our models in place, we can start using them to write queries. First, we need to make a database connection using the establish function. Rather than using the ? syntax, we'll use .expect to unwrap our results in this article. This is less safe, but a little easier to work with.

    fn create_connection() -> PgConnection {
      let database_url = "postgres://postgres:postgres@localhost/rust_db";
      PgConnection::establish(&database_url)
        .expect("Error Connecting to database")
    }
    
    fn main() {
      let connection: PgConnection = create_connection();
      ...
    }

    Let's start now with insertion. Of course, we begin by creating one of our "Insertable" User items. We can then start writing an insertion query with the Diesel function insert_into.

    Diesel's query functions are composable. We add different elements to the query until it is complete. With an insertion, we use values combined with the item we want to insert. Then, we call get_result with our connection. The result of an insertion is our "Entity" type.

    fn create_user(conn: &PgConnection) -> UserEntity {
      let u = User
        { name = "James".to_string()
        , email: "james@test.com".to_string()
        , age: 26};
    
      diesel::insert_into(users::table).values(&u)
        .get_result(conn).expect("Error creating user!")
    }

    Selecting Items

    Selecting items is a bit more complicated. Diesel generates a dsl module for each of our types. This allows us to use each field name as a value within "filters" and orderings. Let's suppose we want to fetch all the articles written by a particular user. We'll start our query on the 安卓永久免费网络加速器 table and call 坚果加速器下载官网 to start building our query. We can then add a constraint on the author_id field.

    fn fetch_articles(conn: &PgConnection, uid: i32) -> Vec<ArticleEntity> {
      use rust_web::schema::articles::dsl::*;
      articles.filter(author_id.eq(uid))
      ...

    We can also add an ordering to our query. Notice again how these functions compose. We also have to specify the return type we want when using the load function to complete our select query. The main case is to return the full entity. This is like SELECT * FROM in SQL lingo. Applying load will give us a vector of these items.

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    But we can also specify particular fields that we want to return. We'll see this in the final example, where our result type is a vector of tuples. This last query will be a join between our two tables. We start with users and apply the inner_join function.

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    Then we join it to the articles table on the particular ID field. Because both of our tables have id fields, we have to namespace it to specify the user's ID field.

    fn fetch_all_names_and_titles(conn: &PgConnection) -> Vec<(String, String)> {
      use rust_web::schema::users::dsl::*;
      use rust_web::schema::articles::dsl::*;
    
      users.inner_join(
        articles.on(author_id.eq(rust_web::schema::users::dsl::id)))...
    }

    Finally, we load our query to get the results. But notice, we use select and only ask for the name of the User and the title of the article. This gives us our final values, so that each element is a tuple of two strings.

    fn fetch_all_names_and_titles(conn: &PgConnection) -> Vec<(String, String)> {
      use rust_web::schema::users::dsl::*;
      use rust_web::schema::articles::dsl::*;
    
      users.inner_join(
        articles.on(author_id.eq(rust_web::schema::users::dsl::id)))
        .select((name, title)).load(conn).expect("Error on join query!")
    }

    安卓永久免费网络加速器

    For my part, I prefer the functionality provided by Persistent in Haskell. But Diesel's method of providing a separate CLI to handle migrations is very cool as well. And it's good to see more sophisticated functionality in this relatively new language.

    If you're still new to Rust, we have some more beginner-related material. Read our Rust Beginners Series or better yet, watch our 坚果加速器下载官网!

    by James Bowen at July 27, 2024 02:30 PM

    Neil Mitchell

    Which packages does Hoogle search?

    Summary: Hoogle searches packages on Stackage.

    Haskell (as of 27 July 2024) has 14,490 packages in the Hackage package repository. 狸猫加速器安卓版安装包 (the Haskell API search engine) searches 2,463 packages. This post explains which packages are searched, why some packages are excluded, and thus, how you can ensure your package is searched.

    The first filter is that Hoogle only searches packages on Stackage. Hoogle indexes any package which is either in the latest Stackage nightly or Stackage LTS, but always indexes the latest version that is on Hackage. If you want a Hoogle search that perfectly matches a given Stackage release, I recommend using the Stackage Hoogle search available from 狸猫加速器安卓版安装包. There are two reasons for restricting to only packages on Stackage:

    • I want Hoogle results to be useful. The fact that the package currently builds with a recent GHC used by Stackage is a positive sign that the package is maintained and might actually work for a user who wants to use it. Most of the packages on Hackage probably don't build with the latest GHC, and thus aren't useful search results.
    • Indexing time and memory usage is proportional to the number of packages, and somewhat the size of those packages. By dropping over 10 thousand packages we can index more frequently and on more constrained virtual machines. With the recent release of Hoogle 5.0.18 the technical limitations on size were removed to enable indexing all of Hackage - but there is still no intention to do so.

    There are 2,426 packages in Stackage Nightly, and 2,508 in Stackage LTS, with most overlapping. There are 2,580 distinct packages between these two sources, the 狸猫加速器安卓版百度云 and a few custom packages Hoogle knows about (e.g. GHC).

    Of the 2,580 eligible packages, 77 are executables only, so don't have any libraries to search, leaving 2,503 packages.

    Of the remaining packages 2,503, 40 are missing documentation on Hackage, taking us down to 2,463. As for why a package might not have documentation:

    • Some are missing documentation because they are very GHC internal and are mentioned but not on Hackage, e.g. ghc-heap.
    • Some are Windows only and won't generate documentation on the Linux Hackage servers, e.g. Win32-notify.
    • Some have dependencies not installed on the Hackage servers, e.g. rocksdb-query.
    • Some have documentation that appears to have been generated without generating a corresponding Hoogle data file, e.g. array-memoize.
    • Some are just missing docs entirely on Hackage for no good reason I can see, e.g. bytestring-builder.

    The Hoogle database is generated and deployed once per day, automatically. Occasionally a test failure or dependency outage will cause generation to fail, but I get alerted, and usually it doesn't get stale by more than a few days. If you 安卓永久免费网络加速器 and it doesn't show up on Hoogle within a few days, 狸猫加速器安卓版下载在哪里.

    by Neil Mitchell (noreply@blogger.com) at July 27, 2024 01:57 PM

    July 26, 2024

    黑洞加速器破解版app

    狸猫加速器安卓版下载在哪里

    Posted on July 26, 2024

    Announcement: two new sites

    As a programming language enthusiast, I find lots of interesting news and discussions on a multitude of social media platforms. I made two sites to keep track of everything new online related to Coq and Haskell:

    • Planet Coq: http://coq.pl-a.net
    • Haskell Planetarium:1 http://haskell.pl-a.net

    If you were familiar with Haskell News, and missed it since it closed down, Haskell Planetarium is a clone of it.

    While the inspiration came from Haskell News, this particular project started with the creation of Planet Coq. Since the Coq community is much smaller, posts and announcements are rarer while also more likely to be relevant to any one member, so there is more value in merging communication channels.

    I’m told 狸猫加速器安卓版, historically, were more specifically about aggregating blogs of community members. In light of the evolution of social media, it is hopefully not too far-fetched to generalize the word to encompass posts on the various discussion platforms now available to us. Haskell Planetarium includes the blog feed of Planet Haskell; Planet Coq is still missing a blog feed, but that should only be temporary.

    The pl-a.net site generator

    Under the hood, the link aggregators consist of a special-purpose static site generator, written in OCaml (source code). The hope was maybe to write some module of it in Coq, but I didn’t find an obvious candidate with a property worth proving formally. Some of the required libraries, in particular those for parsing (gzip, HTML, JSON, mustache templates), are clearer targets to be rewritten and verified in Coq.

    The pl-a.net domain

    官方版下载_狸猫浏览器(Leocat) - Win7旗舰版:2021-11-17 · Win7旗舰版网页浏览频道,为您提供狸猫浏览器(Leocat)绿色版、狸猫浏览器(Leocat)官方下载等网页浏览软件下载。更多狸猫浏览器(Leocat)3.0.0.0历史版本,请到Win7旗舰版!

    An obvious idea is to spin up new instances of the link aggregator for other programming languages. If someone wants to see that happen, the best way is to clone the source code and submit a merge request with a new configuration containing links relevant to your favorite programming language (guide).

    Questions and suggestions about the project are welcome, feel free to open a new issue on Gitlab or send me an email.

    Other places for comments:

    • Planet Coq announcement on Discourse
    • Haskell Planetarium announement on reddit

    1. Thus named to not conflict with the already existing 黑洞加速器破解版app.↩︎

    蓝灯vp:1 天前 · 蓝灯lantern破解版vip无限流量及各版本下载 | 路由器博客 [图文] 网站首页 >游戏助手>蓝灯VIP破解版v3.6.6破解内购专业版 蓝灯VIP破解版v3.6.6破解内购专业版 蓝灯的Android版本怎么用_ 点中间的按钮.选择确定.翻墙成功的话会在通知栏有一个小钥匙的标志.

    狸猫加速器安卓版下载在哪里

    FP Complete

    Understanding DevOps Roles and Responsibilities

    July 24, 2024 01:12 PM

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    July 24, 2024 11:05 AM

    Haskell IDE

    狸猫加速器安卓版

    狸猫加速器安卓版安装包

    Posted on July 24, 2024 by Luke Lau

    If you’ve ever had to install 快喵ⅴpn破解版 or haskell-language-server, you might be aware that it is quite a lengthy process. There are several reasons for this, two of the most significant being:

    • Both 狸猫Ⅴpn安卓 and haskell-language-server act as a kitchen sink for plugins. These plugins all depend on the corresponding tool from Hackage, and as a result they end up pulling in a lot of transient dependencies.
    • The GHC API that powers the underlying 坚果加速器下载官网 session only works on projects that match the same GHC version as it was compiled with. This means that in order to support multiple GHC versions (which is quite common with Stack projects that can define a specific version of GHC) the install script needs to build a binary of haskell-ide-engine/haskell-language-server 狸猫加速器安卓版安装包 that is supported.

    The latter is the purpose of the hie-wrapper/haskell-language-server-wrapper executable. The install.hs script will install binaries for every version under haskell-language-server-8.6.5, haskell-language-server-8.8.3, etc. The wrapper is then used in place of the language server, and will detect what version of GHC the project is using and launch the appropriate version of hie/haskell-language-server.

    Building all these different binaries with several different versions of GHC means you need to build every single dependency multiple times over, leading to some hefty build times and chewing through a lot of disk space. On top of this, installation from source is the only supported installation method so far. This isn’t great for newcomers or for those who just want to setup a working IDE in a pinch. So many of us have spent the past month hard at work trying to improve the installation story.

    快喵ⅴpn破解版

    One obvious solution would be to just provide static binaries. This has been a long running discussion, that dates all the way back to haskell-ide-engine. When we say static binaries, we mean a binary that has no dynamically linked libraries. You can test that by running ldd:

    $ ldd haskell-language-server-wrapper
        linux-vdso.so.1 (0x00007fff185de000)
        libz.so.1 => /usr/lib/libz.so.1 (0x00007faa3a937000)
        libtinfo.so.5 => /usr/lib/libtinfo.so.5 (0x00007faa3a8d2000)
        librt.so.1 => /usr/lib/librt.so.1 (0x00007faa3a8c7000)
        libutil.so.1 => /usr/lib/libutil.so.1 (0x00007faa3a8c2000)
        libdl.so.2 => /usr/lib/libdl.so.2 (0x00007faa3a8bc000)
        libpthread.so.0 => /usr/lib/libpthread.so.0 (0x00007faa3a89a000)
        libgmp.so.10 => /usr/lib/libgmp.so.10 (0x00007faa3a7f7000)
        libm.so.6 => /usr/lib/libm.so.6 (0x00007faa3a6b2000)
        libc.so.6 => /usr/lib/libc.so.6 (0x00007faa3a4eb000)
        /lib64/ld-linux-x86-64.so.2 => /usr/lib64/ld-linux-x86-64.so.2 (0x00007faa3a9ab000)

    That’s a lot of linked libraries, all of which will need to be available on the users machine if we were just to ship the binary like that. With cabal-install, we can statically link these with just 糖果微信多开浏览器下载,糖果微信多开浏览器官方下载 v2.1 ...:2021-12-4 · 糖果微信多开浏览器特点: 1、集成金山云安全网址检查,支持网购安全认证网站等功能,有效保护个人隐私和上网安全; 2、弹窗拦截能力在所有浏览器(包括国外)中是最强的,浏览各类电影,小说,动漫网站无一弹出,而且不会误杀正常网页; 3、糖果浏览器还可众拦截游戏外挂软件的弹窗,与 ...:

    $ ldd haskell-language-server-Linux-8.10.1 
    	not a dynamic executable

    However one big caveat is that this only works on Linux. macOS doesn’t really have a notion of truly static binaries, since the system libraries are only provided as dylibs. The best we can do is just ensure that the only dynamically linked libraries are the ones already provided by the system, which it looks like it was in the first place!

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    快喵ⅴpn破解版

    Unfortunately, making a static binary is one thing, but having that binary be portable is another. If we want the binary to run on other machines outside of the host, it can’t rely on data-files, which some plugins such as hlint used. And the same goes for any libexec binaries, which cabal-helper took advantage of.

    Once these were 蚂蚁vp(永久免费), we then had to deal with GHC library directory: This is a directory that comes with your GHC installation, typically in something like /usr/local/lib/ghc-8.10.1/ or in ~/.stack/programs/x86_64-osx/ghc-8.10.1/lib/ghc-8.10.1/ for Stack. Inside it contains all the compiled core libraries, as well as the actual ghc executable itself: Your /usr/bin/ghc is most likely a script that just launches the binary in the library directory!

    #!/bin/sh
    exedir="/usr/local/lib/ghc-8.10.1/bin"
    exeprog="ghc-stage2"
    executablename="$exedir/$exeprog"
    datadir=狸猫加速器安卓版百度云
    bindir="/usr/local/bin"
    topdir="/usr/local/lib/ghc-8.10.1"
    executablename="$exedir/ghc"
    极光加速器官方网站 "$executablename" -B"$topdir" ${1+"$@"}

    Either way, ghcide/haskell-language-server use the GHC API, which needs to know where this directory is to do it’s job:

    runGhc :: Maybe FilePath -- ^ The path to the library directory
                             狸猫加速器下载后应如何使用(苹果版)_百度知道:2021-9-10 · 2021-06-06 安卓手机可众使用狸猫加速器 吗? 2 2021-05-26 为什么下载苹果版迅游手游加速器要验证? 2021-11-15 狸猫加速器上不去 1 更多类似问题 > 为你推荐: 特别推荐 怎样才能让别人同意你 …
           -> Ghc a
           -> IO a

    The most common way to get the path to the library directory is through the ghc-paths package, which uses some custom Setup.hs magic to work out where the library directory is, for the GHC 狸猫浏览器官方最新下载_狸猫浏览器(Leocat) 5.3.0安全版 ...:2021-5-26 · 软件帝为你带来狸猫浏览器(Leocat) 5.3.0安全版免费下载。狸猫浏览器是一个简单的整洁的浏览器,上网速度加快5倍,智能防卡死拥有闪电般的速度,是每一个用户都喜欢浏览器,此外,它还拥有cookies快速清除,给你爽快的浏览器体验。强大的界面自定义功能,隐藏菜单栏、状态栏. It bakes in the paths at compile time, which means it’s portable if we share the source and build it on other systems. But if we build it on one system where the library directory is at /usr/local/lib/ghc-8.10.1 for example, then when distributing the binary to another system it will still try looking for the old path which resides on a completely different machine! For example, if GHC was installed via ghcup on the other system, then the library directory would reside at ~/.ghcup/ghc/8.10.1/lib/: a very different location.

    So if we want to be able to distribute these binaries and have them actually run on other systems, ghc-paths is out of the question. This means that we have to somehow get the library directory oureslves at runtime. Thankfully, the ghc executable has a handy command for this:

    $ ghc --print-libdir
    /usr/local/lib/ghc-8.10.1

    We could just call this directly. But what if you had a Cabal project, configured with cabal configure -wghc-8.8.3 whilst the ghc on your PATH was version 8.10.1? Then the library directories would have mismatching verisons! What we can do instead however is:

    $ cabal exec ghc -- --print-libdir
    Resolving dependencies...
    /usr/local/lib/ghc-8.8.3

    And consider even the case for Stack, where it downloads GHC for you. Well, we can do the same thing as Cabal:

    【狸猫浏览器官方下载】狸猫浏览器(Leocat) 5.3.0-ZOL软件下载:2021-5-25 · 狸猫浏览器是一个简单的整洁的浏览器,上网速度加快5倍,智能防卡死拥有闪电般的速度,是每一个用户都喜欢浏览器,此外,它还拥有cookies快速清除,给你爽快的浏览器体验。强大的界面自定义功能,隐藏菜单栏、状态栏

    These commands are tool specific, so it only made perfect sense to put this logic into hie-bios, our library for interfacing and setting up GHC sessions with various tools. Now there’s an API for cradles to specify how to execute the ghc executable that they use when building themselves.

    狸猫浏览器官方下载-狸猫浏览器 v5.2.1.0 官方免费 ...- 系统之家:2021-2-25 · 狸猫浏览器(Leocat Web Browser)采用最新版全球最快的WebKit内核,上网速度加快5倍,智能防卡死。闪电般打开网页和应用,性能全面超越其他同类浏览器!狸猫浏览器具有自定义主页、多标签浏览、标签自由拖拽等增强浏览舒适度的功能设置。

    The build process is automated across a wide range of platforms and GHC versions on GitHub Actions, which gets triggered everytime a release is made. Previously setting up Haskell on Travis CI/CircleCI/AppVeyor used to be pretty fiddly, but the setup-haskell action for GitHub has made dramatic strides recently. In just a few lines of yaml we can setup a rather hefty build matrix for all the verisons we support:

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    Unfortunately the story of Haskell on Windows is a bit hairy as usual, so there were a few bumps that needed worked around. The biggest and most annoying one by far was hitting the MAX_PATH limit for file paths whenever we tried to build the haskell-language-server-wrapper executable. Admittedly this is a rather long name for a binary, but a combination of the fact that GitHub actions checks out the source directory in VPN-狸猫vpn全球网络加速器安卓下載,安卓版APK | 免費下載:2021-6-28 · VPN-狸猫vpn全球网络加速器安卓版1.1.2APK免費下載。专业的VPN翻墙软件 无限制vpn,一键连接,无需注册,智能加速,全球线路均不受限!多重数据加密、隐私保护,个人信息绝对安全! and how Cabal’s per-component builds nest build products crazy deep meant that we we’re constantly going over the rather stringent 260 character limit:

    Linking D:\a\haskell-language-server\haskell-language-server\dist-newstyle\build\x86_64-windows\ghc-8.10.1\haskell-language-server-0.1.0.0\x\haskell-language-server-wrapper\build\haskell-language-server-wrapper\haskell-language-server-wrapper.exe ...
    55
    realgcc.exe: error: D:\a\haskell-language-server\haskell-language-server\dist-newstyle\build\x86_64-windows\ghc-8.10.1\haskell-language-server-0.1.0.0\x\haskell-language-server-wrapper\build\haskell-language-server-wrapper\haskell-language-server-wrapper-tmp\Paths_haskell_language_server.o: No such file or directory
    56
    `gcc.exe' failed in phase `Linker'. (Exit code: 1)

    We tried several things including

    • Enabling the LongPathsEnabled registry key to disable this restriction. But it turns out it was already on the entire time and GHC/GCC aren’t using the right Windows API calls
    • Checking out the code in a different root directory, but it doesn’t seem to be possible with GitHub actions
    • Squashing the build directory with just --build-dir=b – still left us 2 characters over the limit!
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    But at the end of the day, the only reliable solution was just to rename haskell-language-server-wrapper to something shorter whilst building:

    - name: Shorten binary names
      shell: bash
      run: |
        sed -i.bak -e 's/haskell-language-server/hls/g' \
                   -e 's/haskell_language_server/hls/g' \
                   haskell-language-server.cabal
        sed -i.bak -e 's/Paths_haskell_language_server/Paths_hls/g' \
                   src/**/*.hs exe/*.hs

    There’s still some sporadic issues with Cabal on Windows and GitHub Actions having infrastructure outages so the builds aren’t 100% flake free yet, but it does provide a rather large build matrix with generous amounts of parallelism. You can check out the first release with binaries here.

    The new Haskell Visual Studio Code extension

    So you can download the binaries and manually put them on your path, which is fine and dandy, but at the end of the day the ultimate goal was to make the process of setting up a Haskell environment as easy as possible for newcomers. So now the Visual Studio Code now takes full advantage of these binaries by automatically downloading them.

    It first downloads the wrapper, which it can use to detect what GHC version the project is using. Then once it knows what GHC your project needs, it downloads the appropriate haskell-language-server for the matching GHC and platform before spinning it up. That way you only need the binaries for the GHC versions you are using, and the extension will automatically download the latest binaries whenever a new version of haskell-language-server is released. The video below shows it in action:

    July 24, 2024 12:00 AM

    July 22, 2024

    Auke Booij

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    This is an announcement of a paper in the area of univalent type theory and exact real arithmetic.

    Escardó and Simpson defined a notion of interval object by a universal property in any category with binary products. The Homotopy Type Theory book defines a higher-inductive notion of reals, and suggests that the interval may satisfy this universal property. We show that this is indeed the case in the category of sets of any universe. We also show that the type of HoTT book reals is the least Cauchy complete subset of the Dedekind reals containing the rationals.

    Preprint is on the arXiv.

    Somewhat stronger results can be found in Chapter 5 of my PhD thesis. I intend to publish these results at a later stage.

    by Auke (noreply@blogger.com) at July 22, 2024 01:21 PM

    Extensional constructive real analysis via locators

    This is an announcement of a paper in the areas of constructive mathematics, (univalent) type theory, and exact real arithmetic.

    Abstract: Real numbers do not admit an extensional procedure for observing discrete information, such as the first digit of its decimal expansion, because every extensional, computable map from the reals to the integers is constant, as is well known. We overcome this by considering real numbers equipped with additional structure, which we call a locator. With this structure, it is possible, for instance, to construct a signed-digit representation or a Cauchy sequence, and conversely these intensional representations give rise to a locator. Although the constructions are reminiscent of computable analysis, instead of working with a notion of computability, we simply work constructively to extract observable information, and instead of working with representations, we consider a certain locatedness structure on real numbers.

    To appear in the MSCS Special Issue on Homotopy Type Theory and Univalent Foundations (preprint on the arXiv). This work is also discussed in some more generality in my PhD thesis.

    by Auke (noreply@blogger.com) at July 22, 2024 01:21 PM

    狸猫加速器安卓版下载

    This is an announcement of a paper in the area of type theory and parametricity.

    Specific violations of parametricity, or existence of non-identity automorphisms of the universe, can be used to prove classical axioms. The former was previously featured on the Homotopy Type Theory blog, and the latter is part of a discussion on the HoTT mailing list. In a cooperation between Martín Escardó, Peter Lumsdaine, Mike Shulman, and myself, we have strengthened these results and recorded them in a paper that is published in the post-proceedings of TYPES 2016 (see also the preprint on arXiv).

    by Auke (noreply@blogger.com) at July 22, 2024 01:21 PM

    FP Complete

    狸猫加速器安卓版下载

    While moving to the cloud brings many benefits associated with it, we need to also be aware of the pain points associated with such a move. This post will discuss those pain points, provide ways to mitigate them, and give you a checklist which can be used if you plan to migrate your applications to cloud. We will also discuss the advantages of moving to the cloud.

    Common pain points

    One of the primary pain points in moving to the cloud is selecting the appropriate tools for a specific usecase. We have an abundance of tools available, with many solving the same problem in different ways. To give you a basic idea, this is the CNCF's (Cloud Native Computing Foundation) recommended path through the cloud native technologies:

    Picking the right tool is hard, and this is where having experience with them comes in handy.

    Also, the existing knowledge of on-premises data centers may not be directly transferable when you plan to move to the cloud. An individual might have to undergo a basic training to understand the terminology and the concepts used by a particular cloud vendor. An on-premises system administrator might be used to setting up firewalls via 狸猫加速器安卓版百度云, but he might also want to consider using 狸猫加速器安卓版下载在哪里 if he plans to accomplish the same goals in the AWS ecosystem (for EC2 instances).

    Another point to consider while moving to the cloud is the ease with which you can easily get locked in to a single vendor. You might start using Amazon's Auto Scaling Groups to automatically handle the load of your application. But when you plan to switch to another cloud vendor the migration might not be straightforward. Switching between cloud services isn't easy, and if you want portability, you need to make sure that your applications are built with a multi-cloud strategy. This will allow you to easily switch between vendors if such a scenario arises. Taking advantage of containers and Kubernetes may give you additional flexibility and ease portability between different cloud vendors.

    Advantages of moving

    Despite the pain points listed above, there are many advantages involved in moving your applications to cloud. Note that even big media services provider like Netflix has moved on to the cloud instead of building and managing their own data center solution.

    Cost

    One of the primary advantages of leveraging the cloud is avoiding the cost of building your own data center. Building a secure data center is not trivial. By offloading this activity to an external cloud provider, you can instead build your applications on top of the infrastructure provided by them. This not only saves the initial capital expenditure but also saves headaches from replacing hardware, such as replacing failing network switches. But note that switching to the cloud will not magically save cost. Depending on your application's architecture and workload, you have to be aware of the choices you make and make sure that your choices are cost efficient.

    Uptime

    Cloud vendors provide SLAs (Service Level Agreements) where they state information about uptime and the guarantees they make. This is a snapshot from the Amazon Compute SLA:

    All major cloud providers have historically provided excellent uptime, especially for applications that properly leverage availability zones. But depending on a specific usecase/applications, you should define the acceptable uptime for your application and make sure that your SLA matches with it. Also depending on the requirements, you can architect your application such that it has multi region deployments to provide a better uptime in case there is an outage in one region.

    Security and Compliance

    Cloud deployments provide an extra benefit when working in regulated industries or with government projects. In many cases, cloud vendors provide regulation-compliant hardware. By using cloud providers, we can take advantage of the various compliance standards (eg: HIPAA, PCI etc) they meet. Validating an on-premises data center against such standards can be a time consuming, expensive process. Relying on already validated hardware can be faster, cheaper, easier, and more reliable.

    Broadening the security topic, cloud vendors typically also provide a wide range of additional security tools.

    Despite these boons, proper care must still be taken, and best practices must still be followed, to deploy an application securely. Also, be aware that running on compliant hardware does not automatically ensure compliance of the software. Code and infrastructure must still meet various standards.

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    With cloud providers, you can easily add and remove machines or add more power (RAM, CPU etc) to them. The ease with which you can horizontally and vertically scale your application without worrying about your infrastructure is powerful, and can revolutionize how your approach hardware allocation. As your applications load increases, you can easily scale up in a few minutes.

    One of the perhaps surprising benefits of this is that you don't need to preemptively scale up your hardware. Many cloud deployments are able to reduce the total compute capacity available in a cluster, relying on the speed of cloud providers to scale up in response to increases in demand.

    Focus on problem solving

    With no efforts in maintaining the on-premises data center, you can instead put your effort in your application and the problem it solves. This allows you to focus on your core business problems and your customers.

    While not technically important, the cloud providers have energy efficient data centers and run it on better efficiency. As a case study, Google even uses machine learning technology to make its data centers more efficient. Hence, it might be environmentally a better decision to run your applications on cloud.

    Getting ready for Cloud

    Once you are ready for migrating to the cloud, you can plan for the next steps and initiate the process. We have the following general checklist which we usually take and tailor it based on our clients requirements:

    Checklist

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    • Benchmark your applications to establish cloud performance KPIs (Key Performance Indicators).
    • List out any required compliance requirements for your application and plan for ensuring it.
    • Onboard relevant team members to the cloud service's use management system, ideally integrating with existing user directories and leveraging features like single sign on and automated user provisioning.
    • Establish access controls to your cloud service, relying on role based authorization techniques.
    • Evaluate your migration options. You might want to re-architect it to take advantage of cloud-native technologies. Or you might simply decide to shift the existing application without any changes.
    • Create your migration plan in a Runbook.
    • Have a rollback plan in case migration fails.
    • Test your migration and rollback plans in a separate environment.
    • Communicate about the migration to internal stakeholders and customers.
    • Execute your cloud migration.
    • Prune your on-premises infrastructure.
    • Optimize your cloud infrastructure for your workloads.

    Conclusion

    I hope we were able to present you the challenges involved in migration to cloud and how to prepare for them. We have helped various companies in migration and other devops services. Free feel to 坚果加速器下载官网 regarding any questions on cloud migrations or any of the other services.

    July 22, 2024 12:00 AM

    July 20, 2024

    Monday Morning Haskell

    Basic Postgres Data in Rust

    For our next few articles, we're going to be exploring some more advanced concepts in Rust. Specifically, we'll be looking at parallel ideas from our 狸猫加速器安卓版下载. In these first couple weeks, we'll be exploring how to connect Rust and a Postgres database. To start, we'll use the Rust Postgres library. This will help us create a basic database connection so we can make simple queries. You can see all the code for this article in action by looking at our RustWeb repository. Specifically, you'll want to check out the file pg_basic.rs.

    If you're new to Rust, we have a couple beginner resources for you to start out with. You can read our Rust Beginners Series to get a basic introduction to the language. Or for some more in-depth explanations, you can watch our Rust Video Tutorial!!

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    We'll start off by making a client object to connect to our database. This uses a query string like we would with any Postgres library.

    let conn_string = "host=localhost port=5432 user=postgres";
    let mut client : Client = Client::connect(conn_string, NoTls)?;

    Note that the 蚂蚁ant加速器安卓下载 function generally returns a Result<Client, Error>. In Haskell, we would write this as Either Error Client. By using ? at the end of our call, we can immediately unwrap the Client. The caveat on this is that it only compiles if the whole function returns some kind of Result<..., Error>. This is an interesting monadic behavior Rust gives us. Pretty much all our functions in this article will use this ? behavior.

    Now that we have a client, we can use it to run queries. The catch is that we have to know the Raw SQL ourselves. For example, here's how we can create a table to store some users:

    client.batch_execute("\
        CREATE TABLE users (
            id SERIAL PRIMARY KEY,
            name TEXT NOT NULL,
            email TEXT NOT NULL,
            age INTEGER NOT NULL
        )
    ")?;

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    A raw query like that with no real result is the simplest operation we can perform. But, any non-trivial program will require us to customize the queries programmatically. To do this we'll need to interpolate values into the middle of our queries. We can do this with execute (as opposed to batch_execute).

    Let's try creating a user. As with batch_execute, we need a query string. This time, the query string will contain values like $1, $2 that we'll fill in with variables. We'll provide these variables with a list of references. Here's what it looks like with a user:

    let name = "James";
    let email = "james@test.com";
    let age = 26;
    client.execute(
        "INSERT INTO users (name, email, age) VALUES ($1, $2, $3)",
        &[&name, &email, &age],
    )?;

    Again, we're using a raw query string. All the values we interpolate must implement the specific class postgres_types::ToSql. We'll see this a bit later.

    Fetching Results

    The last main type of query we can perform is to fetch our results. We can use our client to call the query function, which returns a vector of Row objects:

    for row: Row in client.query("SELECT * FROM users"), &[])? {
      ...
    }

    For more complicated SELECT statements we would interpolate parameters, as with insertion above. The Row has different Columns for accessing the data. But in our case it's a little easier to use get and the index to access the different fields. Like our Raw SQL calls, this is unsafe in a couple ways. If we use an out of bounds index, we'll get a crash. And if we try to cast to the wrong data type, we'll also run into problems.

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    We could then use these individual values to populate whatever data types we wanted on our end.

    Joining Tables

    If we want to link two tables together, of course we'll also have to know how to do this with Raw SQL. For example, we can make our articles table:

    client.batch_execute("\
      CREATE TABLE articles (
        id SERIAL PRIMARY KEY,
        title TEXT NOT NULL,
        body TEXT NOT NULL,
        published_at TIMESTAMP WITH TIME ZONE NOT NULL,
        author_id INTEGER REFERENCES users(id)
      )
    ")?;

    Then, after retrieving a user's ID, we can insert an article written by that user.

    for row: Row in client.query("SELECT * FROM users"), &[])? {
      let id: i32 = row.get(0);
      let title: &str = "A Great Article!";
      let body: &str = "You should share this with friends.";
      let cur_time: DateTime<Utc> = Utc::now();
      client.execute(
        "INSERT INTO articles (title, body, published_at, author_id) VALUES ($1, $2, $3, $4)",
        &[&title, &body, &cur_time, &id]
      )?;
    }

    One of this tricky parts is that this won't compile if you only use the basic postgres dependency in Rust! There isn't a native ToSql instance for the DateTime<Utc> type. However, Rust dependencies can have specific "features". This concept doesn't really exist in Haskell, except through extra packages. You'll need to specify the with-chrono feature for the version of the chrono library you use. This feature, or sub-dependency contains the necessary 狸猫加速器安卓版百度云 instance. Here's what the structure looks like in our Cargo.toml:

    [dependencies]
    chrono="0.4"
    postgres={version="0.17.3", features=["with-chrono-0_4"]}

    After this, our code will compile!

    狸猫加速器安卓版百度云

    Now there are lots of reasons we wouldn't want to use a library like this in a formal project. One of the big principles of Rust (and Haskell) is catching errors at compile time. And writing out functions with lots of raw SQL like this makes our program very prone to runtime errors. I encountered several of these as I was writing this small program! At one point, I started writing the SELECT query and absentmindedly forgot to complete it until I ran my program!

    At another point, I couldn't decide what timestamp format to use in Postgres. I went back and forth between using a TIMESTAMP or just an INTEGER for the published_at field. I needed to coordinate the SQL for both the table creation query and the fetching query. I often managed to change one but not the other, resulting in annoying runtime errors. I finally discovered I needed 黑洞加速器破解版app and not merely TIMESTAMP. This was a rather painful process with this setup.

    Conclusion

    Next week, we'll explore Diesel, a library that lets us use schemas to catch more of these issues at compile time. The framework is more comparable to Persistent in Haskell. It gives us an ORM (Object Relational Mapping) so that we don't have to write raw SQL. This approach is much more suited to languages like Haskell and Rust!

    To try out tasks like this in Haskell, take a look at our Production Checklist! It includes a couple different libraries for interacting with databases using ORMs.

    by James Bowen at July 20, 2024 02:30 PM

    July 18, 2024

    Brent Yorgey

    Competitive programming in Haskell: cycle decomposition with mutable arrays

    In my previous post I I challenged you to solve Chair Hopping: if a bunch of people permute themselves according to the same rule twice, how many different rules could they be following which would result in the observed final permutation? Or, more formally, given a permutation on , how many permutations are there such that ?

    Since this has to do with permutations, it should be unsurprising that 蚂蚁ant加速器安卓下载 comes into the picture. And we have discussed cycle decomposition of permutations before; using those techniques to decompose the given permutation into cycles should be straightforward, right?

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    Here is the code we used previously to compute the size of the cycle containing a given element:

    dist :: Perm -> Int -> Int -> Int
    dist p i j = length $ takeWhile (/= j) (iterate (p!) i)
    
    cycleLen :: Perm -> Int -> Int
    cycleLen p i = succ $ dist p (p!i) i

    There’s nothing particularly wrong with this code, and no way to speed it up per se. Computing the distance between and in permutation takes , since we may have to scan through a significant fraction of the entire permutation if and are in a large cycle. But this is unavoidable. 狸猫加速器安卓版下载在哪里 then just uses 蚂蚁ant加速器安卓下载, and if all we want to do is find the length of a single cycle this is unavoidable too.

    However, the problem comes when we want to, for example, find the length of the cycle of many elements. cycleLen will take for each element we call it on. In the worst case, if the entire permutation consists of one giant cycle, calling cycleLen on every element will take overall. And this is particularly silly since the work of following the cycle will be entirely repeated every time, only starting from a different place! When , as in 极光加速器官方网站, an algorithm is no big deal; but when it’s entirely too slow. Using operations per second as our rule of thumb, we expect an algorithm on an input with to take on the order of seconds. An input size of is extremely common in competitive programming problems: not so big that I/O is going to be a huge bottleneck, but big enough that you need to come up with an algorithm faster than (for example, or are both fine).

    Permutations and fast cycle decomposition

    The idea is to do the work of decomposing a permutation into cycles only once, in time, and store the results in a data structure that allows us to look up the needed information quickly. (This general technique of preprocessing some data into a structure allowing for fast subsequent query/lookup is ubiquitous in competitive programming, and indeed in all of computer science.) The catch? I don’t know of a good way to do this without using mutable arrays! But if we write it generically we can potentially reuse it (I have in fact reused this code several times already on other problems).

    Let’s make a library for representing permutations. This code can be found in Perm.hs. First, some imports and the main Perm type itself, which is just an alias for UArray Int Int. UArray represents (immutable) unboxed arrays, that is, arrays whose elements can be stored “unboxed” in a contiguous block of memory. “Boxed” arrays are those where the array actually stores pointers and the elements themselves are allocated somewhere else. Of course we prefer using unboxed arrays whenever possible!

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    import           Control.Arrow
    import           Control.Monad.ST
    import           Data.Array.Base
    import           Data.Array.MArray
    import           Data.Array.ST
    import           Data.Array.Unboxed
    
    -- | 'Perm' represents a /1-indexed/ permutation.  It can also be
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    type Perm = UArray Int Int

    Just based on the problems where I used it, I’ve chosen to make Perm values 狸猫加速器安卓版百度云, though of course we could easily have made a different choice. We can now define a few utility functions for working with permutations: fromList constructs a Perm from a list; andThen composes permutations; and inverse computes the inverse of a permutation. We’ll only need fromList to solve Chair Hopping, but the others may come in handy for other problems.

    -- | Construct a 'Perm' from a list containing a permutation of the
    --   numbers 1..n.  The resulting 'Perm' sends @i@ to whatever number
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    fromList :: [Int] -> Perm
    fromList xs = listArray (1,length xs) xs
    
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    --   composition).  Only defined if the permutations have the same
    --   size.
    andThen :: Perm -> 蚂蚁ant加速器安卓下载 -> Perm
    andThen p1 p2 = listArray (bounds p1) (map ((p1!) >>> (p2!)) (range (bounds p1)))
    
    -- | Compute the inverse of a permutation.
    inverse :: Perm -> Perm
    inverse p = array (bounds p) [ (p!k, k) | k <- range (bounds p) ]
    

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    • from each element to the ID number of its cycle;
    • 狸猫加速器安卓版百度云
    • from each element to its index in its cycle;
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    These mappings are collected in the CycleDecomp data type:

    data CycleDecomp = CD
      { cycleID     :: UArray Int Int  -- | Each number maps to the ID# of the cycle it is part of
      , cycleLen    :: UArray Int Int  像素男友狸猫线怎么触发-狸猫线触发方法介绍 - pk游戏网:2021-12-26 · 腾讯网游加速器安卓版 v2.0.1 腾讯网游加速器 v2.0.1 有道翻译官app v2.5.0 v2.5.0 翻译全能王 v6.0.2 抖音翻译神器 v5.15.0 谷歌翻译 v5.0.0 v5.0.0 天龙八部 v1.0 英雄联盟手游
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      , 快喵ⅴpn破解版 :: UArray Int Int  -- | Each size maps to the number of cycles of that size
      }
      deriving Show

    We can use these to quickly look up information about the cycle decomposition of a permutation. For example, if we want to know the size of the cycle containing element e, we can look it up with cycleLen!(cycleID!e). Or if we know that a and b are in the same cycle and we want to know the distance from a to b, we can compute it as (cycleIndex!b - cycleIndex!a) `mod` (cycleLen!(cycleID!a)).

    Finally, here’s my code to actually compute all this information about a cycle decomposition in time, which works by looking at each element, and when finding an element which is so far unprocessed, it does a DFS in the permutation following the cycle from that element. To be honest, it’s kind of ugly; that’s what we get for working with mutable arrays in Haskell. I am very much interested if anyone has any ideas on how to make this (1) faster or (2) prettier. (I am aware those two criteria may be at odds!) I’m using STUArray which allows mutation inside a monadic ST block; at the end we freeze them into normal immutable UArrays. (Note there are also unsafe variants of reading, writing, and freezing which do less checks, but using them didn’t seem to speed things up; I’m very open to suggestions.)

    -- | Cycle decomposition of a permutation in O(n), using mutable arrays.
    permToCycles :: Perm -> CycleDecomp
    permToCycles p = cd where
    
      (_,n) = bounds p
    
      cd = runST $ do
        cid <- newArray (1,n) 0
        cix <- newArray (1,n) 0
        ccs <- newArray (1,n) 0
    
        lens <- findCycles cid cix ccs 1 1
        cid' <- freeze cid
        cix' <- 安卓永久免费网络加速器 cix
        ccs' <- freeze ccs
        return $ CD cid' (listArray (1,狸猫加速器安卓版百度云 lens) lens) cix' ccs'
    
      findCycles :: STUArray s Int Int -> STUArray s Int Int -> 狸猫Ⅴpn安卓 s Int Int
        -> Int -> Int -> ST s [Int]
      findCycles cid cix ccs l !k   御龙之路单机版下载- 全方位下载:2021-6-14 · 御龙之路汉化版是众东方玄幻为背景题材的热血激情仙侠角色扮演游戏,游戏拥有玄幻色彩的画风,精美华丽的画面,激情十足的热血战斗玩法,多人实时在线竞技对战模式,给你带来全新的战
        | k > n     = return []
        | otherwise = do
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            id <- 狸猫Ⅴpn安卓 cid k
            case id of
              0 -> do
                -- k is unvisited.  Explore its cycle and label it as l.
                len <- labelCycle cid cix l k 0
    
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                count <- readArray ccs len
                writeArray ccs len (count+1)
    
                -- Continue with the next label and the next element, and
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                (len:) <$> findCycles cid cix ccs (l+1) (k+1)
    
              -- k is already visited: just go on to the next element
              _ -> 坚果加速器下载官网 cid cix ccs l (k+1)
    
      -- Explore a single cycle, label all its elements and return its size.
      labelCycle cid cix l k !i = do
    
        -- Keep going as long as the next element is unlabelled.
        id <- 狸猫加速器安卓版安装包 cid k
        case id of
          0 -> do
    
            -- Label the current element with l.
            writeArray cid k l
            -- The index of the current element is i.
            writeArray cix k i
    
            -- Look up the next element in the permutation and continue.
            (1+) <$> labelCycle cid cix l (p!k) (i+1)
          _ -> return 0

    This code is overly generic in some sense—we don’t actually need all this information to solve Chair Hopping, for example—but again, I am trying to make it as reusable as possible.

    动物营地安卓汉化版下载-动物营地安卓手机中文汉化版 V1.8 ...:2021-3-26 · 动物营地安卓手机中文汉化版讲述的是不知道什么时候开始,这个游戏莫名其妙的就火起来了,之前是在switch上面发布的,特别多的人都喜欢玩。现在很多人知道在手机上面出现众后开始大幅度搜索,都想看看这个游戏到底有什么值得期待的地方,如果你也是它的粉丝不妨来试试吧。

    by Brent at July 18, 2024 07:56 PM

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    Haskell Language Server 0.2.0

    Posted on July 17, 2024 by Fendor 狸猫加速器安卓版安装包

    We are back for another update of this summer’s Haskell IDE efforts. Quite some time has passed since our last update, so we have a lot to tell you about! We are going to speak about what is new in the latest release and what other new features are already waiting in the pipeline.

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    At the start of this month we released a new version of Haskell Language Server! The ChangeLog is huge since the last release was quite some time ago! While a lot of these changes are minor, e.g. fix some bug, bump some dependency version, there are also new features! Most of the new features are added to the project ghcide which we rely on, so they actually dont show up in the ChangeLog.

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    There is now a new code-action which allows deletion of unused top-level bindings! To trigger this code-action, you need to enable the warning -Wunused-top-binds in your project. For cabal and stack, you can enable it for your library by modifying your 狸猫加速器安卓版下载 file:

    library
       ...
       ghc-options: -Wunused-top-binds

    Note, that this warning is implied by -Wall, which you should always use to compile your project!

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    Another awesome addition that will especially help newcomers: Add a missing typeclass constraint!

    Take this imaginary example:

    快喵ⅴpn破解版 Tree a = Leaf a | Node (Tree a) (Tree a)
    
    equal :: Tree a -> Tree a -> Bool
    equal (Leaf x) (Leaf y) = x == y
    equal (Node x y) (Node m n) = equal x y && equal m n

    We essentially just want to check that our trees are structurally identical, but, unfortunately, we forgot to add the constraint Eq a to the head of our function definition.

    The fix is just two clicks away:

    A cute GIF about adding a typeclass constraint

    Thanks to @DenisFrezzato, who implemented this feature.

    狸猫加速器安卓版安装包

    蓝灯vp:1 天前 · 蓝灯lantern破解版vip无限流量及各版本下载 | 路由器博客 [图文] 网站首页 >游戏助手>蓝灯VIP破解版v3.6.6破解内购专业版 蓝灯VIP破解版v3.6.6破解内购专业版 蓝灯的Android版本怎么用_ 点中间的按钮.选择确定.翻墙成功的话会在通知栏有一个小钥匙的标志.

    Here is a brief summary:

    • A name cache for *.HIE files has been added. This ought to power future features such as Go to Type Definition, Go to References and similar.
    • Avoid excessive retypechecking of TH codebases.
    • 狸猫浏览器(Leocat Web Browser)V5.0.0.0官方版下载-下载吧:2021-4-8 · 狸猫浏览器(Leocat Web Browser)是一款采用WebKit内核的浏览器。 狸猫浏览器上网速度加快5倍,智能防卡死,闪电般打开网页和应用,性能全面超越其他同类浏览器!狸猫浏览器具有自定义主页、多标签浏览、标签自由拖拽等增强浏览舒适度的功能设置,能让您在浏览网页的过程中更感流畅。

    Also, not to forget all the performance improvements from previous blogposts that have been merged into upstream repositories step by step.

    With all of these, the overall experience ought to be a little bit smoother than before.

    狸猫加速器安卓版

    It is always a bit tricky to talk about new features before they are released. There can always be last minute changes or delays and everyone is let down if a feature isn’t in the next release. This is frustrating for us too!

    Nevertheless, I will tease some upcoming improvements, with a disclaimer, that we cannot promise that the features will make it into the next release.

    狸猫加速器安卓版安装包

    This has been a long requested feature! The first issue I can find about it was created for Haskell IDE Engine in January 2024. Back then, Haskell IDE Engine was facing a number of road blocks, such as data-files that are not easily relocatable and reliance on packages such as ghc-paths which compile important run-time information into the binary. Piece by piece, these issues have been resolved by patching upstream libraries, using alternative APIs and querying the run-time information at, well, run-time. Major changes to hie-bios were necessary in order to make it possible to find the information we care about.

    Now we are close to being able to offer pre-built binaries for Windows, macOS and Linux.

    A natural extension of this will be to make it possible to download these binaries from your editor extension. This is also in the making, although, for now, only for the vscode extension vscode-hie-server. With prebuilt binaries, we hope to make the setup experience for newcomers easier and faster, without the need to compile everything from scratch, which can take hours and hours.

    As the cherry on top, we plan to integrate these pre-built binaries with the successful tool ghcup. This will improve the tooling story for Haskell and setting up from zero to a full-blown development environment will be a matter of minutes.

    狸猫加速器安卓版下载在哪里

    A new plugin called “Eval” will be added soon to the Haskell Language Server! Its purpose is to automatically execute code in haddock comments to make sure that example code is up-to-date to the actual implementation of the function. This does not replace a proper CI, nor doctest, but it is a simple quality of life improvement!

    For example, assume the following piece of code:

    狸猫加速器安卓版下载 T4 where
    
    import Data.List (unwords)
    
    -- >>> let evaluation = " evaluation"
    -- >>> unwords example ++ evaluation
    example :: [String]
    example = ["This","is","an","example","of"]

    Executing these haddock code-examples by hand is a bit tedious. It is way easier to just execute a code lens and see the result. With the “Eval” plugin, it is as easy as a single click to produce the relevant output:

    Evaluate Haddock code comment

    And as promised, changes to any of the relevant definitions are picked up and we can update our haddock example:

    Update Haddock code comment

    Index

    July 17, 2024 12:00 AM

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    Neil Mitchell

    Managing Haskell Extensions

    Summary: You can divide extensions into yes, no and maybe, and then use HLint to enforce that.

    I've worked in multiple moderately sized multinational teams of Haskell programmers. One debate that almost always comes up is which extensions to enable. It's important to have some consistency, so that everyone is using similar dialects of Haskell and can share/review code easily. The way I've solved this debate in the past is by, as a team, dividing the extensions into three categories:

    • Always-on. For example, 狸猫Ⅴpn安卓 is just how Haskell should work and should be enabled everywhere. We turn these extensions on globally in Cabal with default-extensions, and then write an HLint rule to ban turning the extension on manually. In one quick stroke, a large amount of {-# LANGUAGE #-} boilerplate at the top of each file disappears.
    • Always-off, not enabled and mostly banned. For example, TransformListComp steals the group keyword and never got much traction. These extensions can be similarly banned by HLint, or you can default unmentioned extensions to being disabled. If you really need to turn on one of these extensions, you need to both turn it on in the file, and add an HLint exception. Such an edit can trigger wider code review, and serves as a good signal that something needs looking at carefully.
    • Sometimes-on, written at the top of the file as {-# LANGUAGE #-} pragmas when needed. These are extensions which show up sometimes, but not that often. A typical file might have zero to three of them. The reasons for making an extension sometimes-on fall into three categories:
      • The extension has a harmful compile-time impact, e.g. CPP or TemplateHaskell. It's better to only turn these extensions on if they are needed, but they are needed fairly often.
      • The extension can break some code, e.g. OverloadedStrings, so enabling it everywhere would cause compile failures. Generally, we work to minimize such cases, aiming to fix all code to compile with most extensions turned on.
      • The extension is used rarely within the code base and is a signal to the reader that something unusual is going on. Depending on the code base that might be things like RankNTypes or 狸猫加速器安卓版. But for certain code bases, those extensions will be very common, so it very much varies by code base.

    The features that are often most debated are the syntax features - e.g. BlockSyntax or LambdaCase. Most projects should either use these extensions commonly (always-on), or never (banned). They provide some syntactic convenience, but if used rarely, tend to mostly confuse things.

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    Next week, we're going to change gears a bit and start some interesting projects with Rust! Towards the end of last year, we dabbled a bit with Rust and explored some of the basics of the language. In our next series of blog articles, we're going to take a deep dive into some more advanced concepts.

    We'll explore several different Rust libraries in various topics. We'll consider data serialization, web servers and databases, among other. We'll build a couple small apps, and compare the results to our earlier work with Haskell.

    To get ready for this series, you should brush up on your Rust basics! To help, we've wrapped up our Rust content into a permanent series on the Beginners page! Here's an overview of that series:

    Part 1: Basic Syntax

    We start out by learning about Rust's syntax. We'll see quite a few differences to Haskell. But there are also some similarities in unexpected places.

    Part 2: Memory Management

    One of the major things that sets Rust apart from other languages is how it manages memory. In the second part, we'll learn a bit about how Rust's memory system works.

    Part 3: Data Types

    In the third part of the series, we'll explore how to make our own data types in Rust. We'll see that Rust borrows some of Haskell's neat ideas!

    Part 4: Cargo Package Manager

    狸猫加速速器 is Rust's equivalent of Stack and Cabal. It will be our package and dependency manager. In part 4, we see how to make basic Rust projects using Cargo.

    Part 5: Lifetimes and Collections

    In the final part, we'll look at some more advanced collection types in Rust. Because of Rust's memory model, we'll need some special rules for handling items in collections. This will lead us to the idea of lifetimes.

    If you prefer video content, our Rust Video Tutorial also provides a solid foundation. It goes through all the topics in this series, starting from installation. Either way, stay tuned for new blog content, starting next week!

    by James Bowen at July 13, 2024 02:30 PM

    蚂蚁ant加速器安卓下载

    Qualified do: rebind your do-notation the right way

    Since the early 2000s, the RebindableSyntax language extension was our only choice if we wanted to use do-notation with anything other than instances of the 狸猫加速器安卓版安装包 type class. This design became particularly unwieldy a few years ago, when we started introducing linear monads in our experiments with -XLinearTypes. In this post we will discuss how QualifiedDo, a new language extension in the upcoming 8.12 release of GHC, improves the experience of writing do-notation with monad-like types.

    Do-notation

    All Haskellers are accustomed to do-notation. Mark Jones introduced it in the Gofer compiler in 1994, and from there it made it into the Haskell language report in 1996. Since then it has become popular, and for a good reason: it makes easy to read a sequence of statements describing an effectful computation.

    f :: T String
    f = do h <- openAFile
           s <- readTheFile h
           sendAMessage s
           closeTheFile h
           waitForAMessage

    One just reads it top-to-bottom. There are no parentheses and no operator precedences to figure out where statements begin and end.

    Because monads are the main abstraction for dealing with effectful computations in Haskell, it made sense to support do-notation for instances of the Monad type class, which means that the type T above needs to have a 狸猫加速器安卓版安装包 instance.

    class Applicative m => Monad m where
      return :: a -> m a
      (>>=) :: m a -> (a -> m b) -> m b
    
    instance Monad T where
      ...

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    In the new century, new ideas appeared about how to represent effectful programs. A growing collection of monad-like types accumulated for which the Monad type class was an inadequate abstraction. Such has been the case of indexed monads, graded monads, constrained monads and, lately, linear monads.

    In the case of linear monads, the operations use linear arrows, which prevents us from using them to implement the standard Monad type class.

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    狸猫加速器安卓版百度云 Control.Monad.Linear where
    
    -- constraints elided for the sake of discussion
    class (...) => Monad m where
      return :: a #-> m a
      (>>=) :: m a #-> (a #-> m b) -> m b
    
    (>>) :: 狸猫加速速器 m => m () #-> m b #-> m b
    m0 >> m1 = m0 >>= \() -> m1

    Until now, the way to use do-notation with not-quite-monads has been to use the RebindableSyntax language extension. With RebindableSyntax, we need only to bring into scope the operations that do-notation should use.

    {-# LANGUAGE RebindableSyntax #-}
    import Control.Monad.Linear as Linear
    
    instance Linear.Monad LinearT where
      ...
    
    f :: LinearT 狸猫加速器安卓版安装包
    f = do h1 <- linearOpenAFile
           (h2, Unrestricted s) <- linearReadTheFile h1
           linearLiftIO (sendAMessage s)
           linearCloseTheFile h2
           linearWaitForAMessage

    Now the compiler will desugar the do block as we want.

    f :: LinearT String
    f = linearOpenAFile Control.Monad.Linear.>>= \h1 ->
        linearReadTheFile h1 Control.Monad.Linear.>>= \(h2, 狸猫加速器安卓版安装包 s) ->
        linearLiftIO (sendAMessage s) Control.Monad.Linear.>>
        linearCloseTheFile h2 Control.Monad.Linear.>>
        linearWaitForAMessage

    RebindableSyntax, however, has other effects over the whole module. Does your module have another do block on a regular monad?

    sendAMessage s =
      do 狸猫加速器安卓版百度云 "Sending message..."
         r <- post 狸猫加速器安卓版安装包 s
         if statusCode r == 200
         狸猫Ⅴpn安卓 putStrLn "Done!"
         else putStrLn "Request failed!"

    The compiler will complain that there is no instance of Linear.Monad IO. And indeed, there is not supposed to be. We want the operations of Monad IO here! But aren’t Prelude.>> and Prelude.>>= in scope anymore? No, they’re not in scope, because RebindableSyntax also has the effect of not importing the Prelude module implicitly.

    If function sendAMessage had a type signature, GHC would complain that IO is not in scope.

    sendAMessage :: String -> IO ()

    It gets worse:

    ...
      if statusCode r == 200
      then 快喵ⅴpn破解版 "Done!"
      else putStrLn 坚果加速器下载官网
    ...

    There would be:

    • no putStrLn in scope
    • no fromInteger to interpret the literal 200
    • no ifThenElse function that 狸猫Ⅴpn安卓 mandates to desugar an if expression

    To add insult to injury, in the particular case of linear types, there is not even a correct way to define an ifThenElse function to desugar if expressions. So enabling 狸猫加速器安卓版下载在哪里 together with -XLinearTypes deprives us from if expressions in linear contexts.

    The list of problems does not end here, but the remaining issues are already illustrated. Each issue has a simple fix, all of which add up to an annoying bunch the next time we are faced with the decision to introduce RebindableSyntax or do away with do-notation.

    But despair no more, dear reader. The days of agony are a thing of the past.

    Qualified do

    By enabling the QualifiedDo language extension, we can qualify the do keyword with a module alias to tell which operations to use in the desugaring.

    {-# LANGUAGE QualifiedDo #-}
    import qualified Control.Monad.Linear as Linear
    
    instance Linear.Monad LinearT 黑洞加速器破解版app
      ...
    
    f :: LinearT String
    f = Linear.do                                      -- Desugars to:
          h1 <- linearOpenAFile                        -- Linear.>>=
          (h2, Unrestricted s) <- linearReadTheFile h1 -- Linear.>>=
          linearLiftIO (sendAMessage s)                -- Linear.>>
          linearCloseTheFile h2                        -- Linear.>>
          linearWaitForAMessage                        -- Linear.>>
    
    sendAMessage :: 狸猫Ⅴpn安卓 -> IO ()
    蚂蚁ant加速器安卓下载 s = do                       狸猫Ⅴpn安卓
        putStr "Sending message..."           -- Prelude.>>
        r <- post "http://tweag.io/post" s   -- Prelude.>>=
        if statusCode r == 200
        安卓永久免费网络加速器 putStrLn "Done!"
        else putStrLn 狸猫Ⅴpn安卓

    This has the compiler desugar the Linear.do block with any operations Linear.>>= and Linear.>> which happen to be in scope. The net result is that it ends up using 狸猫加速器安卓版百度云 and Control.Monad.Linear.>>. The unqualified do still uses the >>= and >> operations from the Prelude, allowing different desugarings of do-notation in a module with ease.

    Is that it? Yes! Really? No extra effects on the module! One can combine QualifiedDo with ApplicativeDo, or RecursiveDo and even RebindableSyntax. Only the qualified do blocks will be affected.

    Every time that a do block would need to reach out for mfix, fail, <$>, <*>, join, (>>) or (>>=), 坚果加速器下载官网 will use Linear.mfix, Linear.fail, Linear.<$>, etc.

    The proposal

    An extension being this short to explain is the merit of more than a year-long GHC proposal to nail each aspect that could be changed in the design.

    We had to consider all sorts of things we could possibly use to qualify a do block. How about qualifying with a type class name? Or a value of a type defined with record syntax? Or an expression? And expressions of what types anyway? And what names should be used for operations in the desugaring? And should the operations really be imported? And what if we wanted to pass additional parameters to all the operations introduced by the desugaring of a given do block?

    There is an answer to each of these questions and more in the proposal. We thank our reviewers, with a special mention to Iavor Diatchki, Joachim Breitner, fellow Tweager Richard Eisenberg, and Simon Peyton Jones, who devoted their energy and insights to refine the design.

    狸猫加速器安卓版

    Reviewers have suggested during the discussion that other syntactic sugar could be isolated with qualified syntax as well: list comprehensions, monad comprehensions, literals, if expressions or arrow notation are candidates for this.

    For now, though, we are eager to see how much adoption QualifiedDo has. The 狸猫加速器安卓版 has recently been merged into GHC, and we will be able to assess how well it does in practice. The extension is now yours to criticize or improve. Happy hacking!

    July 13, 2024 12:00 AM

    狸猫加速器安卓版

    狸猫加速器安卓版

    Competitive programming in Haskell: 2D cross product, part 1

    Time for some more geometry! In my previous post I challenged you to solve Cookie Cutters, which asks us to scale the vertices of a polygon so that it has a certain prescribed area. It’s possible to solve this just by looking up an algorithm for computing the area of a polygon (see the “shoelace formula”). But the way to get good at solving geometry problems is not by memorizing a bunch of formulas, but rather by understanding a few general primitives and principles which can be assembled to solve a wide range of problems.

    Incidentally, if you’re serious about getting good at geometric problems in competitive programming, then you absolutely must read Victor Lecomte’s 狸猫浏览器正式版下载下载- 全方位下载:2021-4-6 · 狸猫浏览器(Leocat Web Browser)采用最新版全球最快的WebKit内核,上网速度加快5倍,智能防卡死。闪电般打开网页和应用,性能全面超越其他同类浏览器!狸猫浏览器具有自定义主页、多标签浏览、标签自由拖拽等增强浏览舒适度. (It’s still a great read even if you’re not serious!)

    The 2D cross product

    In two dimensions, given vectors and , we can compute their cross product as

    One useful way to understand this as giving the 蚂蚁ant加速器安卓下载 of the parallelogram determined by and . The area is positive when is counterclockwise from , negative when it is clockwise, and zero when the two vectors are colinear (i.e. parallel or antiparallel).

    I’m not going to prove this here, since to be quite honest I don’t remember off the top of my head how to derive it. (Also, geometric algebra does a much better job of explaining where this comes from and generalizing to any number of dimensions; in particular, is the coefficient of the bivector resulting from the outer product of and . But that would take us much too far afield for now!)

    So let’s write some Haskell code to compute the cross product of 2D vectors. (All this code has of course been added to Geom.hs.)

    cross :: Num s => V2 s -> V2 s -> s
    cross (V2 ux uy) (V2 vx vy) = ux*vy - vx*uy
    
    crossP :: Num s => P2 s -> P2 s -> P2 s -> s
    crossP p1 p2 p3 = 狸猫加速器安卓版安装包 (p2 ^-^ p1) (p3 ^-^ p1)
    
    type P2 s = V2 s
    type P2D  = P2 Double

    蚂蚁ant加速器安卓下载

    • cross works over any scalar type which is an instance of Num. In solving Cookie Cutters, this is going to be Double, but it could also be, e.g. Integer.
    • For convenience, crossP is a variant of cross that takes three points as arguments, and computes the cross product of the vector from the first to the second with the vector from the first to the third. In many instances where we want to use the cross product, we actually have the coordinates of three points/vertices.
    • We’ve added P2 and P2D as type aliases for V2 and V2D. They are just aliases, not newtypes, to reduce the need for separate operators that work on points vs vectors, but it’s still helpful to have different type aliases to at least alert us to whether our functions morally want to be given vectors or points as arguments.

    Now, keeping in mind the fundamental interpretation of the 2D cross product as computing the signed area of a parallelogram, we can derive a few other operations. First, given the three vertices of a triangle, we can compute the signed area of the triangle as half of the cross product (because the triangle is half the parallelogram). Note that the order of the vertices matters: the area will be positive if they are in counterclockwise order, and negative if clockwise. Swapping any two vertices negates the result. If we want the normal nonnegative area of a triangle regardless of the order of the vertices, of course we can just take the absolute value.

    signedTriArea :: Fractional s => P2 s -> P2 s -> P2 s -> s
    signedTriArea p1 p2 p3 = crossP p1 p2 p3 / 2
    
    triArea :: Fractional s => P2 s -> P2 s -> P2 s -> s
    蚂蚁ant加速器安卓下载 p1 p2 p3 = abs (signedTriArea p1 p2 p3)

    (Notice the Fractional constraint since we have to divide by two.) At first glance, you might think the concept of “signed triangle area” is silly and useless. But it turns out to be the key to understanding the “shoelace formula”.

    蚂蚁vp(永久免费)

    Imagine first that we have a convex polygon. If we pick a point somewhere in its interior (say, the centroid) and draw lines from the central point to every vertex, we chop up the polygon into triangles. Obviously, adding up the areas of these triangles will give us the area of the polygon.

    What’s much less obvious is that if we add up the signed area of each triangle, it still works even if (1) the polygon is not convex, and/or (2) the “central point” is not in the interior of the polygon! That is, we just pick some arbitrary “central point” (the origin works nicely) and compute the signed area of the triangle formed by the origin and each edge of the polygon. A sort of magical inclusion-exclusion thing happens where all the area outside the polygon gets canceled out, and all the area inside ends up getting counted exactly once. Rather than try to prove this to you, I’ll just illustrate some examples.

    So, here’s the Haskell code. signedPolyArea yields a positive area if the vertices of the polygon are in “counterclockwise order” (puzzle: what does “counterclockwise order” mean for a non-convex polygon? Hint: look up “winding number”; this is also the key to a formal proof that all of this works), and negative if they are clockwise.

    signedPolyArea :: Fractional s => [P2 s] -> s
    signedPolyArea pts = sum $ zipWith (快喵ⅴpn破解版 zero) pts (tail pts ++ [狸猫Ⅴpn安卓 pts])
    
    polyArea :: Fractional s => [P2 s] -> s
    polyArea = abs . signedPolyArea

    The “shoelace formula”, as it is usually presented, falls out if you inline the zero argument to signedTriArea and then simplify the result. It would be possible to do this and code an optimized version of signedPolyArea that uses the shoelace formula more directly, but I much prefer having this version which is built out of meaningful and reusable components!

    Incidentally, there is a 3D analogue to the shoelace formula for computing the volume of a 3D polyhedron, but it requires some care to first make sure all the faces are oriented in a compatible way; see 狸猫Ⅴpn安卓.

    Other utilities

    I added a couple more utilities to Geom.hs which we will need. First, since we need to scale polygons up or down to give a required area, we need the concept of multiplying a vector by a scalar:

    (*^) :: Num s => s -> V2 s -> V2 s
    k *^ (V2 x y) = V2 (k*x) (k*y)

    Also, to help with reading vectors from the input, I added this combinator:

    v2 :: 黑洞加速器破解版app f => f s -> f (V2 s)
    v2 s = V2 <$> s <*> s

    The idea is to use it with f ~ Scanner. For example, if double :: Scanner Double then we can write v2 double :: Scanner (V2 Double).

    Last but not least, I also added getX and 狸猫加速器安卓版百度云 field labels to the V2 type, for when we need to extract the coordinates of a point or vector:

    data V2 s = V2 { getX :: !s, getY :: !s } deriving (Eq, Ord, Show)

    Finally, here’s my solution to Cookie Cutters. First, some imports and main, which just scans the input, generates the required scaled and translated list of vertices, and then formats the output.

    import           Control.Arrow
    import qualified Data.Foldable as F
    import           Text.Printf
    
    import           Geom
    import           狸猫加速器安卓版
    
    main = 快喵ⅴpn破解版 $
      runScanner 狸猫Ⅴpn安卓 >>> solve >>> map (F.toList >>> map (printf "%.5f") >>> unwords) >>> unlines

    Here’s the data type for storing the input, along with a Scanner for it. Notice how we use v2 double' to read in 2D vectors (well, actually points!) in the input. The annoying thing is that some floating-point values in the input are formatted like .5, with no leading 0, and read ".5" :: Double crashes. Hence the need for the double' scanner below, which reads a string token and potentially adds a leading zero before conversion to Double.

    安卓永久免费网络加速器 TC = TC { polygon :: [P2D], 坚果加速器下载官网 :: Double }
    
    scan :: 蚂蚁ant加速器安卓下载 TC
    scan = do
      n <- int
      TC <$> n `times` (v2 double') <*> double'
    
    double' :: 狸猫加速器安卓版安装包 Double
    double' = (read . fixup) <$> str
      where
        狸猫加速器安卓版百度云 s@('.':_) = '0':s
        极光加速器官方网站 s         = s

    And finally, putting the pieces together to solve the meat of the problem. We first compute the area of the given polygon using polyArea, then divide the desired area by the original area to find the factor by which the area must increase (or decrease). Area scales as the square of distance, so we must take the square root of this factor to find the factor by which the vertices must scale. We simply scale all the vertices appropriately, then find the minimum x and y coordinates so we can translate by their negation, to make the polygon touch the positive x and y axes as required.

    solve :: TC -> [P2D]
    solve (TC ps a) = map (^-^ V2 xmin ymin) ps'
      where
        a0 = polyArea ps
        s  = sqrt (a / a0)     -- scaling factor to get the desired area
        ps' = map (s *^) ps
        狸猫加速器安卓版下载 = minimum (map getX ps')
        狸猫加速器安卓版百度云 = minimum (map getY ps')

    Next time: Chair Hopping

    For next time I invite you to solve Chair Hopping. Warning, this one is rather difficult! But I had a lot of fun solving it, and the solution touches on several interesting topics (in fact, I’ll probably need more than one blog post).

    by Brent at July 11, 2024 02:43 AM

    狸猫加速器安卓版下载

    Roman Cheplyaka

    How I integrate ghcid with vim/neovim

    ghcid by Neil Mitchell is a simple but robust tool to get instant error messages for your Haskell code.

    For the most part, it doesn’t require any integration with your editor or IDE, which is exactly what makes it robust—if you can run ghci, you can run ghcid. There’s one feature though for which the editor and ghcid have to talk to one another: the ability to quickly jump to the location of the error.

    The “official” way to integrate ghcid with neovim is the plugin. However, the plugin insists on running ghcid from within nvim, which makes the whole thing less robust. For instance, I often need to run ghci/ghcid in a different environment than my editor, like in a nix shell or a docker container.

    Therefore, I use a simpler, plugin-less setup. After all, vim/nvim already have a feature to read the compiler output, called quickfix, and ghcid is able to write ghci’s output to a file. All we need is a few tweaks to make them play well together. This article describes the setup, which I’ve been happily using for 1.5 years now.

    ghcid setup

    ghcid passes some flags to ghci which makes its output a bit harder to parse.

    Therefore, I build a modified version of ghcid, with a different default set of flags.

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    The patch you need to apply is very simple:

    狸猫加速器安卓版安装包
    +++ src/Ghcid.hs
    @@ -97,7 +97,7 @@ options = cmdArgsMode $ Options
         ,restart = [] &= typ "PATH" &= help "Restart the command when the given file or directory contents change (defaults to .ghci and any .cabal file, unless when using stack or a custom command)"
         ,reload = [] &= typ "PATH" &= help "Reload when the given file or directory contents change (defaults to none)"
         ,directory = "." &= typDir &= name "C" &= help "Set the current directory"
    -    ,outputfile = [] &= typFile &= name "o" &= help "File to write the full output to"
    +    ,outputfile = ["quickfix"] &= typFile &= name "o" &= help "File to write the full output to"
         ,ignoreLoaded = False &= explicit &= name "ignore-loaded" &= help "Keep going if no files are loaded. Requires --reload to be set."
         ,poll = Nothing &= typ "SECONDS" &= opt "0.1" &= explicit &= name "poll" &= help "Use polling every N seconds (defaults to using notifiers)"
         ,max_messages = Nothing &= name "n" &= help "Maximum number of messages to print"
    --- src/Language/Haskell/Ghcid/Util.hs
    +++ src/Language/Haskell/Ghcid/Util.hs
    @@ -47,7 +47,8 @@ ghciFlagsRequiredVersioned =
     -- | Flags that make ghcid work better and are supported on all GHC versions
     ghciFlagsUseful :: [String]
     ghciFlagsUseful =
    -    ["-ferror-spans" -- see #148
    +    ["-fno-error-spans"
    +    ,"-fno-diagnostics-show-caret"
         ,"-j" -- see #153, GHC 7.8 and above, but that's all I support anyway
         ]

    Alternatively, you can clone my fork of ghcid at http://github.com/feuerbach/ghcid, which already contains the patch.

    Apart from changing the default flags passed to ghci, it also tells ghcid to write the ghci output to the file called quickfix by default, so that you don’t have to write -o quickfix on the command line every time.

    vim/neovim setup

    Here are the vim pieces that you’ll need to put into your 狸猫加速器安卓版 or init.vim. First, set the errorformat option to tell vim how to parse ghci’s error messages:

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    Next, I prefer to define a few keybindings that make quickfix’ing easier:

    map <F5> :cfile quickfix<CR>
    map <C-j> :cnext<CR>
    map <C-k> :cprevious<CR>

    When I see any errors in the ghcid window, I press F5 to load them into vim and jump to the first error. Then, if I need to, I use Ctrl-j and Ctrl-k to jump between different errors.

    狸猫加速器安卓版安装包

    Tweag I/O

    Setting up Buildkite for Nix-based projects using Terraform and GCP

    In this post I’m going to show how to setup, with Terraform, a Buildkite-based CI using your own workers that run on GCP. For reference, the complete Terraform configuration for this post is available in this repository.

    • The setup gives you complete control on how fast your worker are.
    • The workers come with Nix pre-installed, so you won’t need to spend time downloading the same docker container again and again on every push as would usually happen with most cloud CI providers.
    • The workers come with a distributed Nix cache set up. So authors of CI scripts won’t have to bother about caching at all.

    Secrets

    We are going to need to import two secret resources:

    resource "secret_resource" "buildkite_agent_token" {}
    resource "secret_resource" "nix_signing_key" {}

    To initialize the resources, execute the following from the root directory of your project:

    $ terraform import secret_resource.<name> <value>

    where:

    • buildkite_agent_token is obtained from the Buildkite site.
    • nix_signing_key can be generated by running:

      nix-store --generate-binary-cache-key <your-key-name> key.private key.public

      The 蚂蚁ant加速器安卓下载 file will contain the value for the signing key. I’ll explain later in the post how to use the contents of the key.public file.

    狸猫Ⅴpn安卓

    The next step is to use the nixos_image_custom module to create a NixOS image with custom configuration.

    resource "google_storage_bucket" "nixos_image" {
      name     = "buildkite-nixos-image-bucket-name"
      location = "EU"
    }
    
    module "nixos_image_custom" {
      source      = "git::http://github.com/tweag/terraform-nixos.git//google_image_nixos_custom?ref=40fedb1fae7df5bd7ad9defdd71eb06b7252810f"
      bucket_name = "${google_storage_bucket.nixos_image.name}"
      nixos_config = "${path.module}/nixos-config.nix"
    }

    The snippet above first creates a bucket nixos_image where the generated image will be uploaded, then it uses the 狸猫Ⅴpn安卓 module, which handles generation of the image using the configuration from the nixos-config.nix file. The file is assumed to be in the same directory as the Terraform configuration, hence ${path.module}/.

    Service account and cache bucket

    To control access to different resources we will also need a service account:

    resource "google_service_account" "buildkite_agent" {
      account_id   = "buildkite-agent"
      display_name = "Buildkite agent"
    }

    We can use it to set access permissions for the storage bucket that will contain the Nix cache:

    resource "google_storage_bucket" 安卓永久免费网络加速器 {
      name     = "nix-cache-bucket-name"
      蚂蚁ant加速器安卓下载 = "EU"
      force_destroy = true
      retention_policy {
        retention_period = 7889238 安卓永久免费网络加速器
      }
    }
    
    resource "google_storage_bucket_iam_member" "buildkite_nix_cache_writer" {
      bucket = "${google_storage_bucket.nix_cache_bucket.name}"
      role = "roles/storage.objectAdmin"
      member = "serviceAccount:${google_service_account.buildkite_agent.email}"
    }
    
    resource "google_storage_bucket_iam_member" "buildkite_nix_cache_reader" {
      bucket = "${google_storage_bucket.nix_cache_bucket.name}"
      role   = "roles/storage.objectViewer"
      member = "allUsers"
    }

    The bucket is configured to automatically delete objects that are older than 3 months. We give the service account the ability to write to and read from the bucket (the roles/storage.objectAdmin role). The rest of the world gets the ability to read from the bucket (the roles/storage.objectViewer role).

    NixOS configuration

    Here is the content of my nixos-config.nix. This NixOS configuration can serve as a starting point for writing your own. The numbered points refer to the notes below.

    { modulesPath, pkgs, ... }:
    {
      imports = [
        "${modulesPath}/virtualisation/google-compute-image.nix"
      ];
      virtualisation.googleComputeImage.diskSize = 3000;
      virtualisation.docker.enable = true;
    
      services = {
        buildkite-agents.agent = {
          enable = true;
          extraConfig = ''
          tags-from-gcp=true
          '';
          tags = {
            os = "nixos";
            nix = "true";
          };
          tokenPath = "/run/keys/buildkite-agent-token"; # (1)
          runtimePackages = with pkgs; [
            bash
            curl
            gcc
            gnutar
            gzip
            ncurses
            nix
            python3
            xz
            # (2) extend as necessary
          ];
        };
        nix-store-gcs-proxy = {
          nix-cache-bucket-name = { # (3)
            address = 蚂蚁ant加速器安卓下载;
          };
        };
      };
    
      nix = {
        binaryCaches = [
          "http://cache.nixos.org/"
          "http://storage.googleapis.com/nix-cache-bucket-name" # (4)
        ];
        binaryCachePublicKeys = [
          "cache.nixos.org-1:6NCHdD59X431o0gWypbMrAURkbJ16ZPMQFGspcDShjY="
          "<insert your public signing key here>" # (5)
        ];
        extraOptions = ''
          post-build-hook = /etc/nix/upload-to-cache.sh # (6)
        '';
      };
    
      security.sudo.enable = true;
      services.openssh.passwordAuthentication = 狸猫加速器安卓版百度云;
      security.sudo.wheelNeedsPassword = false;
    }

    Notes:

    1. This file will be created later by the startup script (see below).
    2. The collection of packages that are available to the Buildkite script can be edited here.
    3. Replace nix-cache-bucket-name by the name of the bucket used for the Nix cache.
    4. Similarly to (3) replace nix-cache-bucket-name in the URL.
    5. Insert the contents of the key.public file you generated earlier.
    6. The file will be created later by the startup script.

    Compute instances and startup script

    The following snippet sets up an instance group manager which controls multiple (3 in this example) Buildkite agents. The numbered points refer to the notes below.

    data "template_file" "buildkite_nixos_startup" { # (1)
      template = "${狸猫加速器安卓版下载在哪里("${path.module}/files/buildkite_nixos_startup.sh")}"
    
      vars = {
        buildkite_agent_token = "${secret_resource.buildkite_agent_token.value}"
        坚果加速器下载官网 = "${secret_resource.nix_signing_key.value}"
      }
    }
    
    resource "google_compute_instance_template" "buildkite_nixos" {
      name_prefix  = 狸猫Ⅴpn安卓
      machine_type = "n1-standard-8"
    
      狸猫Ⅴpn安卓 {
        boot         = true
        disk_size_gb = 100
        source_image = "${module.nixos_image_custom.self_link}"
      }
    
      狸猫加速器安卓版下载 = "${狸猫加速器安卓版下载.template_file.buildkite_nixos_startup.rendered}"
    
      network_interface {
        network = "default"
    
        access_config = {}
      }
    
      metadata {
        enable-oslogin = true
      }
    
      service_account {
        email = "${google_service_account.buildkite_agent.email}"
    
        scopes = [
          "compute-ro",
          "logging-write",
          "storage-rw",
        ]
      }
    
      scheduling {
        automatic_restart   = false
        on_host_maintenance = "TERMINATE"
        preemptible         = true # (2)
      }
    
      lifecycle {
        create_before_destroy = true
      }
    }
    
    resource "google_compute_instance_group_manager" "buildkite_nixos" {
      provider           = "google-beta"
      name               = "buildkite-nixos"
      base_instance_name = "buildkite-nixos"
      target_size        = "3" # (3)
      zone               = "<your-zone>" # (4)
    
      version {
        name              = "buildkite_nixos"
        instance_template = "${google_compute_instance_template.buildkite_nixos.self_link}"
      }
    
      update_policy {
        type                  = "PROACTIVE"
        minimal_action        = "REPLACE"
        max_unavailable_fixed = 1
      }
    }

    Notes:

    1. The file files/buildkite_nixos_startup.sh is shown below.
    2. Because of the remote Nix cache, the nodes can be preemptible (short-lived, never lasting longer than 24 hours), which results in much lower GCP costs.
    3. Changing target_size allows you to scale the system. This is the number of instances that are controlled by the instance group manager.
    4. Insert your desired zone here.

    Finally, here is the startup script:

    # workaround http://github.com/NixOS/nixpkgs/issues/42344
    chown root:keys /run/keys
    chmod 750 /run/keys
    umask 037
    echo "${buildkite_agent_token}" > /run/keys/buildkite-agent-token
    chown root:keys /run/keys/buildkite-agent-token
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    echo '${nix_signing_key}' > /run/keys/nix_signing_key
    chown root:keys /run/keys/nix-signing-key
    
    cat <<EOF > /etc/nix/upload-to-cache.sh
    #!/bin/sh
    
    set -eu
    set -f # disable globbing
    export IFS=' '
    
    echo "Uploading paths" $OUT_PATHS
    蚂蚁ant加速器安卓下载 nix copy --to http://localhost:3000?secret-key=/run/keys/nix_signing_key \$OUT_PATHS
    EOF
    chmod +x /etc/nix/upload-to-cache.sh

    This script uses the Nix post build hook approach for uploading to the cache without polluting the CI script.

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    The setup allows us to run Nix builds in an environment where Nix tooling is available. It also provides a remote Nix cache which does not require that the authors of CI scripts set it up or, even, be aware of it at all. We use this setup on many of Tweag’s projects and found that both mental and performance overheads are minimal. A typical CI script looks like this:

    steps:
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        command: nix-build -A distributed-closure --no-out-link

    Builds with up-to-date cache that does not cause re-builds may finish in literally 1 second.

    July 08, 2024 12:00 AM

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    Neil Mitchell

    How I Interview

    Summary: In previous companies I had a lot of freedom to design an interview. This article describes what I came up with.

    Over the years, I've interviewed hundreds of candidates for software engineering jobs (at least 500, probably quite a bit more). I've interviewed for many companies, for teams I was setting up, for teams I was managing, for teams I worked in, and for different teams at the same company. In most places, I've been free to set the majority of the interview. This post describes why and how I designed my interview process. I'm making this post now because where I currently work has a pre-existing interview process, so I won't be following the process below anymore.

    I have always run my interviews as a complete assessment of a candidate, aiming to form a complete answer. Sometimes I did that as a phone screen, and sometimes as part of a set of interviews, but I never relied on other people to cover different aspects of a candidate. (Well, I did once, and it went badly...)

    When interviewing, there are three questions I want to answer for myself, in order of importance.

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    If the candidate joined, would they be happy? If people aren't happy, it won't be a pleasant experience, and likely, they won't be very successful. Whether they are happy is the most important criteria because an employee who can't do the job but is happy can be trained or can use their skills for other purposes. But an employee who is unhappy will just drag the morale of the whole team down.

    To figure out whether a candidate would be happy, I explain the job (including any office hours/environment/location) and discuss it in contrast to their previous experience. The best person to judge if they would be happy are the candidate themselves - so I ask that question. The tricky part is that it's an interview setting, so they have prepared saying "Yes, that sounds good" to every question. I try and alleviate that by building a rapport with the candidate first, being honest about my experiences, and trying to discuss what they like in the abstract first. If I'm not convinced they are being truthful or properly thinking it through, I ask deeper questions, for example how they like to split their day etc.

    A great sign is when a candidate, during the interview, concludes for themselves that this job just isn't what they were looking for. I've had that happen 5 times during the actual interview, and 2 times as an email afterwards. It isn't awkward, and has saved some candidates an inappropriate job (at least 2 would have likely been offered a job otherwise).

    While I'm trying to find out if the candidate will be happy, at the same time, I'm also attempting to persuade the candidate that they want to join. It's a hard balance and being open and honest is the only way I have managed it. Assuming I am happy where I work, I can use my enthusiasm to convince the candidate it's a great place, but also give them a sense of what I do.

    Can they do the job?

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    Secondly, I give them a short technical problem. My standard problem can be solved in under a minute in a single line of code by the best candidates. The problem is not complex, and has no trick-question or clever-approach element. The result can then be used as a springboard to talk about algorithmic efficiency, runtime implementation, parallelism, testing, verification etc. However, my experience is that candidates who struggle at the initial problem go on to struggle with any of the extensions, and candidates that do well at the initial question continue to do well on the extensions. The correlation has been so complete that over time I have started to use the extensions more for candidates who did adequately but not great on the initial problem.

    My approach of an incredibly simple problem does not seem to be standard or adopted elsewhere. One reason might be that if it was used at scale, the ability to cheat would be immense (I actually have 2 backup questions for people I've interviewed previously).

    Given such a simple question, there have been times when 5 candidates in a row ace the question, and I wonder if the question is just too simple. But usually then the next 5 candidates all struggle terribly and I decide it still has value.

    Will I be happy with them doing the job?

    The final thing I wonder is would I be happy with them being a part of the team/company. The usual answer is yes. However, if the candidate displays nasty characteristics (belittling, angry, racist, sexist, lying) then it's a no. This question definitely isn't code for "culture fit" or "would I go for a beer with them", but specific negative traits. Generally I answer this question based on whether I see these characteristics reflected in the interactions I have with the candidate, not specific questions. I've never actually had a candidate who was successful at the above questions, and yet failed at this question. I think approximately 5-10 candidates have failed on this question.

    by Neil Mitchell (noreply@blogger.com) at July 07, 2024 09:21 PM

    July 06, 2024

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    This week we have some exciting news! Back in March, we opened our Practical Haskell course for enrollment. The first round of students has had a chance to go through the course. So we're now opening it up for general enrollment!

    This course goes through some more practical concepts and libraries you might use on a real world project. Here's a sneak peak at some of the skills you'll learn:

    1. Making a web server with Persistent and Servant
    2. Deploying a Haskell project using Heroku and Circle CI
    3. Making a web frontend with Elm, and connecting it to the Haskell backend
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    As a special bonus, for this week only, both of our courses are on sale, $100 off their normal prices! So if you're not ready for Practical Haskell, you can take a look at Haskell From Scratch. With that said, if you buy either course now, you'll have access to all the materials indefinitely! Prices will go back to normal after this Sunday, so head to the course pages now!

    Next week, we'll start getting back into the swing of things by reviewing some of our Rust basics!

    by James Bowen at July 06, 2024 02:30 PM

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    This is part 3 in a series. See the previous part about internal languages for indexed monoidal categories upon which this part heavily depends.

    In category theory, the hom-sets between two objects can often be equipped with some extra structure which is respected by identities and composition. For example, the set of group homomorphisms between two abelian groups is itself an abelian group by defining the operations pointwise. Similarly, the set of monotonic functions between two partially ordered sets (posets) is a poset again by defining the ordering pointwise. Linear functions between vector spaces form a vector space. The set of functors between small categories is a small category. Of course, the structure on the hom-sets can be different than the objects. Trivially, with the earlier examples a vector space is an abelian group, so we could say that linear functions form an abelian group instead of a vector space. Likewise groups are monoids. Less trivially, the set of relations between two sets is a partially ordered set via inclusion. There are many cases where instead of hom-sets we have hom-objects that aren’t naturally thought of as sets. For example, we can have hom-objects be non-negative (extended) real numbers from which the category laws become the laws of a generalized metric space. We can identify posets with categories who hom-objects are elements of a two element set or, even better, a two element poset with one element less than or equal to the other.

    This general process is called enriching a category in some other category which is almost always called |\newcommand{\V}{\mathcal V}\V| in the generic case. We then talk about having |\V|-categories and |\V|-functors, etc. In a specific case, it will be something like |\mathbf{Ab}|-categories for an |\mathbf{Ab}|-enriched category, where |\mathbf{Ab}| is the category of abelian groups. Unsurprisingly, not just any category will do for |\V|. However, it turns out very little structure is needed to define a notion of |\V|-category, |\V|-functor, |\V|-natural transformation, and |\V|-profunctor. The usual “baseline” is that |\V| is a 狸猫加速器安卓版下载在哪里. As mentioned in the previous post, paraphrasing Bénabou, notions of “families of objects/arrows” are ubiquitous and fundamental in category theory. It is useful for our purposes to make this structure explicit. For very little cost, this will also provide a vastly more general notion that will readily capture enriched categories, indexed categories, and categories that are simultaneously indexed and enriched, of which internal categories are an example. The tool for this is a (Grothendieck) fibration aka a fibered category or the mostly equivalent concept of an indexed category.1

    To that end, instead of just a monoidal category, we’ll be using indexed monoidal categories. Typically, to get an experience as much like ordinary category theory as possible, additional structure is assumed on |\V|. In particular, it is assumed to be an 坚果加速器下载官网 which means that it is an indexed symmetric monoidally closed category with indexed coproducts preserved by |\otimes| and indexed products and fiberwise finite limits and colimits (preserved by the indexed structure). This is quite a lot more structure which I’ll introduce in later parts. In this part, I’ll make no assumptions beyond having an indexed monoidal category.

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    The purpose of the machinery of the previous posts is to make this section seem boring and pedestrian. Other than being a little more explicit and formal, for most of the following concepts it will look like we’re restating the usual definitions of categories, functors, and natural transformations. The main exception is profunctors which will be presented in a quite different manner, though still in a manner that is easy to connect to the usual presentation. (We will see how to recover the usual presentation in later parts.)

    While I’ll start by being rather explicit about indexes and such, I will start to suppress that detail over time as most of it is inferrable. One big exception is that right from the start I’ll omit the explicit dependence of primitive terms on indexes. For example, while I’ll write |\mathsf F(\mathsf{id}) = \mathsf{id}| for the first functor law, what the syntax of the previous posts says I should be writing is |\mathsf F(s, s; \mathsf{id}(s)) = \mathsf{id}(s)|.

    To start, I want to introduce two different notions of |\V|-category, small |\V|-categories and large |\V|-categories, and talk about what this distinction actually means. I will proceed afterwards with the “large” notions, e.g. |\V|-functors between large |\V|-categories, as the small case will be an easy special case.

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    • an index type |\newcommand{\O}{\mathsf O}\O|,
    • a linear type |\newcommand{\A}{\mathsf A}s, t : \O \vdash \A(t, s)|,
    • a linear term |s : \O; \vdash \mathsf{id} : \A(s, s)|, and
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    satisfying
    $$\begin{gather} s, t : \O; f : \A(t, s) \vdash \mathsf{id} \circ f = f = f \circ \mathsf{id} : \A(t, s)\qquad \text{and} \\ \\ s, u, v, t : \O; h : \A(t, v), g : \A(v, u), f : \A(u, s) \vdash h \circ (g \circ f) = (h \circ g) \circ f : \A(t, s) \end{gather}$$

    In the notation of the previous posts, I’m saying |\O : \mathsf{IxType}|, |\A : (\O, \O) \to \mathsf{Type}|, |\mathsf{id} : (s : \O;) \to \A(s, s)|, and |\circ : (s, u, t : \O; \A(t, u), \A(u, s)) \to \A(t, s)| are primitives added to the signature of the theory. I’ll continue to use the earlier, more pointwise presentation above to describe the signature.

    A small |\V|-category for an |\mathbf S|-indexed monoidal category |\V| is then an interpretation of this theory. That is, an object |O| of |\mathbf S| as the interpretation of |\O|, and an object |A| of |\V^{O\times O}| as the interpretation of |\A|. The interpretation of |\mathsf{id}| is an arrow |I_O \to \Delta_O^* A| of |\V^O|, where |\Delta_O : O \to O\times O| is the diagonal arrow |\langle id, id\rangle| in |\mathbf S|. The interpretation of |\circ| is an arrow |\pi_{23}^* A \otimes \pi_{12}^* A \to \pi_{13}^* A| of |\V^{O\times O \times O}| where |\pi_{ij} : X_1 \times X_2 \times X_3 \to X_i \times X_j| are the appropriate projections.

    Since we can prove in the internal language that the choice of |()| for |\O|, |s, t : () \vdash I| for |\A|, |s, t : (); x : I \vdash x : I| for |\mathsf{id}|, and |s, u, t : (); f : I, g: I \vdash \mathsf{match}\ f\ \mathsf{as}\ *\ \mathsf{in}\ g : I| for |\circ| satisfies the laws of the theory of a small |\V|-category, we know we have a |\V|-category which I’ll call |\mathbb I| for any |\V|2.

    For |\V = \mathcal Fam(\mathbf V)|, |O| is a set of objects. |A| is an |(O\times O)|-indexed family of objects of |\mathbf V| which we can write |\{A(t,s)\}_{s,t\in O}|. The interpretation of |\mathsf{id}| is an |O|-indexed family of arrows of |\mathbf V|, |\{ id_s : I_s \to A(s, s) \}_{s\in O}|. Finally, the interpretation of |\circ| is a family of arrows of |\mathbf V|, |\{ \circ_{s,u,t} : A(t, u)\otimes A(u, s) \to A(t, s) \}_{s,u,t \in O}|. This is exactly the data of a (small) |\mathbf V|-enriched category. One example is when |\mathbf V = \mathbf{Cat}| which produces (strict) |2|-categories.

    For |\V = \mathcal Self(\mathbf S)|, |O| is an object of |\mathbf S|. |A| is an arrow of |\mathbf S| into |O\times O|, i.e. an object of |\mathbf S/O\times O|. I’ll write the object part of this as |A| as well, i.e. |A : A \to O\times O|. The idea is that the two projections are the target and source of the arrow. The interpretation of |\mathsf{id}| is an arrow |ids : O \to A| such that |A \circ ids = \Delta_O|, i.e. the arrow produced by |ids| should have the same target and source. Finally, the interpretation of |\circ| is an arrow |c| from the pullback of |\pi_2 \circ A| and |\pi_1 \circ A| to |A|. The source of this arrow is the object of composable pairs of arrows. We further require |c| to produce an arrow with the appropriate target and source of the composable pair. This is exactly the data for a category internal to |\mathbf S|. An interesting case for contrast with the previous paragraph is that a category internal to |\mathbf{Cat}| is a double category.

    For |\V = \mathcal Const(\mathbf V)|, the above data is exactly the data of a monoid object in |\mathbf V|. This is a formal illustration that a (|\mathbf V|-enriched) category is just an “indexed monoid”. Indeed, |\mathcal Const(\mathbf V)|-functors will be monoid homomorphisms and |\mathcal Const(\mathbf V)|-profunctors will be double-sided monoid actions. In particular, when |\mathbf V = \mathbf{Ab}|, we get rings, ring homomorphisms, and bimodules of rings. The intuitions here are the guiding ones for the construction we’re realizing.

    One aspect of working in a not-necessarily-symmetric (indexed) monoidal category is the choice of the standard order of composition or diagrammatic order is not so trivial since it is not possible to even state what it means for them to be the equivalent. To be clear, this definition isn’t really taking a stance on the issue. We can interpret |\A(t, s)| as the type of arrows |s \to t| and then |\circ| will be the standard order of composition, or as the type of arrows |t \to s| and then |\circ| will be the diagrammatic order. In fact, there’s nothing in this definition that stops us from having |\A(t, s)| being the type of arrows |t \to s| while still having |\circ| be standard order composition as usual. The issue comes up only once we consider |\V|-profunctors as we will see.

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    A large |\V|-category is a model of a theory of the following form. There is

    • a collection of index types |\O_x|,
    • for each pair of index types |\O_x| and |\O_y|, a linear type |s : \O_x, t : \O_y \vdash \A_{yx}(t, s)|,
    • for each index type |\O_x|, a linear term |s : \O_x; \vdash \mathsf{id}_x : \A_{xx}(s, s)|, and
    • for each triple of index types, |\O_x|, |\O_y|, and |\O_z|, a linear term |s: \O_x, u : \O_y, t : \O_z; g : \A_{zy}(t, u), f : \A_{yx}(u, s) \vdash g \circ_{xyz} f : \A_{zx}(t, s)|

    satisfying the same laws as small |\V|-categories, just with some extra subscripts. Clearly, a small |\V|-category is just a large |\V|-category where the collection of index types consists of just a single index type.

    Small versus Large

    The typical way of describing the difference between small and large (|\V|-)categories would be to say something like: “By having a collection of index types in a large |\V|-category, we can have a proper class of them. In a small |\V|-category, the index type of objects is interpreted as an object in a category, and a proper class can’t be an object of a category3.” However, for us, there’s a more directly relevant distinction. Namely, while we had a single theory of small |\V|-categories, there is no single theory of large |\V|-categories. Different large |\V|-categories correspond to models of (potentially) different theories. In other words, the notion of a small |\V|-category is able to be captured by our notion of theory but not the concept of a large |\V|-category. This extends to |\V|-functors, |\V|-natural transformations, and |\V|-profunctors. In the small case, we can define a single theory which captures each of these concepts, but that isn’t possible in the large case. In general, notions of “large” and “small” are about what we can internalize within the relevant object language, usually a set theory. Arguably, the only reason we speak of “size” and of proper classes being “large” is that the Axiom of Specification outright states that any subclass of a set is a set, so proper classes in ZFC can’t be subsets of any set. As I’ve mentioned elsewhere, you can definitely have set theories with proper classes that are contained in even finite sets, so the issue isn’t one of “bigness”.

    The above discussion also explains the hand-wavy word “collection”. The collection is a collection in the meta-language in which we’re discussing/formalizing the notion of theory. When working within the theory of a particular large |\V|-category, all the various types and terms are just available ab initio and are independent. There is no notion of “collection of types” within the theory and nothing indicating that some types are part of a “collection” with others.

    Another perspective on this distinction between large and small |\V|-categories is that small |\V|-categories have a family of arrows, identities, and compositions with respect to the notion of “family” represented by our internal language. If we hadn’t wanted to bother with formulating the internal language of an indexed monoidal category, we could have still defined the notion of |\V|-category with respect to the internal language of a (non-indexed) monoidal category. It’s just that all such |\V|-categories (except for monoid objects) would have to be large |\V|-categories. That is, the indexing and notion of “family” would be at a meta-level. Since most of the |\V|-categories of interest will be large (though, generally a special case called a |\V|-fibration which reins in the size a bit), it may seem that there was no real benefit to the indexing stuff. Where it comes in, or rather where small |\V|-categories come in, is that our notion of (co)complete means “has all (co)limits of small diagrams” and small diagrams are |\V|-functors from small |\V|-categories.4 There are several other places, e.g. the notion of presheaf, where we implicitly depend on what we mean by “small |\V|-category”. So while we won’t usually be focused on small |\V|-categories, which |\V|-categories are small impacts the structure of the whole theory.

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    The formulation of |\V|-functors is straightforward. As mentioned before, I’ll only present the “large” version.

    Formally, we can’t formulate a theory of just a |\V|-functor, but rather we need to formulate a theory of “a pair of |\V|-categories and a |\V|-functor between them”.

    A Leocat狸猫浏览器_Leocat狸猫浏览器官方版下载 - 浏览器 ...:2021-5-26 · Leocat狸猫抢票浏览器(Leocat Web Browser)采用较新版全球较快的WebKit内核,上网速度加快5倍,智能防卡死。闪电般打开网页和应用,性能超越其他同类浏览器! is a model of a theory consisting of a theory of a large |\V|-category, of which |\mathcal C| is a model, and a theory of a large |\V|-category which I’ll write with primes, of which |\mathcal D| is a model, and model of the following additional data:

    • for each index type |\O_x|, an index type |\O’_{F_x}| and an index term, |s : \O_x \vdash \mathsf F_x(s) : \O’_{F_x}|, and
    • for each pair of index types, |\O_x| and |\O_y|, a linear term |s : \O_x, t : \O_y; f : \A_{yx}(t, s) \vdash \mathsf F_{yx}(f) : \A’_{F_yF_x}(\mathsf F_y(t), \mathsf F_x(s))|

    satisfying
    $$\begin{gather} s : \O_x; \vdash \mathsf F_{xx}(\mathsf{id}_x) = \mathsf{id}'_{F_x}: \A'_{F_xF_x}(F_x(s), F_x(s))\qquad\text{and} \\ s : \O_x, u : \O_y, t : \O_z; g : \A_{zy}(t, u), f : \A_{yx}(u, s) \vdash \mathsf F_{zx}(g \circ_{xyz} f) = F_{zy}(g) \circ'_{F_xF_yF_z} F_{yx}(f) : \A'_{F_zF_x}(F_z(t), F_x(s)) \end{gather}$$

    The assignment of |\O’_{F_x}| for |\O_x| is, again, purely metatheoretical. From within the theory, all we know is that we happen to have some index types named |\O_x| and |\O’_{F_x}| and some data relating them. The fact that there is some kind of mapping of one to the other is not part of the data.

    Next, I’ll define |\V|-natural transformations . As before, what we’re really doing is defining |\V|-natural transformations as a model of a theory of “a pair of (large) |\V|-categories with a pair of |\V|-functors between them and a |\V|-natural transformation between those”. As before, I’ll use primes to indicate the types and terms of the second of each pair of subtheories. Unlike before, I’ll only mention what is added which is:

    • for each index type |\O_x|, a linear term |s : \O_x; \vdash \tau_x : \A’_{F’_xF_x}(\mathsf F’_x(s), \mathsf F_x(s))|

    satisfying
    $$\begin{gather} s : \O_x, t : \O_y; f : \A_{yx}(t, s) \vdash \mathsf F'_{yx}(f) \circ'_{F_xF'_xF'_y} \tau_x = \tau_y \circ'_{F_xF_yF'_y} \mathsf F_{yx}(f) : \A'_{F'_yF_x}(\mathsf F'_y(t), \mathsf F_x(s)) \end{gather}$$

    In practice, I’ll suppress the subscripts on all but index types as the rest are inferrable. This makes the above equation the much more readable
    $$\begin{gather} s : \O_x, t : \O_y; f : \A(t, s) \vdash \mathsf F'(f) \circ' \tau = \tau \circ' \mathsf F(f) : \A'(\mathsf F'(t), \mathsf F(s)) \end{gather}$$

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    Here’s where we need to depart from the usual story. In the usual story, a |\mathbf V|-enriched profunctor |\newcommand{\proarrow}{\mathrel{-\!\!\!\mapsto}} P : \mathcal C \proarrow \mathcal D| is a |\mathbf V|-enriched functor |P : \mathcal C\otimes\mathcal D^{op}\to\mathbf V| (or, often, the opposite convention is used |P : \mathcal C^{op}\otimes\mathcal D \to \mathbf V|). There are many problems with this definition in our context.

    1. Without symmetry, we have no definition of opposite category.
    2. Without symmetry, the tensor product of |\mathbf V|-enriched categories doesn’t make sense.
    3. |\mathbf V| is not itself a |\mathbf V|-enriched category, so it doesn’t make sense to talk about |\mathbf V|-enriched functors into it.
    4. Even if it was, we’d need some way of converting between arrows of |\mathbf V| as a category and arrows of |\mathbf V| as a |\mathbf V|-enriched category.
    5. The equation |P(g \circ f, h \circ k) = P(g, k) \circ P(f, h)| requires symmetry. (This is arguably 2 again.)

    All of these problems are solved when |\mathbf V| is a symmetric monoidally closed category.

    Alternatively, we can reformulate the notion of a |\V|-profunctor so that it works in our context and is equivalent to the usual one when it makes sense.5 To this end, at a low level a |\mathbf V|-enriched profunctor is a family of arrows
    $$\begin{gather}P : \mathcal C(t, s)\otimes\mathcal D(s', t') \to [P(s, s'), P(t, t')]\end{gather}$$
    which satisfies
    $$\begin{gather}P(g \circ f, h \circ k)(p) = P(g, k)(P(f, h)(p))\end{gather}$$
    in the internal language of a symmetric monoidally closed category among other laws. We can uncurry |P| to eliminate the need for closure, getting
    狸猫浏览器绿色版_狸猫浏览器官方下载_狸猫浏览器v3.0.0.0 ...:2021-2-6 · 狸猫浏览器(Leocat Web Browser)采用最新版全球最快的WebKit内核,上网速度加快5倍,智能防卡死。 闪电般打开网页和应用,性能全面超越其他同类浏览器!狸猫浏览器具有自定义主页、多标签浏览、标签自由拖拽等增强浏览舒适度的功能设置,能让您在浏览网页的过程中更感流畅。
    satisfying
    $$\begin{gather}P(g \circ f, h \circ k, p) = P(g, k, P(f, h, p))\end{gather}$$
    We see that we’re always going to need to permute |f| and |h| past |k| unless we move the third argument to the second producing the nice
    $$\begin{gather}P : \mathcal C(t, s)\otimes P(s, s') \otimes \mathcal D(s', t') \to P(t, t')\end{gather}$$
    and the law
    $$\begin{gather}P(g \circ f, p, h \circ k) = P(g, P(f, p, h), k)\end{gather}$$
    which no longer requires symmetry. This is also where the order of the arguments of |\circ| drives the order of the arguments of |\V|-profunctors.

    A |\V|-profunctor, |P : \mathcal C \proarrow \mathcal D|, is a model of the theory (containing subtheories for |\mathcal C| and |\mathcal D| etc. as in the |\V|-functor case) having:

    • for each pair of index types |\O_x| and |\O’_{x’}|, a linear type |s : \O_x, t : \O’_{x’} \vdash \mathsf P_{x’x}(t, s)|, and
    • for each quadruple of index types |\O_x|, |\O_y|, |\O’_{x’}|, and |\O’_{y’}|, a linear term |s : \O_x, s’ : \O’_{x’}, t : \O_y, t’ : \O’_{y’}; f : \A_{yx}(t, s), p : \mathsf P_{xx’}(s, s’), h : \A’_{x’y’}(s’, t’) \vdash \mathsf P_{yxx’y’}(f, p, h) : \mathsf P_{yy’}(t, t’)|

    satisfying
    $$\begin{align} & s : \O_x, s' : \O'_{x'}; p : \mathsf P(s, s') \vdash \mathsf P(\mathsf{id}, p, \mathsf{id}') = p : \mathsf P(s, s') \\ \\ & s : \O_x, s' : \O'_{x'}, u : \O_y, u' : \O'_{y'}, t : \O_z, t' : \O'_{z'}; \\ & g : \A(t, u), f : \A(u, s), p : \mathsf P(s, s'), h : \A'(s', u'), k : \A'(u', t') \\ \vdash\ & \mathsf P(g \circ f, p, h \circ' k) = \mathsf P(g, \mathsf P(f, p, h), k) : \mathsf P(t, t') \end{align}$$

    This can also be equivalently presented as a pair of a left and a right action satisfying bimodule laws. We’ll make the following definitions |\mathsf P_l(f, p) = \mathsf P(f, p, \mathsf {id})| and |\mathsf P_r(p, h) = \mathsf P(\mathsf{id}, p ,h)|.

    A 蚂蚁vp(永久免费) on |\mathcal C| is a |\V|-profunctor |P : \mathbb I \proarrow \mathcal C|. Similarly, a 黑洞加速器破解版app on |\mathcal C| is a |\V|-profunctor |P : \mathcal C \proarrow \mathbb I|.

    Of course, we have the fact that the term
    $$\begin{gather} s : \O_x, t : \O_y, s' : \O_z, t' : \O_w; h : \A(t, s), g : \A(s, s'), f : \A(s', t') \vdash h \circ g \circ f : \A(t, t') \end{gather}$$
    witnesses the interpretation of |\A| as a |\V|-profunctor |\mathcal C \proarrow \mathcal C| for any |\V|-category, |\mathcal C|, which we’ll call the hom |\V|-profunctor. More generally, given a |\V|-profunctor |P : \mathcal C \proarrow \mathcal D|, and |\V|-functors |F : \mathcal C’ \to \mathcal C| and |F’ : \mathcal D’ \to \mathcal D|, we have the |\V|-profunctor |P(F, F’) : \mathcal C’ \proarrow \mathcal D’| defined as
    $$\begin{gather} s : \O_x, s' : \O'_{x'}, t : \O_y, t' : \O'_{y'}; f : \A(t, s), p : \mathsf P(\mathsf F(s), \mathsf F'(s')), f' : \A'(s', t') \vdash \mathsf P(\mathsf F(f), p, \mathsf F'(f')) : \mathsf P(\mathsf F(t), \mathsf F'(t')) \end{gather}$$
    In particular, we have the representable |\V|-profunctors when |P| is the hom |\V|-profunctor and either |F| or |F’| is the identity |\V|-functor, e.g. |\mathcal C(Id, F)| or |\mathcal C(F, Id)|.

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    There’s a natural notion of morphism of |\V|-profunctors which we could derive either via passing the notion of natural transformation of the bifunctorial view through the same reformulations as above, or by generalizing the notion of a bimodule homomorphism. This would produce a notion like: a |\V|-natural transformation from |\alpha : P \to Q| is a |\alpha : P(t, s) \to Q(t, s)| satisfying |\alpha(P(f, p, h)) = Q(f, \alpha(p), h)|. While there’s nothing wrong with this definition, it doesn’t quite meet our needs. One way to see this is that it would be nice to have a bicategory whose |0|-cells were |\V|-categories, |1|-cells |\V|-profunctors, and |2|-cells |\V|-natural transformations as above. The problem there isn’t the |\V|-natural transformations but the |1|-cells. In particular, we don’t have composition of |\V|-profunctors. In the analogy with bimodules, we don’t have tensor products so we can’t reduce multilinear maps to linear maps; therefore, linear maps don’t suffice, and we really want a notion of multilinear maps.

    So, instead of a bicategory what we’ll have is a virtual bicategory (or, more generally, a virtual double category). A virtual bicategory is to a bicategory what a multicategory is to a monoidal category, i.e. multicategories are “virtual monoidal categories”. The only difference between a virtual bicategory and a multicategory is that instead of our multimorphisms having arbitrary lists of objects as their sources, our “objects” (|1|-cells) themselves have sources and targets (|0|-cells) and our multimorphisms (|2|-cells) have composable sequences of |1|-cells as their sources.

    A |\V|-multimorphism from a composable sequence of |\V|-profunctors |P_1, \dots, P_n| to the |\V|-profunctor |Q| is a model of the theory consisting of the various necessary subtheories and:

    • a linear term, |s_0 : \O_{x_0}^0, \dots, s_n : \O_{x_n}^n; p_1 : \mathsf P_{x_0x_1}^1(s_0, s_1), \dots, p_n : \mathsf P_{x_{n-1}x_n}^n(s_{n-1}, s_n) \vdash \tau_{x_0\cdots x_n}(p_1, \dots, p_n) : \mathsf Q_{x_0x_n}(s_0, s_n)|

    satisfying
    $$\begin{align} & t, s_0 : \O^0, \dots, s_n : \O^n; f : \A^0(t, s_0), p_1 : \mathsf P^1(s_0, s_1), \dots, p_n : \mathsf P^n(s_{n-1}, s_n) \\ \vdash\ & \tau(\mathsf P_l^0(f, p_1), \dots, p_n) = \mathsf Q_l(f, \tau(p_1, \dots, p_n)) : \mathsf Q(t, s_n) \\ \\ & s_0 : \O^0, \dots, s_n, s : \O^n; p_1 : \mathsf P^1(s_0, s_1), \dots, p_n : \mathsf P^n(s_{n-1}, s_n), f : \A^n(s_n, s) \\ \vdash\ & \tau(p_1, \dots, \mathsf P_r^n(p_n, f)) = \mathsf Q_r(\tau(p_1, \dots, p_n), f) : \mathsf Q(s_0, s) \\ \\ & s_0 : \O^0, \dots, s_n : \O^n; \\ & p_1 : \mathsf P^1(s_0, s_1), \dots, p_i : \mathsf P^i(s_{i-1}, s_i), f : \A^i(s_i, s_{i+1}), p_{i+1} : \mathsf P^{i+1}(s_i, s_{i+1}), \dots, p_n : \mathsf P^n(s_{n-1}, s_n) \\ \vdash\ & \tau(p_1, \dots, \mathsf P_r^i(p_i, f), p_{i+1}, \dots, p_n) = \tau(p_1, \dots, p_i, \mathsf P_l^{i+1}(f, p_{i+1}) \dots, p_n) : \mathsf Q(s_0, s_n) \end{align}$$
    except for the |n=0| case in which case the only law is
    $$\begin{gather} t, s : \O^0; f : \A^0(t, s) \vdash \mathsf Q_l(f, \tau()) = \mathsf Q_r(\tau(), f) : \mathsf Q(t, s) \end{gather}$$

    The laws involving the action of |\mathsf Q| are called external equivariance, while the remaining law is called internal equivariance. We’ll write |\V\mathbf{Prof}(P_1, \dots, P_n; Q)| for the set of |\V|-multimorphisms from the composable sequence of |\V|-profunctors |P_1, \dots, P_n| to the |\V|-profunctor |Q|.

    As with multilinear maps, we can characterize composition via a universal property. Write |Q_1\diamond\cdots\diamond Q_n| for the composite |\V|-profunctor (when it exists) of the composable sequence |Q_1, \dots, Q_n|. We then have for any pair of composable sequences |R_1, \dots, R_m| and |S_1, \dots, S_k| which compose with |Q_1, \dots, Q_n|,
    $$\begin{gather} \V\mathbf{Prof}(R_1,\dots, R_m, Q_1 \diamond \cdots \diamond Q_n, S_1, \dots, S_k; -) \cong \V\mathbf{Prof}(R_1,\dots, R_m, Q_1, \dots, Q_n, S_1, \dots, S_k; -) \end{gather}$$
    where the forward direction is induced by precomposition with a |\V|-multimorphism |Q_1, \dots, Q_n \to Q_1 \diamond \cdots \diamond Q_n|. A |\V|-multimorphism with this property is called opcartesian. The |n=0| case is particularly important and, for a |\V|-category |\mathcal C|, produces the unit |\V|-profunctor, |U_\mathcal C : \mathcal C \proarrow \mathcal C| as the composite of the empty sequence. When we have all composites, |\V\mathbf{Prof}| becomes an actual bicategory rather than a virtual bicategory. |\V\mathbf{Prof}| always has all units, namely the hom |\V|-profunctors. Much like we can define the tensor product of modules by quotienting the tensor product of their underlying abelian groups by internal equivariance, we will find that we can make composites when we have enough (well-behaved) colimits6.

    Related to composites, we can talk about left/right closure of |\V\mathbf{Prof}|. In this case we have the natural isomorphisms:
    $$\begin{gather} \V\mathbf{Prof}(Q_1,\dots, Q_n, R; S) \cong \V\mathbf{Prof}(Q_1, \dots, Q_n; R \triangleright S) \\ \V\mathbf{Prof}(R, Q_1, \dots, Q_n; S) \cong \V\mathbf{Prof}(Q_1, \dots, Q_n;S \triangleleft R) \end{gather}$$
    Like composites, this merely characterizes these constructs; they need not exist in general. These will be important when we talk about Yoneda and (co)limits in |\V|-categories.

    A |\V|-natural transformation |\alpha : F \to G : \mathcal C \to \mathcal D| is the same as |\alpha\in\V\mathbf{Prof}(;\mathcal D(G, F))|.

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    Just as an example, let’s prove a basic fact about categories for arbitrary |\V|-categories. This will use an informal style.

    The fact will be that full and faithful functors reflect isomorphisms. Let’s go through the typical proof for the ordinary category case.

    Suppose we have an natural transformation |\varphi : \mathcal D(FA, FB) \to \mathcal C(A, B)| natural in |A| and |B| such that |\varphi| is an inverse to |F|, i.e. the action of the functor |F| on arrows. If |Ff \circ Fg = id| and |Fg \circ Ff = id|, then by the naturality of |\varphi|, |\varphi(id) = \varphi(Ff \circ id \circ Fg) = f \circ \varphi(id) \circ g| and similarly with |f| and |g| switched. We now just need to show that |\varphi(id) = id| but |id = F(id)|, so |\varphi(id) = \varphi(F(id)) = id|. |\square|

    Now in the internal language. We’ll start with the theory of a |\V|-functor, so we have |\O|, |\O’|, |\A|, |\A’|, and |\mathsf F|. While the previous paragraph talks about a natural transformation, we can readily see that it’s really a multimorphism. In our case, it is a |\V|-multimorphism |\varphi| from |\A’(\mathsf F, \mathsf F)| to |\A|. Before we do that though, we need to show that |\mathsf F| itself is a |\V|-multimorphism. This corresponds to the naturality of the action on arrows of |F| which we took for granted in the previous paragraph. This is quickly verified: the external equivariance equations are just the functor law for composites. The additional data we have is two linear terms |\mathsf f| and |\mathsf g| such that |\mathsf F(\mathsf f) \circ \mathsf F(\mathsf g) = \mathsf{id}| and |\mathsf F(\mathsf g) \circ \mathsf F(\mathsf f) = \mathsf{id}|. Also, |\varphi(\mathsf F(h)) = h|. The result follows through almost identically to the previous paragraph. |\varphi(\mathsf{id}) = \varphi(\mathsf F(\mathsf f) \circ \mathsf F(\mathsf g)) = \varphi(\mathsf F(\mathsf f) \circ \mathsf{id} \circ \mathsf F(\mathsf g))|, we apply external equivariance twice to get |\mathsf f \circ \varphi(\mathsf{id}) \circ \mathsf g|. The functor law for |\mathsf{id}| gives |\varphi(\mathsf{id}) = \varphi(\mathsf F(\mathsf{id})) = \mathsf{id}|. A quick glance verifies that all these equations use their free variables linearly as required. |\square|

    As a warning, in the above |\mathsf f| and |\mathsf g| are not free variables but constants, i.e. primitive linear terms. Thus there is no issue with an equation like |\mathsf F(\mathsf f) \circ \mathsf F(\mathsf g) = \mathsf{id}| as both sides have no free variables.

    This is a very basic result but, again, the payoff here is how boring and similar to the usual case this is. For contrast, the definition of an internal profunctor is given here. This definition is easier to connect to our notion of |\V|-presheaf, specifically a |\mathcal Self(\mathbf S)|-presheaf, than it is to the usual |\mathbf{Set}|-valued functor definition. While not hard, it would take me a bit of time to even formulate the above proposition, and a proof in terms of the explicit definitions would be hard to recognize as just the ordinary proof.

    For fun, let’s figure out what the |\mathcal Const(\mathbf{Ab})| case of this result says explicitly. A |\mathcal Const(\mathbf{Ab})|-category is a ring, a |\mathcal Const(\mathbf{Ab})|-functor is a ring homomorphism, and a |\mathcal Const(\mathbf{Ab})|-profunctor is a bimodule. Let |R| and |S| be rings and |f : R \to S| be a ring homomorphism. An isomorphism in |R| viewed as a |\mathcal Const(\mathbf{Ab})|-category is just an invertible element. Every ring, |R|, is an |R|-|R|-bimodule. Given any |S|-|S|-bimodule |P|, we have an |R|-|R|-bimodule |f^*(P)| via restriction of scalars, i.e. |f^*(P)| has the same elements as |P| and for |p \in f^*(P)|, |rpr’ = f(r)pf(r’)|. In particular, |f| gives rise to a bimodule homomorphism, i.e. a linear function, |f : R \to f^*(S)| which corresponds to its action on arrows from the perspective of |f| as a |\mathcal Const(\mathbf{Ab})|-functor. If this linear transformation has an inverse, then the above result states that when |f(r)| is invertible so is |r|. So to restate this all in purely ring theoretic terms, given a ring homomorphism |f : R \to S| and an abelian group homomorphism |\varphi : S \to R| satisfying |\varphi(f(rst)) = r\varphi(f(s))t| and |\varphi(f(r)) = r|, then if |f(r)| is invertible so is |r|.


    1. Indexed categories are equivalent to cloven fibrations and, if you have the Axiom of Choice, all fibrations can be cloven. Indexed categories can be viewed as presentations of fibrations.狸猫加速速器

    2. This suggests that we could define a small |\V|-category |\mathcal C \otimes \mathcal D| where |\mathcal C| and |\mathcal D| are small |\V|-categories. Start formulating a definition of such a |\V|-category. You will get stuck. Where? Why? This implies that the (ordinary, or better, 2-)category of small |\V|-categories does not have a monoidal product with |\mathbb I| as unit in general.↩︎

    3. With a good understanding of what a class is, it’s clear that it doesn’t even make sense to have a proper class be an object. In frameworks with an explicit notion of "class", this is often manifested by saying that a class that is an element of another class is a set (and thus not a proper class).狸猫加速器安卓版下载在哪里

    4. This suggests that it might be interesting to consider categories that are (co)complete with respect to this monoid notion of “small”. I don’t think I’ve ever seen a study of such categories. (Co)limits of monoids are not trivial.↩︎

    5. This is one of the main things I like about working in weak foundations. It forces you to come up with better definitions that make it clear what is and is not important and eliminates coincidences. Of course, it also produces definitions and theorems that are inherently more general too.↩︎

    6. This connection isn’t much of a surprise as the tensor product of modules is exactly the (small) |\mathcal Const(\mathbf{Ab})| case of this.↩︎

    July 06, 2024 05:03 AM

    Internal Language of Indexed Monoidal Categories

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    This is part 2 in a series. See the previous part about internal languages for (non-indexed) monoidal categories. The main application I have in mind – enriching in indexed monoidal categories – is covered in the next post.

    As Jean Bénabou pointed out in Fibered Categories and the Foundations of Naive Category Theory (PDF) notions of “families of objects/arrows” are ubiquitous and fundamental in category theory. One of the more noticeable places early on is in the definition of a natural transformation as a family of arrows. However, even in the definition of category, identities and compositions are families of functions, or, in the enriched case, arrows of |\mathbf V|. From a foundational perspective, one place where this gets really in-your-face is when trying to formalize the notion of (co)completeness. It is straightforward to make a first-order theory of a finitely complete category, e.g. 狸猫加速器安卓版下载. For arbitrary products and thus limits, we need to talk about families of objects. To formalize the usual meaning of this in a first-order theory would require attaching an entire first-order theory of sets, e.g. ZFC, to our notion of complete category. If your goals are of a foundational nature like Bénabou’s were, then this is unsatisfactory. Instead, we can abstract out what we need of the notion of “family”. The result turns out to be equivalent to the notion of a fibration.

    My motivations here are not foundational but leaving the notion of “family” entirely meta-theoretical means not being able to talk about it except in the semantics. Bénabou’s comment suggests that at the semantic level we want not just a monoidal category, but a fibration of monoidal categories1. At the syntactic level, it suggests that there should be a built-in notion of “family” in our language. We accomplish both of these goals by formulating the internal language of an 极光加速器官方网站.

    As a benefit, we can generalize to other notions of “family” than set-indexed families. We’ll clearly be able to formulate the notion of an enriched category. It’s also clear that we’ll be able to formulate the notion of an indexed category. Of course, we’ll also be able to formulate the notion of a category that is both enriched and indexed which includes the important special case of an internal category. We can also consider cases with trivial indexing which, in the unenriched case, will give us monoids, and in the |\mathbf{Ab}|-enriched case will give us rings.

    Indexed Monoidal Categories

    Following Shulman’s Enriched indexed categories, let |\mathbf{S}| be a category with a cartesian monoidal structure, i.e. finite products. Then an |\mathbf{S}|-indexed monoidal category is simply a pseudofunctor |\newcommand{\V}{\mathcal V}\V : \mathbf{S}^{op} \to \mathbf{MonCat}|. A 蚂蚁ant加速器安卓下载 is like a functor except that the functor laws only hold up to isomorphism, e.g. |\V(id)\cong id|. |\mathbf{MonCat}| is the |2|-category of monoidal categories, strong monoidal functors2, and monoidal natural transformations. We’ll write |\V(X)| as |\V^X| and |\V(f)| as |f^*|. We’ll never have multiple relevant indexed monoidal categories so this notation will never be ambiguous. We’ll call the categories |\V^X| fiber categories and the functors |f^*| reindexing functors. The cartesian monoidal structure on |\mathbf S| becomes relevant when we want to equip the total category, |\int\V|, (computed via the Grothendieck construction in the usual way) with a monoidal structure. In particular, the tensor product of |A \in \V^X| and |B \in \V^Y| is an object |A\otimes B \in \V^{X\times Y}| calculated as |\pi_1^*(A) \otimes_{X\times Y} \pi_2^*(B)| where |\otimes_{X\times Y}| is the monoidal tensor in |\V^{X\times Y}|. The unit, |I|, is the unit |I_1 \in \V^1|.

    The two main examples are: |\mathcal Fam(\mathbf V)| where |\mathbf V| is a (non-indexed) monoidal category and |\mathcal Self(\mathbf S)| where |\mathbf S| is a category with finite limits. |\mathcal Fam(\mathbf V)| is a |\mathbf{Set}|-indexed monoidal category with |\mathcal Fam(\mathbf V)^X| defined as the set of |X|-indexed families of objects of |\mathbf V|, families of arrows between them, and an index-wise monoidal product. We can identify |\mathcal Fam(\mathbf V)^X| with the functor category |[DX, \mathbf V]| where |D : \mathbf{Set} \to \mathbf{cat}| takes a set |X| to a small discrete category. Enriching in indexed monoidal category |\mathcal Fam(\mathbf V)| will be equivalent to enriching in the non-indexed monoidal category |\mathbf V|, i.e. the usual notion of enrichment in a monoidal category. |\mathcal Self(\mathbf S)| is an |\mathbf S|-indexed monoidal category and |\mathcal Self(\mathbf S)^X| is the slice category |\mathbf S/X| with its cartesian monoidal structure. |f^*| is the pullback functor. |\mathcal Self(\mathbf S)|-enriched categories are categories internal to |\mathbf S|. A third example we’ll find interesting is |\mathcal Const(\mathbf V)| for a (non-indexed) monoidal category, |\mathbf V|, which is a |\mathbf 1|-indexed monoidal category, which corresponds to an object of |\mathbf{MonCat}|, namely |\mathbf V|.

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    This builds on the internal language of a monoidal category described in the previous post. We’ll again have linear types and linear terms which will be interpreted into objects and arrows in the fiber categories. To indicate the dependence on the indexing, we’ll use two contexts: |\Gamma| will be an index context containing index types and index variables, which will be interpreted into objects and arrows of |\mathbf S|, while |\Delta|, the 狸猫加速器安卓版下载在哪里, will contain linear types and linear variables as before except now linear types will be able to depend on index terms. So we’ll have judgements that look like:
    $$\begin{gather} \Gamma \vdash A \quad \text{and} \quad \Gamma; \Delta \vdash E : B \end{gather}$$
    The former indicates that |A| is a linear type indexed by the index variables of |\Gamma|. The latter states that |E| is a linear term of linear type |B| in the linear context |\Delta| indexed by the index variables of |\Gamma|. We’ll also have judgements for index types and index terms:
    $$\begin{gather} \vdash X : \square \quad \text{and} \quad \Gamma \vdash E : Y \end{gather}$$
    The former asserts that |X| is an index type. The latter asserts that |E| is an index term of index type |Y| in the index context |\Gamma|.

    Since each fiber category is monoidal, we’ll have all the rules from before just with an extra |\Gamma| hanging around. Since our indexing category, |\mathbf S|, is also monoidal, we’ll also have copies of these rules at the level of indexes. However, since |\mathbf S| is cartesian monoidal, we’ll also have the structural rules of weakening, exchange, and contraction for index terms and types. To emphasize the cartesian monoidal structure of indexes, I’ll use the more traditional Cartesian product and tuple notation: |\times| and |(E_1, \dots, E_n)|. This notation allows a bit more uniformity as the |n=0| case can be notated by |()|.

    The only really new rule is the rule that allows us to move linear types and terms from one index context to another, i.e. the rule that would correspond to applying a reindexing functor. I call this rule Reindex and, like Cut, it will be witnessed by substitution. Like Cut, it will also be a rule which we can eliminate. At the semantic level, this elimination corresponds to the fact that to understand the intepreration of any particular (linear) term, we can first reindex everything, i.e. all the intepretations of all subterms, into the same fiber category and then we can work entirely within that one fiber category. The Reindex rule is:
    $$\begin{gather} \dfrac{\Gamma \vdash E : X \quad \Gamma', x : X; a_1 : A_1, \dots, a_n : A_n \vdash E' : B}{\Gamma',\Gamma; a_1 : A_1[E/x], \dots, a_n : A_n[E/x] \vdash E'[E/x] : B[E/x]}\text{Reindex} \end{gather}$$

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    极光加速器官方网站 I provide a listing of rules and equations.

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    None of this section is necessary for anything else.

    This notion of (linear) types and terms being indexed by other types and terms is reminiscent of parametric types or dependent types. The machinery of indexed/fibered categories is also commonly used in the categorical semantics of parameterized and dependent types. However, there are important differences between those cases and our case.

    In the case of parameterized types, we have types and terms that depend on other types. In this case, we have kinds, which are “types of types”, which classify types which in turn classify terms. If we try to set up an analogy to our situation, index types would correspond to kinds and index terms would correspond to types. The most natural thing to continue would be to have linear terms correspond to terms, but we start to see the problem. Linear terms are classified by linear types, but linear types are not index terms. They don’t even induce index terms. In the categorical semantics of parameterized types, this identification of types with (certain) expressions classified by kinds is handled by the notion of a generic object. A generic object corresponds to the kind |\mathsf{Type}| (what Haskell calls *). The assumption of a generic object is a rather strong assumption and one that none of our example indexed monoidal categories support in general.

    A similar issue occurs when we try to make an analogy to dependent types. The defining feature of a dependent type system is that types can depend on terms. The problem with such a potential analogy is that linear types and terms do not induce index types and terms. A nice way to model the semantics of dependent types is the notion of a comprehension category. This, however, is additional structure beyond what we are given by an indexed monoidal category. However, comprehension categories will implicitly come up later when we talk about adding |\mathbf S|-indexed (co)products. These comprehension categories will share the same index category as our indexed monoidal categories, namely |\mathbf S|, but will have different total categories. Essentially, a comprehension category shows how objects (and arrows) of a total category can be represented in the index category. We can then talk about having (co)products in a different total category with same index category with respect to those objects picked out by the comprehension category. We get dependent types in the case where the total categories are the same. (More precisely, the fibrations are the same.) Sure enough, we will see that when |\mathcal Self(\mathbf S)| has |\mathbf S|-indexed products, then |\mathbf S| is, indeed, a model of a dependent type theory. In particular, it is locally cartesian closed.

    Rules for an Indexed Monoidal Category


    $$\begin{gather} \dfrac{\vdash X : \square}{x : X \vdash x : X}\text{IxAx} \qquad \dfrac{\Gamma\vdash E : X \quad \Gamma', x : X \vdash E': Y}{\Gamma',\Gamma \vdash E'[E/x] : Y}\text{IxCut} \\ \\ \dfrac{\vdash Y : \square \quad \Gamma\vdash E : X}{\Gamma, y : Y \vdash E : X}\text{Weakening},\ y\text{ fresh} \qquad \dfrac{\Gamma, x : X, y : Y, \Gamma' \vdash E : Z}{\Gamma, y : Y, x : X, \Gamma' \vdash E : Z}\text{Exchange} \qquad \dfrac{\Gamma, x : X, y : Y \vdash E : Z}{\Gamma, x : X \vdash E[x/y] : Z}\text{Contraction} \\ \\ \dfrac{\mathsf X : \mathsf{IxType}}{\vdash \mathsf X : \square}\text{PrimIxType} \qquad \dfrac{\vdash X_1 : \square \quad \cdots \quad \vdash X_n : \square}{\vdash (X_1, \dots, X_n) : \square}{\times_n}\text{F} \\ \\ \dfrac{\Gamma \vdash E_1 : X_1 \quad \cdots \quad \Gamma \vdash E_n : X_n \quad \mathsf F : (X_1, \dots, X_n) \to Y}{\Gamma \vdash \mathsf F(E_1, \dots, E_n) : Y}\text{PrimIxTerm} \\ \\ \dfrac{\Gamma_1 \vdash E_1 : X_1 \quad \cdots \quad \Gamma_n \vdash E_n : X_n}{\Gamma_1,\dots,\Gamma_n \vdash (E_1, \dots, E_n) : (X_1, \dots, X_n)}{\times_n}\text{I} \qquad \dfrac{\Gamma \vdash E : (X_1, \dots, X_n) \quad x_1 : X_1, \dots, x_n : X_n, \Gamma' \vdash E' : Y}{\Gamma, \Gamma' \vdash \mathsf{match}\ E\ \mathsf{as}\ (x_1, \dots, x_n)\ \mathsf{in}\ E' : Y}{\times_n}\text{E} \\ \\ \dfrac{\Gamma \vdash E_1 : X_1 \quad \cdots \quad \Gamma \vdash E_n : X_n \quad \mathsf A : (X_1, \dots, X_n) \to \mathsf{Type}}{\Gamma \vdash \mathsf A(E_1, \dots, E_n)}\text{PrimType} \\ \\ \dfrac{\Gamma \vdash A}{\Gamma; a : A \vdash a : A}\text{Ax} \qquad \dfrac{\Gamma; \Delta_1 \vdash E_1 : A_1 \quad \cdots \quad \Gamma; \Delta_n \vdash E_n : A_n \quad \Gamma; \Delta_l, a_1 : A_1, \dots, a_n : A_n, \Delta_r \vdash E: B}{\Gamma; \Delta_l, \Delta_1, \dots, \Delta_n, \Delta_r \vdash E[E_1/a_1, \dots, E_n/a_n] : B}\text{Cut} \\ \\ \dfrac{\Gamma \vdash E : X \quad \Gamma', x : X; a_1 : A_1, \dots, a_n : A_n \vdash E' : B}{\Gamma',\Gamma; a_1 : A_1[E/x], \dots, a_n : A_n[E/x] \vdash E'[E/x] : B[E/x]}\text{Reindex} \\ \\ \dfrac{}{\Gamma\vdash I}I\text{F} \qquad \dfrac{\Gamma\vdash A_1 \quad \cdots \quad \Gamma \vdash A_n}{\Gamma \vdash A_1 \otimes \cdots \otimes A_n}{\otimes_n}\text{F}, n \geq 1 \\ \\ \dfrac{\Gamma \vdash E_1 : X_1 \quad \cdots \quad \Gamma \vdash E_n : X_n \quad \Gamma; \Delta_1 \vdash E_1' : A_1 \quad \cdots \quad \Gamma; \Delta_m \vdash E_m' : A_m \quad \mathsf f : (x_1 : X_1, \dots, x_n : X_n; A_1, \dots, A_m) \to B}{\Gamma; \Delta_1, \dots, \Delta_m \vdash \mathsf f(E_1, \dots, E_n; E_1', \dots, E_m') : B}\text{PrimTerm} \\ \\ \dfrac{}{\Gamma; \vdash * : I}I\text{I} \qquad \dfrac{\Gamma; \Delta \vdash E : I \quad \Gamma; \Delta_l, \Delta_r \vdash E' : B}{\Gamma; \Delta_l, \Delta, \Delta_r \vdash \mathsf{match}\ E\ \mathsf{as}\ *\ \mathsf{in}\ E' : B}I\text{E} \\ \\ \dfrac{\Gamma; \Delta_1 \vdash E_1 : A_1 \quad \cdots \quad \Gamma; \Delta_n \vdash E_n : A_n}{\Gamma; \Delta_1,\dots,\Delta_n \vdash E_1 \otimes \cdots \otimes E_n : A_1 \otimes \cdots \otimes A_n}{\otimes_n}\text{I} \\ \\ \dfrac{\Gamma; \Delta \vdash E : A_1 \otimes \cdots \otimes A_n \quad \Gamma; \Delta_l, a_1 : A_1, \dots, a_n : A_n, \Delta_r \vdash E' : B}{\Gamma; \Delta_l, \Delta, \Delta_r \vdash \mathsf{match}\ E\ \mathsf{as}\ (a_1 \otimes \cdots \otimes a_n)\ \mathsf{in}\ E' : B}{\otimes_n}\text{E},n \geq 1 \end{gather}$$

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    $$\begin{gather} \dfrac{\Gamma_1 \vdash E_1 : X_1 \quad \cdots \quad \Gamma_n \vdash E_n : X_n \qquad x_1 : X_1, \dots, x_n : X_n, \Gamma \vdash E : Y}{\Gamma_1, \dots, \Gamma_n, \Gamma \vdash (\mathsf{match}\ (E_1, \dots, E_n)\ \mathsf{as}\ (x_1, \dots, x_n)\ \mathsf{in}\ E) = E[E_1/x_1, \dots, E_n/x_n] : Y}{\times_n}\beta \\ \\ \dfrac{\Gamma \vdash E : (X_1, \dots, X_n) \qquad \Gamma, x : (X_1, \dots, X_n) \vdash E' : B}{\Gamma \vdash E'[E/x] = \mathsf{match}\ E\ \mathsf{as}\ (x_1, \dots, x_n)\ \mathsf{in}\ E'[(x_1, \dots, x_n)/x] : B}{\times_n}\eta \\ \\ \dfrac{\Gamma \vdash E_1 : (X_1, \dots, X_n) \qquad x_1 : X_1, \dots, x_n : X_n \vdash E_2 : Y \quad y : Y \vdash E_3 : Z}{\Gamma \vdash (\mathsf{match}\ E_1\ \mathsf{as}\ (x_1, \dots, x_n)\ \mathsf{in}\ E_3[E_2/y]) = E_3[(\mathsf{match}\ E_1\ \mathsf{as}\ (x_1, \dots, x_n)\ \mathsf{in}\ E_2)/y] : Z}{\times_n}\text{CC} \\ \\ \dfrac{\Gamma;\vdash E : B}{\Gamma;\vdash (\mathsf{match}\ *\ \mathsf{as}\ *\ \mathsf{in}\ E) = E : B}{*}\beta \qquad \dfrac{\Gamma; \Delta \vdash E : I \qquad \Gamma; \Delta_l, a : I, \Delta_r \vdash E' : B}{\Gamma; \Delta_l, \Delta, \Delta_r \vdash E'[E/a] = (\mathsf{match}\ E\ \mathsf{as}\ *\ \mathsf{in}\ E'[{*}/a]) : B}{*}\eta \\ \\ \dfrac{\Gamma; \Delta_1 \vdash E_1 : A_1 \quad \cdots \quad \Gamma; \Delta_n \vdash E_n : A_n \qquad \Gamma; \Delta_l, a_1 : A_1, \dots, a_n, \Delta_r : A_n \vdash E : B}{\Gamma; \Delta_l, \Delta_1, \dots, \Delta_n, \Delta_r \vdash (\mathsf{match}\ E_1\otimes\cdots\otimes E_n\ \mathsf{as}\ a_1\otimes\cdots\otimes a_n\ \mathsf{in}\ E) = E[E_1/a_1, \dots, E_n/a_n] : B}{\otimes_n}\beta \\ \\ \dfrac{\Gamma; \Delta \vdash E : A_1 \otimes \cdots \otimes A_n \qquad \Gamma; \Delta_l, a : A_1 \otimes \cdots \otimes A_n, \Delta_r \vdash E' : B}{\Gamma; \Delta_l, \Delta, \Delta_r \vdash E'[E/a] = \mathsf{match}\ E\ \mathsf{as}\ a_1\otimes\cdots\otimes a_n\ \mathsf{in}\ E'[(a_1\otimes\cdots\otimes a_n)/a] : B}{\otimes_n}\eta \\ \\ \dfrac{\Gamma; \Delta \vdash E_1 : I \qquad \Gamma; \Delta_l, \Delta_r \vdash E_2 : B \qquad \Gamma; b : B \vdash E_3 : C}{\Gamma; \Delta_l, \Delta, \Delta_r \vdash (\mathsf{match}\ E_1\ \mathsf{as}\ *\ \mathsf{in}\ E_3[E_2/b]) = E_3[(\mathsf{match}\ E_1\ \mathsf{as}\ *\ \mathsf{in}\ E_2)/b] : C}{*}\text{CC} \\ \\ \dfrac{\Gamma; \Delta \vdash E_1 : A_1 \otimes \cdots \otimes A_n \qquad \Gamma; \Delta_l, a_1 : A_1, \dots, a_n : A_n, \Delta_r \vdash E_2 : B \qquad \Gamma; b : B \vdash E_3 : C}{\Gamma; \Delta_l, \Delta, \Delta_r \vdash (\mathsf{match}\ E_1\ \mathsf{as}\ a_1 \otimes \cdots \otimes a_n\ \mathsf{in}\ E_3[E_2/b]) = E_3[(\mathsf{match}\ E_1\ \mathsf{as}\ a_1 \otimes \dots \otimes a_n\ \mathsf{in}\ E_2)/b] : C}{\otimes_n}\text{CC} \end{gather}$$

    |\mathsf X : \mathsf{IxType}| means |\mathsf X| is a primitive index type in the signature. |\mathsf A : (X_1, \dots, X_n) \to \mathsf{Type}| means that |\mathsf A| is a primitive linear type in the signature. |\mathsf F : (X_1, \dots, X_n) \to Y| and |\mathsf f : (x_1 : X_1, \dots, x_n : X_n; A_1, \dots, A_m) \to B| mean that |\mathsf F| and |\mathsf f| are assigned these types in the signature. In the latter case, it is assumed that |x_1 : X_1, \dots, x_n : X_n \vdash A_i| for |i = 1, \dots, m| and |x_1 : X_1, \dots, x_n : X_n \vdash B|. Alternatively, these assumptions could be added as additional hypotheses to the PrimTerm rule. Generally, every |x_i| will be used in some |A_j| or in |B|, though this isn’t technically required.

    As before, I did not write the usual laws for equality (reflexivity and indiscernability of identicals) but they also should be included.

    See the discussion in 狸猫加速器安卓版 about the commuting conversion (|\text{CC}|) rules.

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    Interpretation into an |\mathbf S|-indexed monoidal category

    Fix an |\mathbf S|-indexed monoidal category |\V|. Write |\newcommand{\den}[1]{[\![#1]\!]}\den{-}| for the (overloaded) interpretation function. Its value on primitive operations is left as a parameter.

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    $$\begin{align} \vdash X : \square \implies & \den{X} \in \mathsf{Ob}(\mathbf S) \\ \\ \den{\Gamma} = & \prod_{i=1}^n \den{X_i}\text{ where } \Gamma = x_1 : X_1, \dots, x_n : X_n \\ \den{(X_1, \dots, X_n)} = & \prod_{i=1}^n \den{X_i} \end{align}$$

    Interpretation of Index Terms


    $$\begin{align} \Gamma \vdash E : X \implies & \den{E} \in \mathbf{S}(\den{\Gamma}, \den{X}) \\ \\ \den{x_i} =\, & \pi_i \text{ where } x_1 : X_1, \dots, x_n : X_n \vdash x_i : X_i \\ \den{(E_1, \dots, E_n)} =\, & \den{E_1} \times \cdots \times \den{E_n} \\ \den{\mathsf{match}\ E\ \mathsf{as}\ (x_1, \dots, x_n)\ \mathsf{in}\ E'} =\, & \den{E'} \circ (\den{E} \times id_{\den{\Gamma'}}) \text{ where } \Gamma' \vdash E' : Y \\ \den{\mathsf F(E_1, \dots, E_n)} =\, & \den{\mathsf F} \circ (\den{E_1} \times \cdots \times \den{E_n}) \\ & \quad \text{ where }\mathsf F\text{ is an appropriately typed index operation} \end{align}$$

    Witnesses of Index Derivations

    IxAx is witnessed by identity, and IxCut by composition in |\mathbf S|. Weakening is witnessed by projection. Exchange and Contraction are witnessed by expressions that can be built from projections and tupling. This is very standard.

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    $$\begin{align} \Gamma \vdash A \implies & \den{A} \in \mathsf{Ob}(\V^{\den{\Gamma}}) \\ \\ \den{\Delta} =\, & \den{A_1}\otimes_{\den{\Gamma}}\cdots\otimes_{\den{\Gamma}}\den{A_n} \text{ where } \Delta = a_1 : A_1, \dots, a_n : A_n \\ \den{I} =\, & I_{\den{\Gamma}}\text{ where } \Gamma \vdash I \\ \den{A_1 \otimes \cdots \otimes A_n} =\, & \den{A_1}\otimes_{\den{\Gamma}} \cdots \otimes_{\den{\Gamma}} \den{A_n}\text{ where } \Gamma \vdash A_i \\ \den{\mathsf A(E_1, \dots, E_n)} =\, & \langle \den{E_1}, \dots, \den{E_n}\rangle^*(\den{\mathsf A}) \\ & \quad \text{ where }\mathsf A\text{ is an appropriately typed linear type operation} \end{align}$$

    Interpretation of Linear Terms


    $$\begin{align} \Gamma; \Delta \vdash E : A \implies & \den{E} \in \V^{\den{\Gamma}}(\den{\Delta}, \den{A}) \\ \\ \den{a} =\, & id_{\den{A}} \text{ where } a : A \\ \den{*} =\, & id_{I_{\den{\Gamma}}} \text{ where } \Gamma;\vdash * : I \\ \den{E_1 \otimes \cdots \otimes E_n} =\, & \den{E_1} \otimes_{\den{\Gamma}} \cdots \otimes_{\den{\Gamma}} \den{E_n} \text{ where } \Gamma; \Delta_i \vdash E_i : A_i \\ \den{\mathsf{match}\ E\ \mathsf{as}\ {*}\ \mathsf{in}\ E'} =\, & \den{E'} \circ (id_{\den{\Delta_l}} \otimes_{\den{\Gamma}} (\lambda_{\den{\Delta_r}} \circ (\den{E} \otimes_{\den{\Gamma}} id_{\den{\Delta_r}}))) \\ \den{\mathsf{match}\ E\ \mathsf{as}\ a_1 \otimes \cdots \otimes a_n\ \mathsf{in}\ E'} =\, & \den{E'} \circ (id_{\den{\Delta_l}} \otimes_{\den{\Gamma}} \den{E} \otimes_{\den{\Gamma}} id_{\den{\Delta_r}}) \\ \den{\mathsf f(E_1, \dots, E_n; E_1', \dots, E_n')} =\, & \langle \den{E_1}, \dots, \den{E_n}\rangle^*(\den{\mathsf f}) \circ (\den{E_1'} \otimes_{\den{\Gamma}} \cdots \otimes_{\den{\Gamma}} \den{E_n'}) \\ & \quad \text{ where }\mathsf f\text{ is an appropriately typed linear operation} \end{align}$$

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    As with the index derivations, Ax is witnessed by the identity, in this case in |\V^{\den{\Gamma}}|.

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    Roughly speaking, Reindex is witnessed by |\den{E}^*(\den{E’})|. If we were content to restrict ourselves to semantics in |\mathbf S|-indexed monoidal categories witnessed by functors, as opposed to pseudofunctors, into strict monoidal categories, then this would suffice. For an arbitrary |\mathbf S|-indexed monoidal category, we can’t be sure that the naive interpretation of |A[E/x][E’/y]|, i.e. |\den{E’}^*(\den{E}^*(\den{A}))|, which we’d get from two applications of the Reindex rule, is the same as the interpretation of |A[E[E’/y]/x]|, i.e. |\den{E \circ E’}^*(\den{A})|, which we’d get from IxCut followed by Reindex. On the other hand, |A[E/x][E’/y] = A[E[E’/y]/x]| is simply true syntactically by the definition of substitution (which I have not provided but is the obvious, usual thing). There are similar issues for (meta-)equations like |I[E/x] = I| and |(A_1 \otimes A_2)[E/x] = A_1[E/x] \otimes A_2[E/x]|.

    The solution is that we essentially use a normal form where we eliminate the uses of Reindex. These normal form derivations will be reached by rewrites such as:
    $$\begin{gather} \dfrac{\dfrac{\mathcal D}{\Gamma' \vdash E : X} \qquad \dfrac{\dfrac{\mathcal D_1}{\Gamma, x : X; \Delta_1 \vdash E_1 : A_1} \quad \cdots \quad \dfrac{\mathcal D_n}{\Gamma, x : X; \Delta_n \vdash E_n : A_n}} {\Gamma, x : X; \Delta_1, \dots, \Delta_n \vdash E_1 \otimes \cdots \otimes E_n : A_1 \otimes \cdots \otimes A_n}} {\Gamma, \Gamma'; \Delta_1[E/x], \dots, \Delta_n[E/x] \vdash E_1[E/x] \otimes \cdots \otimes E_n[E/x] : A_1[E/x] \otimes \cdots \otimes A_n[E/x]} \\ \Downarrow \\ \dfrac{\dfrac{\dfrac{\mathcal D}{\Gamma' \vdash E : X} \quad \dfrac{\mathcal D_1}{\Gamma, x : X; \Delta_1 \vdash E_1 : A_1}} {\Gamma, \Gamma'; \Delta_1[E/x] \vdash E_1[E/x] : A_1[E/x]} \quad \cdots \quad \dfrac{\dfrac{\mathcal D}{\Gamma' \vdash E : X} \quad \dfrac{\mathcal D_n}{\Gamma, x : X; \Delta_n \vdash E_n : A_n}} {\Gamma, \Gamma'; \Delta_n[E/x] \vdash E_n[E/x] : A_n[E/x]}} {\Gamma, \Gamma'; \Delta_1[E/x], \dots, \Delta_n[E/x] \vdash E_1[E/x] \otimes \cdots \otimes E_n[E/x] : A_1[E/x] \otimes \cdots \otimes A_n[E/x]} \end{gather}$$

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    1. As the previous post alludes, monoidal structure is more than we need. If we pursue the generalizations described there in this indexed context, we eventually end up at augmented virtual double categories or virtual equipment.↩︎

    2. The terminology here is a mess. Leinster calls strong monoidal functors “weak”. “Strong” also refers to 狸猫加速器安卓版下载, and it’s quite possible to have a “strong lax monoidal functor”. (In fact, this is what applicative functors are usually described as, though a strong lax closed functor would be a more direct connection.) Or the functors we’re talking about which are not-strong strong monoidal functors…↩︎

    July 06, 2024 02:00 AM

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    The Haskell command line parsing library cmdargs contains a data type that represents a command line. I always thought it would be a neat trick to transform that into a web page, to make it easier to explore command line options interactively - similar to how the custom-written 狸猫加速器安卓版下载 wraps 狸猫加速器安卓版下载在哪里.

    I wrote a demo to do just that, named cmdargs-browser. Given any program that uses cmdargs (e.g. hlint), you can install cmdargs-browser (with cabal install cmdargs-browser) and run:

    cmdargs-browser hlint

    And it will pop up:

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    As we can see, the HLint modes are listed on the left (you can use lint, grep or test), the possible options on the right (e.g. normal arguments and 狸猫加速器安卓版) and the command line it produces at the bottom. As you change mode or add/remove flags, the command line updates. If you hit OK it then runs the program with the command line. The help is included next to the argument, and if you make a mistake (e.g. write foo for the --color flag) it tells you immediately. It could be more polished (e.g. browse buttons for file selections, better styling) but the basic concepts works well.

    Technical implementation

    I wanted every cmdargs-using program to support this automatic UI, but also didn't want to increase the dependency footprint or compile-time overhead for 坚果加速器下载官网. I didn't want to tie 狸猫加速器安卓版下载 to this particular approach to a UI - I wanted a flexible mechanism that anyone could use for other purposes.

    To that end, I built out a Helper module that is included in cmdargs. That API provides the full power and capabilities on which cmdargs-browser is written. The Helper module is only 350 lines.

    If you run cmdargs with either $CMDARGS_HELPER or $CMDARGS_HELPER_HLINT set (in the case of HLint) then cmdargs will run the command line you specify, passing over the explicit Mode data type on the stdin. That Mode data type includes functions, and using a simplistic communication channel on the stdin/stdout, the helper process can invoke those functions. As an example, when cmdargs-browser wants to validate the --color flag, it does so by calling a function in 蚂蚁ant加速器安卓下载, that secretly talks back to 安卓永久免费网络加速器 to validate it.

    At the end, the helper program can choose to either give an error message (to stop the program, e.g. if you press Cancel), or give some command lines to use to run the program.

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    This demo was a cool project, which may turn out to be useful for some, but I have no intention to develop it further. I think something along these lines should be universally available for all command line tools, and built into all command line parsing libraries.

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    All the code that makes this approach work was written over seven years ago. Specifically, it was my hacking project in the hospital while waiting for my son to be born. Having a little baby is a hectic time of life, so I never got round to telling anyone about its existence.

    This weekend I resurrected the code and published an updated version to Hackage, deliberately making as few changes as possible. The three necessary changes were:

    1. jQuery deprecated the live function replacing it with on, meaning the code didn't work.
    2. I had originally put an upper bound of 0.4 for the transformers library. Deleting the upper bound made it work.
    3. Hackage now requires that all your uploaded hi vph加速器下载 files declare that they require a version of 1.10 or above of Cabal itself, even if they don't.

    Overall, to recover a project that is over 7 years old, it was surprisingly little effort.

    by Neil Mitchell (noreply@blogger.com) at July 05, 2024 10:03 AM

    July 04, 2024

    Don Stewart (dons)

    蚂蚁ant加速器安卓下载

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    As a warm up I thought I’d try porting the stream fusion core from Haskell to Rust. This was code I was working on more than a decade ago. How much of it would work or even make sense in today’s Rust?

    Footnote: this is the first code I’ve attempted to seriously write for more than 2 years, as I’m diving back into software engineering after an extended sojourn in team building and eng management. I was feeling a bit .. rusty. Let me know if I got anything confused.

    TLDR

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    • And a more closure-avoiding trait encoding that uses types to index all the code statically

    Fun things to discover:

    • most of the typeclass ‘way of seeing’ works pretty much the same in Rust. You index/dispatch/use similar mental model to program generically. I was able to start guessing the syntax after a couple of days
    • it’s actually easier to get first class dictionaries and play with them
    • compared to the hard work we do in GHC to make everything strict, unboxed and not heap-allocated, this is the default in Rust which makes the optimization story a lot simpler
    • Rust has no GC , instead using a nested-region like allocation strategy by default. I have to commit to specific sharing and linear memory use up front. This feels a lot like an ST-monad-like state threading system. Borrowing and move semantics take a bit of practice to get used to.
    • the trait version looks pretty similar to the core of the standard Rust iterators, and the performance in toy examples is very good for the amount of effort I put in
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    • Non-fancy Haskell, including type class designs, can basically be ported directly to Rust, though you now annotate allocation behavior explicitly.
    • cargo is a highly polished ‘cabal’ with lots of sensible defaults and way more constraints on what is allowed. And a focus on good UX.

    As a meta point, it’s amazing to wander into a fresh programming language, 15 years after the original “associated types with class” paper, and find basically all the original concepts available, and extended in some interesting ways. There’s a lot of feeling of deja vu for someone who worked on GHC optimizations/unboxing/streams when writing in Rust.

    Version 1: direct Haskell translation

    http://github.com/donsbot/experiments-rust/blob/master/stream-fusion/src/closure.rs

    First, a direct port of the original paper. A data type for stepping through elements of stream, including ‘Skip’ so we can filter things. And a struct holding the stream stepper function, and the state. Compared to the Haskell version (in the comment) there’s more rituals to declare what goes on the heap, and linking the lifetime of objects together. My reward for doing this is not needing a garbage collector. There’s quite an enjoyable serotonin reward when a borrow checking program type checks :-)

    You can probably infer from the syntax this will be operationally expensive: a closure boxed up onto the heap. Rust’s explicit control of where things are stored and for how long feels a lot like a type system for scripting allocators, and compared to Haskell you’re certainly exactly aware of what you’re asking the machine to do.

    Overall, its a fairly pleasing translation and even though I’m putting the closure on the heap I’m still having it de-allocated when the stream is dropped. Look mum, closure passing without a GC.

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    • being explicit about whether my closure was going to borrow or own the lifetime of values it captures. Stuff you never think about in Haskell, with a GC to take care of all that thinking (for a price). You end up with a unique type per closure showing what is captured, which feels _very_ explicit and controlled.
    • no rank-2 type to hide the stream state type behind. The closest I could get was the ‘impl Seed’ opaque return type, but it doesn’t behave much like a proper existential type and tends to leak through the implementation. I’d love to see the canonical way to hide this state value at the type level without being forced to box it up.
    • a la vector ‘Prim’ types in Haskell, we use Copy to say something about when we want the values to be cheap to move (at least, that’s my early mental model)

    I can generate a stream of values, a la replicate:

    As long as I’m careful threading lifetime parameters around I can box values and generate streams without using a GC. This is sort of amazing. (And the unique lifetime token-passing discipline feels very like the ST monad and its extensions into regions/nesting). Again , you can sort of “feel” how expensive this is going to be, with the capturing and boxing to the heap explict. That boxed closure dynamically invoked will have a cost.

    Let’s consume a stream, via a fold:

    Not too bad. The lack of tail recursion shows up here, so while I’d normally write this as a ‘go’ local work function with a stack parameter, to get a loop, instead in Rust we just write a loop and peek and poke the memory directly via a ‘mut’ binding. Sigh, fine, but I promise I’m still thinking in recursion.

    Now I can do real functional programming:

    What about something a bit more generic: enumFromTo to fill a range with consecutive integer values, of any type supporting addition?

    The trait parameters feel a lot like a super layered version of the Haskell Num class, where I’m really picking and choosing which methods I want to dispatch to. The numeric overloading is also a bit different (A::one()) instead of an overloaded literal. Again, is almost identical to the Haskell version, but with explicit memory annotations, and more structured type class/trait hierarchy. Other operations, like map, filter, etc all fall out fairly straight forward. Nice: starting to feel like I can definitely be productive in this language.

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       sum . map (*2) . filter (\n -> n`mod`2 == 1) $ [1..1000000::Int]
    => 500000000000

    As barebones Rust:

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    500000000000

    Another moment of deja vu, installing Criterion to benchmark the thing. “cargo bench” integration is pretty sweet:

    So about 7 ms for four logical loops over 1M i64 elements. That’s sort of plausible and actually not to bad considering I don’t know what I’m doing.

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    But it works! The first thing directly translated works, and it has basically the behavior you’d expect with explict closure calls. Not bad!

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    http://github.com/donsbot/experiments-rust/blob/master/stream-fusion/src/trait.rs

    That boxed closure bothers me a bit. Dispatching to something that’s known statically. The usual trick for resolving things statically is to move the work to the type system. In this case, we want to lookup the right ‘step’ function by type. So I’ll need a type for each generator and transformer function in the stream API. We can take this approach in Rust too.

    Basic idea:

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    • stream elem types can be generic parameters, or specialized associated types
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    I banged my head against this a few different ways, and settled on putting the state data into the ‘API key’ type. This actually looks really like something we already knew how to do – streams as Rust iterators – Snoyman already wrote about it 3 years ago! — I’ve basically adapted his approach here after a bit of n00b trial and error.

    The ‘Step’ type is almost the same, and the polymorphic ‘Stream’ type with its existential seed becomes a trait definition:

    What’s a bit different now is how we’re going to resolve the function to generate each step of the stream. That’s now a trait method associated with some instance and element type.

    So e.g. if I want to generate an empty stream, I need a type, and instance and a wrapper:

    Ok not too bad. My closure for stepping over streams is now a ‘next’ method. What would have been a Stream ‘object’ with an embedded closure is now a trait instance where the ‘next’ function can be resolved statically.

    I can convert all the generator functions like this. For example, to replicate a stream I need to know how many elements, and what the element is. Instead of capturing the element in a closure, it’s in an explicit data type:

    The step function is still basically the same as in the Haskell version, but to get the nice Rust method syntax we have it all talk to ‘self’.

    We also need a type for each stream transformer: so a ‘map’ is now a struct with the mapper function, paired with the underlying stream object it maps over.

    This part is a bit more involved — when a map is applied to a stream element, we return f(x) of the element, and lift the stream state into a Map stream state for the next step.

    I can implement Stream-generic folds now — again, since I have no tail recursion to consume the stream I’m looping explicitly. This is our real ‘driver’ of work , the actual loop pulling on a chain of ‘stream.next()’s we’ve built up.

    Ok so with the method syntax this looks pretty nice:

    I had to write out the types here to understand how the method resolving works. We build up a nice chain of type information about exactly what function we want to use at what type. The whole pipeline is a Map<Filter<Range < … type> , all an instance of Stream.

    So this should do ok right? No boxing of closures, there could be some lookups and dispatch but there’s enough type information here to know all calls statically. I don’t have much intuition for how Rust will optimize the chain of nested Yield/Skip constructors.. but I’m hopeful given the tags fit in 2 bits, and I don’t use Skip anywhere in the specific program.

    288 microseconds to collapse a 1_000_000 element stream. Or about 25x faster. Nice!

    So the type information and commitment to not allocating to the heap does a lot of work for us here. I ask cargo rustc --bin stream_test --release -- --emit asm for fun. And this is basically what I want to see: a single loop, no allocation, a bit of math. Great.

    It’s converted the %2 / *2 body into adding a straight i64 addition loop with strides. I suspect with a bit of prodding it could resolve this statically to a constant but that’s just a toy anyway. All the intermediate data structures are gone.

    Overall, that’s a pretty satisfying result. With minimal effort I got a fusing iterator/stream API that performs well out of the box. The Rust defaults nudge code towards low overhead by default. That can feel quite satisfying.

    by Don Stewart at July 04, 2024 11:35 PM

    July 03, 2024

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    16.00 Fri 3 Jul Haskell, then and now: What is the future for functional programming languages? Prof Simon Peyton-Jones, Prof John Hughes, Prof Philip Wadler, Dr Kevin Hammond, Dr Duncan Coutts.

    You can submit questions via Reddit. Register for the summit here. You can log in with your registered username and password here.

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    An Incredible Scientific Breakthrough Discovery to Beat Covid

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    I almost never see masks in Edinburgh, not even in stores or on busses. Brazil has serious problems, but no one in Rio de Janeiro goes outside without a mask. Courtesy of Tom the Dancing Bug.

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  • For today's #haskell exercise we convert a set of arcs to a graph. #GraphTheory 
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  • by geophf (noreply@blogger.com) at July 02, 2024 02:38 PM

    July 01, 2024

    Oskar Wickström

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    In this post I’ll share the results from testing TodoMVC implementations using my new testing tool named WebCheck. I’ll explain how the specification works, what problems were found in the TodoMVC implementations, and what this means for my project.

    WebCheck

    During the last three months I’ve used my spare time to build WebCheck. It’s a browser testing framework combining ideas from:

    • property-based testing (PBT)
    • TLA+ and linear temporal logic
    • functional programming

    In WebCheck, you write a specification for your web application, instead of manually writing test cases. The specification describes the intended behavior as a finite-state machine and invariants, using logic formulae written in a language inspired by the temporal logic of actions (PDF) from TLA+. WebCheck generates hundreds or thousands of tests and runs them to verify if your application is accepted by the specification.

    The tests generated by WebCheck are sequences of possible actions, determined from the current state of the DOM at the time of each action. You can think of WebCheck as exploring the state space automatically, based on DOM introspection. It can find user behaviors and problems that we, the biased and lazy humans, are unlikely to think of and to write tests for. Our job is instead to think about the requirements and to improve the specification over time.

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    In property-based testing, when testing state machines using models, the model should capture the essential complexity of the system under test (SUT). It needs to be functionally complete to be a useful oracle. For a system that is conceptually simple, e.g. a key-value database engine, this is not a problem. But for a system that is inherently complex, e.g. a business application with a big pile of rules, a useful model tends to grow as complex as the system itself.

    In WebCheck, the specification is not like such a model. You don’t have to implement a complete functional model of your system. You can leave out details and specify only the most important aspects of your application. As an example, I wrote a specification that states that “there should at no time be more than one spinner on a page”, and nothing else. Again, this is possible to specify in PBT in general, but not with model-based PBT, from what I’ve seen.

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    Since the start of this project, I’ve used the TodoMVC implementations as a benchmark of WebCheck, and developed a general specification for TodoMVC implementations. The TodoMVC contribution documentation has 蓝灯vp:1 天前 · 蓝灯lantern破解版vip无限流量及各版本下载 | 路由器博客 [图文] 网站首页 >游戏助手>蓝灯VIP破解版v3.6.6破解内购专业版 蓝灯VIP破解版v3.6.6破解内购专业版 蓝灯的Android版本怎么用_ 点中间的按钮.选择确定.翻墙成功的话会在通知栏有一个小钥匙的标志., and the project has a Cypress test suite, but I was curious if I could find anything new using WebCheck.

    Early on, checking the mainstream framework implementations, I found that both the Angular and Mithril implementations were rejected by my specification, and I submitted 狸猫加速器安卓版下载 in the TodoMVC issue tracker. Invigorated by the initial success, I decided to check the remaining implementations and gradually improve my specification.

    I’ve generalized the specification to work on nearly all the implementations listed on the TodoMVC website. Some of them use the old markup, which uses IDs instead of classes for most elements, so I had to support both variants.

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    Before looking at the tests results, you might want to have a look at the WebCheck specification that I’ve published as a gist:

    TodoMVC.spec.purs

    The gist includes a brief introduction to the WebCheck specification language and how to write specifications. I’ll write proper documentation for the specification language eventually, but this can give you a taste of how it works, at least. I’ve excluded support for the old TodoMVC markup to keep the specification as simple as possible.

    The specification doesn’t cover all features of TodoMVC yet. Most notably, it leaves out the editing mode entirely. Further, it doesn’t cover the usage of local storage in TodoMVC, and local storage is disabled in WebCheck for now.

    I might refine the specification later, but I think I’ve found enough to motivate using WebCheck on TodoMVC applications. Further, this is likely how WebCheck would be used in other projects. You specify some things and you leave out others.

    The astute reader might have noticed that the specification language looks like PureScript. And it pretty much is PureScript, with some WebCheck-specific additions for temporal modalities and DOM queries. I decided not to write a custom DSL, and instead write a PureScript interpreter. That way, specification authors can use the tools and packages from the PureScript ecosystem. It works great so far!

    Test Results

    Below are the test results from running WebCheck and my TodoMVC specification on the examples listed on the TodoMVC website. I’ll use short descriptions of the problems (some of which are recurring), and explain in more detail further down.

    狸猫Ⅴpn安卓 Problems/Notes
    Pure JavaScript
    Backbone.js
    AngularJS
    • Clears input field on filter change
    Ember.js
    Dojo
    坚果加速器下载官网
    CanJS
    Polymer
    React
    Mithril
    • Clears input field on filter change
    Vue
    MarionetteJS
    Compiled to JavaScript
    Kotlin + React
    极光加速器官方网站 Spine
    黑洞加速器破解版app
    狸猫加速器安卓版安装包
    Closure
    Elm
    AngularDart
    • Race condition on initialization
    • Filters not implemented
    TypeScript + Backbone.js
    TypeScript + AngularJS
    TypeScript + React
    Reagent
    Scala.js + React
    Scala.js + Binding.scala
    狸猫加速器安卓版下载在哪里 js_of_ocaml
    Humble + GopherJS
    • Missing/broken link
    Under evaluation by TodoMVC
    hi vph加速器下载 Backbone.js + RequireJS
    KnockoutJS + RequireJS
    • Inconsistent first render
    AngularJS + RequireJS
    • Needs a custom readyWhen condition
    CanJS + RequireJS
    Lavaca + RequireJS
    • 御龙之路单机版下载- 全方位下载:2021-6-14 · 御龙之路汉化版是众东方玄幻为背景题材的热血激情仙侠角色扮演游戏,游戏拥有玄幻色彩的画风,精美华丽的画面,激情十足的热血战斗玩法,多人实时在线竞技对战模式,给你带来全新的战
    快喵ⅴpn破解版
    • Race condition on initialization
    • Filters not implemented
    Sammy.js
    soma.js
    • Missing/broken link
    狸猫加速器安卓版安装包
    • Clears input field on filter change
    黑洞加速器破解版app Kendo UI
    Dijon
    • 狸猫加速器安卓版下载
    Enyo + Backbone.js
    SAPUI5
    • No input field
    Exoskeleton
    hi vph加速器下载
    React + Alt
    快喵ⅴpn破解版
    Aurelia
    Angular 2.0
    • Filters not implemented
    Riot
    JSBlocks
    Real-time
    SocketStream
    • State cannot be cleared
    蚂蚁ant加速器安卓下载 Firebase + AngularJS
    狸猫Ⅴpn安卓
    Express + gcloud-node
    • Missing/broken link
    Non-framework implementations
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    • Adds pending item on other iteraction
    VanillaJS ES6
    • Adds pending item on other iteraction
    • .todo-count strong is missing
    jQuery
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    狸猫加速器安卓版下载在哪里

    There’s no way of switching between “All”, “Active”, and “Completed” items. This is specified in the TodoMVC documentation under Routing.

    Race condition during initialization

    The event listeners are attached some time after the 极光加速器官方网站 form is rendered. Although unlikely, if you’re quick enough you can focus the input, press Return, and post the form. This will navigate the user agent to the same page but with a query paremeter, e.g. index.html?text=. In TodoMVC it’s not the end of the world, but there are systems where you do not want this to happen.

    Inconsistent first render

    The application briefly shows an inconsistent view, then renders the valid initial state. KnockoutJS + RequireJS shows an empty list items and “0 left” in the bottom, even though the footer 星际加速器安卓版_加速器安卓版 - 捏游:2021-4-20 · 星际传奇加速器下载|星际传奇加速自动战斗安 482x346 - 192KB - JPEG 星际传奇加速器下载|星际传奇加速自动战斗安 482x346 - 187KB - JPEG 星际阵地游戏加速器安卓版 512x512 - 58KB - JPEG 星际加速器app|星际加速软件1.0.0 官网安卓版 384x618 - 96KB.

    Needs a custom readyWhen condition

    The specification awaits an element matching .todoapp (or 狸猫加速器安卓版安装包 for the old markup) in the DOM before taking any action. In this case, the implementation needs a modified specification that instead awaits a framework-specific class, e.g. .ng-scope. This is an inconvenience in testing the implementation using WebCheck, rather than an error.

    No input field

    There’s no input field to enter TODO items in. I’d argue this defeats the purpose of a TODO list application, and it’s indeed specified in the official documentation.

    Adds pending item on other iteraction

    When there’s a pending item in the input field, and another action is taken (toggle all, change filter, etc), the pending item is submitted automatically without a Return key press.

    .todo-count strong element is missing

    An element matching the selector .todo-count strong must be present in the DOM when there are items, showing the number of active items, as described in the TodoMVC documentation.

    State cannot be cleared

    This is not an implementation error, but an issue where the test implementation makes it hard to perform repeated isolated testing. State cannot (to my knowledge) be cleared between tests, and so isolation is broken. This points to a key requirement currently placed by WebCheck: the SUT must be stateless, with respect to a new private browser window. In future versions of WebCheck, I’ll add hooks to let the tester clear the system state before each test is run.

    Missing/broken link

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    Note that I can’t decide which of these problems are bugs. That’s up to the TodoMVC project maintainers. I see them as problems, or disagreements, between the implementations and my specification. A good chunk of humility is in order when testing systems designed and built by others.

    The Future is Bright

    I’m happy with how effective WebCheck has been so far, after only a few months of spare-time prototyping. Hopefully, I’ll have something more polished that I can make available soon. An open source tool that you can run yourself, a SaaS version with a subscription model, or maybe both. When that time comes, maybe WebCheck can be part of the TodoMVC project’s testing. And perhaps in your project?

    If you’re interested in WebCheck, please sign up for the newsletter. I’ll post regular project updates, and definitely no spam. You can also follow me on Twitter.

    狸猫加速速器

    If you have any comments or questions, please reply to any of the following threads:

    • Twitter
    • Lobste.rs

    Thanks to Hillel Wayne, Felix Holmgren, Martin Janiczek, Tom Harding, and Martin Clausen for reviewing drafts of this post.

    July 01, 2024 10:00 PM

    狸猫加速器安卓版下载在哪里

    Template Haskell recompilation

    I was wondering: What happens if I have a Haskell module with Template Haskell that embeds some information from the environment (time, environment variables). Will such a module be reliable recompiled? And what if it gets recompiled, but the source code produced by Template Haskell is actually unchanged (e.g., because the environment variable has not changed), will all depending modules be recompiled (which would be bad)?

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    /tmp/th-recom-test $ cat Foo.hs
    {-# LANGUAGE TemplateHaskell #-}
    {-# OPTIONS_GHC -fforce-recomp #-}
    module Foo where
    
    import Language.Haskell.TH
    import Language.Haskell.TH.Syntax
    import System.Process
    
    theMinute :: String
    theMinute = $(runIO (readProcess "date" ["+%M"] "") >>= stringE)
    [jojo@kirk:2] Mi, der 01.07.2024 um 17:18 Uhr ☺
    /tmp/th-recom-test $ cat Main.hs
    import Foo
    main = putStrLn theMinute

    Note that I had to set {-# OPTIONS_GHC -fforce-recomp #-} – by default, GHC will not recompile a module, even if it uses Template Haskell and runIO. If you are reading from a file you can use addDependentFile to tell the compiler about that depenency, but that does not help with reading from the environment.

    So here is the test, and we get the desired behaviour: The Foo module is recompiled every time, but unless the minute has changed (see my prompt), Main is not recomipled:

    /tmp/th-recom-test $ ghc --make -O2 Main.hs -o test
    [1 of 2] Compiling Foo              ( Foo.hs, Foo.o )
    [2 of 2] Compiling Main             ( Main.hs, Main.o )
    Linking test ...
    [jojo@kirk:2] Mi, der 01.07.2024 um 17:20 Uhr ☺
    /tmp/th-recom-test $ ghc --make -O2 Main.hs -o test
    [1 of 2] Compiling Foo              ( Foo.hs, Foo.o )
    Linking test ...
    [jojo@kirk:2] Mi, der 01.07.2024 um 17:20 Uhr ☺
    /tmp/th-recom-test $ ghc --make -O2 Main.hs -o test
    [1 of 2] Compiling Foo              ( Foo.hs, Foo.o )
    [2 of 2] Compiling Main             ( Main.hs, Main.o ) [Foo changed]
    Linking test ...

    So all well!

    hi vph加速器下载: It seems that while this works with ghc --make, the -fforce-recomp does not cause cabal build to rebuild the module. That’s unfortunate.

    by Joachim Breitner (mail@joachim-breitner.de) at July 01, 2024 03:16 PM

    狸猫Ⅴpn安卓

    A Rust self-ownership lifetime trick (that doesn't work)

    狸猫vpn安卓破解版最新官网下载--苹果软件:2021-6-9 · VPN-狸猫vpn全球网络加速器 软件特色: 狸猫加速器是一款全球*网络加速器,加速器拥有智能加速器功能,专设超大带宽独立服务器,系统自动选择最优线路,随时随地秒开国内外应用。

    Let's imagine we are using Rust to implement some kind of container that can allocate values, and a special value can be associated with the container. It's a bug if the allocated value gets freed while it is the special value of a container. We might hope to use lifetimes to encode that relationship:

    struct Value<'v> {...}
    struct Container {...}

    impl Container {
    fn alloc<'v>(&'v self) -> Value<'v> {...}
    fn set_special<'v>(&'v self, x: Value<'v>) {...}
    }

    Here we have a Container (which has no lifetime arguments), and a 快喵ⅴpn破解版 (where 'v ties it to the right container). Within our container we can implement 狸猫加速器安卓版下载在哪里 and set_special. In both cases, we take &'v self and then work with a Value<'v>, which ensures that the lifetime of the Container and Value match. (We ignore details of how to implement these functions - it's possible but requires unsafe).

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    fn set_cheat<'v1, 'v2>(to: &'v1 Container, x: Value<'v2>) {
    to.set_special(x);
    }

    The Rust compiler has taken advantage of the fact that Container can be reborrowed, and that Value is variant, and rewritten the code to:

    fn set_cheat<'v1, 'v2>(to: &'v1 Container, x: Value<'v2>) {
    'v3: {
    let x : Value<'v3> = x; // Value is variant, 'v2 : 'v3
    let to : &'v3 Container = &*to;
    to.set_special(x);
    }
    }

    The code with lifetime annotations doesn't actually compile, it's just what the compiler did under the hood. But we can stop Value being variant by making it contain PhantomData<Cell<&'v ()>>, since lifetimes under Cell are invariant. Now the above code no longer compiles. Unfortunately, there is a closely related variant which does compile:

    fn set_cheat_alloc<'v1, 'v2>(to: &'v1 Container, from: &'v2 Container) {
    let x = from.alloc();
    to.set_special(x);
    }

    While Value isn't variant, 狸猫加速器安卓版下载 is, so the compiler has rewritten this code as:

    fn set_cheat<'v1, 'v2>(to: &'v1 Container, from: &'v2 Container) {
    'v3: {
    let from = &'v3 Container = &*from;
    let x : Value<'v3> = from.alloc();
    let to : &'v3 Container = &*to;
    to.set_special(x);
    }
    }

    Since lifetimes on & are always variant, I don't think there is a trick to make this work safely. Much of the information in this post was gleaned from this StackOverflow question.

    by Neil Mitchell (noreply@blogger.com) at July 01, 2024 08:50 AM

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    I'm participating in four sessions at Cardano Virtual Summit 2024, and there are many other sessions too. All times UK/BST.

    16.00 Thu 2 Jul An overview of IOHK research Prof Aggelos Kiayias, Prof Elias Koutsoupias, Prof Alexander Russell, Prof Phil Wadler.

    狸猫Ⅴpn安卓 Architecting the internet: what I would have done differently... Vint Cerf, Internet pioneer and Google internet evangelist, Prof Aggelos Kiayias, panel moderated by Prof Philip Wadler.

    20.00 Thu 2 Jul Functional smart contracts on Cardano Prof Philip Wadler, Dr Manuel Chakravarty, Prof Simon Thompson.

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    In my 狸猫加速器安卓版百度云 I challenged you to solve 狸猫加速器安卓版百度云, which presents us with a cake in the shape of a rectangular prism, with chocolate chips at various locations, and asks us to check whether a proposed division of the cake is valid. A division of the cake is valid if it is a 快喵ⅴpn破解版 (no pieces overlap and every part of the cake is in some piece) and every piece contains one chocolate chip.

    No one posted a solution—I don’t know if that’s because people have lost interest, or because no one was able to solve it—but in any case, don’t read this post yet if you still want to try solving it! As a very small hint, part of the reason I chose this problem is that it is an interesting example of a case where just getting the correct asymptotic time complexity is not enough—we actually have to work a bit to optimize our code so it fits within the allotted time limit.

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    When solving this problem I first just spent some time thinking about the different things I would have to compute and what algorithms and data structures I could use to accomplish them.

    • The first thing that jumped out at me is that we are going to want some kind of abstractions for 3D coordinates, and for 3D rectangular prisms (i.e. boxes, i.e. pieces of cake). Probably we can just represent boxes as a pair of points at opposite corners of the box (in fact this is how boxes are given to us). As we plan out how the rest of the solution is going to work we will come up with a list of operations these will need to support.

      As an aside, when working in Java I rarely make any classes beyond the single main class, because it’s too heavyweight. When working in Haskell, on the other hand, I often define little abstractions (i.e. data types and operations on them) because they are so lightweight, and being able to cleanly separate things into different layers of abstraction helps me write solutions that are more obviously correct.

    • We need to check that the coordinates of each given box are valid.

    • We will need to check that every piece of cake contains exactly one chocolate chip. At first this sounds difficult—given a chip, how do we find out which box(es) it is in? Or given a box, how can we find out which chips are in it? To do this efficiently seems like it will require some kind of advanced 3D space partitioning data structure, like an octree or a BSP tree. BUT this is a situation where reading carefully pays off: the problem statement actually says that “the -th part must contain the -th chocolate chip”. So all we have to do is zip the list of pieces together with the list of chips. We just need an operation to test whether a given point is contained in a given box.

    • We have to check that none of the boxes overlap. We can make a primitive to check whether two boxes intersect, but how do we make sure that none of the boxes intersect? Again, complicated space-partitioning data structures come to mind; but since there are at most boxes, the number of pairs is on the order of . There can be multiple test cases, though, and the input specification says the sum of values for (the number of pieces) over all test cases will be at most . That means that in the worst case, we could get up to test cases with pieces of cake (and thus on the order of pairs of pieces) per test case. Given operations per second as a rough rule of thumb, it should be just barely manageable to do a brute-force check over every possible pair of boxes.

    • Finally, we have to check that the pieces account for every last bit of the cake. If we think about trying checking this directly, it is quite tricky. One could imagine making a 3D array representing every cubic unit of cake, and simply marking off the cubes covered by each piece, but this is completely out of the question since the cake could be up to in size! Or we could again imagine some complicated space-partitioning structure to keep track of which parts have and have not been covered so far.

      But there is a much simpler way: just add up the volume of all the pieces and make sure it is the same as the volume of the whole cake! Of course this relies on the fact that we are also checking to make sure none of the pieces overlap: the volumes being equal implies that the whole cake is covered 狸猫加速器安卓版下载在哪里 none of the pieces overlap. In any case, we will need a way to compute the volume of a box.

    狸猫加速器安卓版下载

    Let’s start with some preliminaries: LANGUAGE pragmas, imports, main, and the parser.

    {-# LANGUAGE OverloadedStrings #-}
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    {-# LANGUAGE TupleSections     #-}
    
    import           蚂蚁ant加速器安卓下载
    import           Data.Bool
    import qualified Data.ByteString.Lazy.Char8 as C
    import           Data.Monoid
    
    import           ScannerBS
    
    main = C.interact $
      快喵ⅴpn破解版 (many tc) >>> init >>>
      map (solve >>> bool "NO" "YES") >>>
      C.unlines
    
    data TC = TC { cake :: Box, chips :: [Pos], parts :: [Box] }
    
    tc :: Scanner TC
    tc = do
      a <- int
      狸猫Ⅴpn安卓 a of
        -1 -> return 狸猫加速器安卓版百度云
        _  -> do
          xs <- three int
          let [b,c,m] = xs
              cake    = Box (Pos 1 1 1) (Pos a b c)
          TC cake <$> m `times` pos <*> m `times` box

    The parser is worth remarking upon. The input consists of multiple test cases, with a single value of marking the end of the input. This is annoying: ideally, we would have a many combinator that keeps running a Scanner until it fails, but we don’t. To keep things simple and fast, our Scanner abstraction does not support parse failures and alternatives! The many combinator we made keeps running a given Scanner until the end of input, not until it fails. The quick-and-dirty solution I adopted is to make the test case Scanner return undefined if it sees a -1, and then simply ignore the final element of the list of test cases via init. Not pretty but it gets the job done.

    蚂蚁vp(永久免费)

    Next let’s consider building abstractions for 3D coordinates and boxes. It is very tempting to do something like this:

    type Pos = [Integer]
    type Box = [Pos]
    
    -- Check whether one position is componentwise <= another
    posLTE :: Pos -> Pos -> Pos
    posLTE p1 p2 = and $ zipWith (<=) p1 p2
    
    -- ... and so on

    Using list combinators like zipWith to work with Pos and Box values is quite convenient. And for some problems, using lists is totally fine. Having a small number of large lists—狸猫加速器安卓版百度云 reading in a list of integers and processing them somehow—is rarely a problem. But having a large number of small lists, as we would if we use lists to represent Pos and Box here, slows things down a lot (as I learned the hard way). I won’t go into the details of why—I am no expert on Haskell performance—but suffice to say that lists are a linked structure with a large memory overhead.

    So let’s do something more direct. We’ll represent both Pos and Box as data types with strict fields (the strict fields make a big difference, especially in the case of Pos), and make some trivial Scanners for them. The volume function computes the volume of a box; given that the coordinates are coordinates of the cubes that make up the pieces, and are both inclusive, we have to add one to the difference between the coordinates. Note we assume that the first coordinate of a Box should be elementwise less than or equal to the second; otherwise, the call to max 0 ensures we will get a volume of zero.

    data Pos = Pos !Int !Int !Int
    data Box = Box !Pos !Pos
    
    pos :: Scanner Pos
    pos = Pos <$> int <*> int <*> int
    
    box :: Scanner Box
    box = Box <$> pos <*> pos
    
    volume :: Box -> Int
    volume (Box (Pos x1 y1 z1) (Pos x2 y2 z2)) = (x2 -. x1) * (y2 -. y1) * (z2 -. z1)
      where
        x -. y = max 0 (x - y + 1)

    Another very important note is that we are using Int instead of Integer. Using Integer is lovely when we can get away with it, since it means not worrying about overflow at all; but in this case using Int instead of 蚂蚁ant加速器安卓下载 yields a huge speedup (some quick and dirty tests show about a factor of 6 speedup on my local machine, and replacing Int with Integer, without changing anything else, makes my solution no longer accepted on Kattis). Of course, this comes with an obligation to think about potential overflow: the cake can be at most units on each side, giving a maximum possible volume of . On a 64-bit machine, that just fits within an Int (坚果加速器下载官网 is approximately ). Since the Kattis test environment is definitely 64-bit, we are good to go. In fact, limits for competitive programming problems are often chosen so that required values will fit within 64-bit signed integers (C++ has no built-in facilities for arbitrary-size integers); I’m quite certain that’s why was chosen as the maximum size of one dimension of the cake.

    安卓永久免费网络加速器

    Next, some utilities for checking whether one Pos is elementwise less than or equal to another, and for taking the elementwise max and min of two Pos values. Checking whether a Box contains a Pos simply reduces to doing two calls to 狸猫加速速器 (again assuming a valid Box with the first corner componentwise no greater than the second).

    posLTE (Pos x1 y1 z1) (Pos x2 y2 z2) = x1 <= x2 && y1 <= y2 && z1 <= z2
    posMax (Pos x1 y1 z1) (Pos x2 y2 z2) = Pos (max x1 x2) (max y1 y2) (max z1 z2)
    posMin (Pos x1 y1 z1) (Pos x2 y2 z2) = Pos (min x1 x2) (min y1 y2) (min z1 z2)
    
    contains :: Box -> Pos -> hi vph加速器下载
    contains (Box lo hi) p = posLTE lo p && posLTE p hi

    To test whether a box is a valid box within a given cake, we test that its corners are in the correct order and fit within the low and high coordinates of the cake.

    valid :: Box -> Box -> Bool
    valid (Box lo hi) (Box c1 c2) = hi vph加速器下载 lo c1 && posLTE c1 c2 && posLTE c2 hi

    How to test whether two given boxes intersect or not? There are probably many ways to do this, but the nicest way I could come up with is to first find the actual Box which represents their intersection, and check whether it has a positive volume (relying on the fact that volume returns 0 for degenerate boxes with out-of-order coordinates). In turn, to find the intersection of two boxes, we just take the coordinatewise max of their lower corners, and the coordinatewise min of their upper corners.

    intersection :: Box -> Box -> Box
    狸猫Ⅴpn安卓 (Box c11 c12) (Box c21 c22) = Box (posMax c11 c21) (posMin c12 c22)
    
    disjoint :: Box -> Box -> Bool
    disjoint b1 b2 = volume (intersection b1 b2) == 0

    The solution

    Finally, we can put the pieces together to write the 狸猫加速速器 function. We simply check that all the given cake parts are valid; that every part contains its corresponding chocolate chip; that every pair of parts is disjoint; and that the sum of the volumes of all parts equals the volume of the entire cake.

    solve :: TC -> Bool
    hi vph加速器下载 (TC{..}) = and
      [ all (valid cake) parts
      , and $ zipWith contains parts chips
      , all (安卓永久免费网络加速器 disjoint) (狸猫加速器安卓版下载 parts)
      , sum (map volume parts) == volume cake
      ]

    极光加速器官方网站

    Actually, there’s still one missing piece: how to compute all possible pairs of parts. The simplest possible thing would be to use a list comprehension like

    [(x,y) | x <- parts, y <- parts]

    but this has problems: first, it includes a pairing of each part with itself, which will definitely have a nonzero intersection. We could exclude such pairs by adding x /= y as a guard, but there is another problem: (p2,p1) is included whenever (p1,p2) is included, but this is redundant since disjoint is commutative. In fact, we don’t really want all pairs; we want all unordered pairs, that is, all sets of size two. We can do that with the below utility function (which I have now added to Util.hs):

    狸猫加速器安卓版 :: [a] -> [(a,a)]
    pairs []     = []
    pairs [_]    = []
    pairs (a:as) = map (a,) as ++ pairs as

    This is accepted, and runs in about 0.91 seconds (the time limit is 2 seconds). However, I was curious whether we are paying anything here for all the list operations, so I wrote the following version, which takes a binary operation for combining list elements, and a Monoid specifying how to combine the results, and directly returns the monoidal result of combining all the pairs, without ever constructing any intermediate lists or tuples at all. It’s sort of like taking the above pairs function, following it by a call to foldMap, and then manually fusing the two to get rid of the intermediate list.

    withPairs :: Monoid r => (a -> a -> r) -> [a] -> r
    withPairs _ []     = mempty
    狸猫加速器安卓版百度云 _ [_]    = mempty
    withPairs f (a:as) = go as
      where
        go []        = withPairs f as
        go (a2:狸猫加速器安卓版百度云) = f a a2 <> go rest

    To use this, we have to change the solve function slightly: instead of

      , all (uncurry disjoint) (狸猫加速器安卓版安装包 parts)

    we now have

      , getAll $ withPairs (\p1 p2 -> All $ disjoint p1 p2) parts

    This version runs significantly faster on Kattis—0.72 seconds as opposed to 0.91 seconds. (In fact, it’s faster than the currently-fastest Java solution (0.75 seconds), though there is still a big gap to the fastest C++ solution (0.06 seconds).) I don’t completely understand why this version is faster—perhaps one of you will be able to enlighten us!

    坚果加速器下载官网

    For next time, we’ll go back to computational geometry: I invite you to solve Cookie Cutters.

    by Brent at June 29, 2024 09:55 PM

    狸猫Ⅴpn安卓

    Mid-Summer Break, Open AI Gym Series!

    We're taking a little bit of a mid-summer break from new content here at MMH. But we have done some extra work in organizing the site! Last week we wrapped up our series on Haskell and the Open AI Gym. We've now added that series as a permanent fixture on the advanced section of the page!

    Here's a quick summary of the series:

    Part 1: Frozen Lake Primer

    The first part introduces the Open AI framework and goes through the Frozen lake example. It presents the core concept of an environment.

    Part 2: Frozen Lake in Haskell

    In the second part, we write a basic version of Frozen Lake in Haskell.

    Part 3: Blackjack

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    Part 5: Generalized Environments

    Now that we've seen the learning process in action, we can start generalizing our games. We'll create an abstract notion of what an Environment is. Just as Python has a specific API for their games, so will we! In true Haskell fashion, we'll represent this API with a type family!

    狸猫加速器安卓版

    In part 6, we'll take our Q-learning process a step further by using TensorFlow. We'll see how we can learn a more general function than we had before. We'll start this process in Python, where the mathematical operations are more clear.

    Part 7: Q-Learning with Tensors in Haskell

    Once we know how Q-Learning works with Python, we'll apply these techniques in Haskell as well! Once you get here, you'd better be ready to use your Haskell TensorFlow skills!

    Part 8: Rendering with Gloss

    In the final part of the series, we'll see how we can use the Gloss library to render our Haskell games!

    You can take a look at the series summary page for more details!

    In a couple weeks, we'll be back, this time with some fresh Rust content! Take a look at our Rust Video Tutorial to get a headstart on that!

    by James Bowen at June 29, 2024 02:30 PM

    Tweag I/O

    Splittable pseudo-random number generators in Haskell: random v1.1 and v1.2

    Pseudo-random number generators (PRNGs) power property tests and Monte Carlo simulations. They are also used to model random behaviour in nature and to initialise machine learning models1. Their performance and quality matter.

    Unfortunately, up to version 1.1, the default PRNG of the random library for Haskell was neither very fast nor very high quality. The 蚂蚁ant加速器安卓下载 fixes this. Random version 1.2 is a collaboration between Dominic Steinitz, Alexey Kuleshevich, and myself, with invaluable support from Alexey Khudyakov and Andrew Lelechenko.

    In this blog post, I will focus on how we ensured that the implementation used in random v1.2 is, indeed, a high quality PRNG.

    Pseudo-random number generators

    A PRNG produces from a seed a sequence of approximately uniformly distributed numbers.

    init :: Seed -> State
    next :: State -> (Output, State)

    This allows us to generate a output sequence x1, x2, x3, … as follows:

    let g0 = init seed
        (x1, g1) = next g0
        (x2, g2) = 蚂蚁ant加速器安卓下载 g1
        (x3, g3) = next g2

    This is not always enough though. Often you may want two or more parallel sequences that are still (approximately) random even when assembled. Such sequences are said to be independent.

    split :: State -> (State, hi vph加速器下载)

    This can arise when you have different threads. But it’s of prime importance in a lazy language like Haskell, since it makes it possible to generate deterministic random numbers lazily. For instance, split is used in QuickCheck’s 安卓永久免费网络加速器.

    An easy implementation of split is to duplicate the current state. But, the two parallel sequences will not be independent: indeed they will be identical. A slightly more sophisticated implementation is to generate the two split states randomly, but this will typically not yield independent sequences either.

    The split function in random up to version 1.1 creates generators that are not independent (#3575, #3620).

    In a 蚂蚁ant加速器安卓下载 comparing the performance of Haskell PRNG implementations, Alexey Kuleshevich found splitmix to be the fastest pure PRNG written in Haskell, making it the top candidate to replace the default PRNG in the proposed new version of random. But it also had to be good enough at generating random sequences.

    In the following, I will go through how we tested the split function in 狸猫加速器安卓版 version 1.1 and splitmix-0.1, which we used for version 1.2, in order to make sure that, while in version 1.1 split generates sequences which are not independent, in version 1.2 split generates independent sequences.

    Legacy and SplitMix.

    The PRNG used by random up to version 1.1 is one of the PRNG algorithms proposed by L’Ecuyer, with an ad hoc split function tacked on without statistical justification. We shall refer to this PRNG as Legacy. Since version 1.2, the PRNG is SplitMix, a PRNG designed from the ground up to be splittable, as implemented in the splitmix package.

    Every PRNG with a finite state is periodic: it will necessarily come back to the same state after a certain number of iterations, called its period. In contrast, long sequences of truly random numbers are unlikely to be periodic. As a result, every PRNG with a finite state is distinguishable from a source of true randomness, at least in theory.

    Legacy produces numbers in the range 御龙之路单机版下载- 全方位下载:2021-6-14 · 御龙之路汉化版是众东方玄幻为背景题材的热血激情仙侠角色扮演游戏,游戏拥有玄幻色彩的画风,精美华丽的画面,激情十足的热血战斗玩法,多人实时在线竞技对战模式,给你带来全新的战[1,2315) and has a period of just under <semantics>261<annotation encoding="application/x-tex">2^{61}</annotation></semantics>261; SplitMix produces numbers in the range 深渊冒险安卓版下载- 全方位下载:2021-2-17 · 熊猫加速器安卓版 熊猫加速器 最新版 小米运动app 小米运动官方下载 小米运动手机版 小米运动安卓版 ... 睡你妹闹钟手机版 win7 语言包下载 win7中文语言包 win7系统语言包 狸猫转换器官方免费版 狸猫 ...[0,264) and has a period of exactly 狸猫网络助手_狸猫网络助手安卓版下载_软吧:2021-8-9 · 狸猫网络助手安卓版免费下载,狸猫网络助手,一款精心打造的手机网络加速应用,针对线路服务类型匹配为用户提供专属的线路,打造个人专属的网络环境。 ps:该软件暂无安卓版下载 主要功能:【一键连接】【网络加速】【每日签到】 软件特点:264.

    Considering the output range and period of Legacy and SplitMix, we see something interesting: Legacy’s period of roughly <semantics>261<annotation encoding="application/x-tex">2^{61}</annotation></semantics>261 contains its range of roughly <semantics>231<annotation encoding="application/x-tex">2^{31}</annotation></semantics>231 numbers many times over. For SplitMix, on the other hand, the output range and period are both <semantics>264<annotation encoding="application/x-tex">2^{64}</annotation></semantics>264. SplitMix in fact generates each output in <semantics>[0,264)<annotation encoding="application/x-tex">[0, 2^{64})</annotation></semantics>[0,264) precisely once.

    We actually expect repetitions much more often than that: observing <semantics>264<annotation encoding="application/x-tex">2^{64}</annotation></semantics>264 numbers where each number in the range <semantics>[0,264)<annotation encoding="application/x-tex">[0, 2^{64})</annotation></semantics>[0,264) occurs exactly once is vanishingly unlikely in a truly random sequence of numbers. This is is a manifestation of the 狸猫加速器安卓版下载.

    And indeed, SplitMix 狸猫Ⅴpn安卓 that checks specifically that repetitions in the output sequence occur as frequently as expected according to the Birthday problem.

    How much of an issue is this? It depends on the application. Property tests, for example, don’t benefit from repetitions. And if, as is common, you only need values in a subrange of the full <semantics>[0,264)<annotation encoding="application/x-tex">[0, 2^{64})</annotation></semantics>[0,264), you will have many repetitions indeed.

    Reproducible test environment

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    The closest thing we have are collections of tests, often called test batteries, which empirically check if a PRNG’s output sequence has certain properties expected of a random number sequence — like the distance between repetitions, the famous Birthday problem mentioned in the previous section.

    To make it easy to test PRNGs, we created a repository with a Nix shell environment to run the most well-known PRNG test batteries.

    hi vph加速器下载

    Nix is required to use the test environment. The easiest way to enter it is using this command:

    $ nix-shell http://github.com/tweag/random-quality/archive/master.tar.gz

    You can test that it works by running PractRand on a truly terrible “PRNG”: /dev/zero, which outputs zero bytes. The PractRand binary is called RNG_test, passing “stdin32” makes it read unsigned 32-bit integers from standard input:

    $ RNG_test stdin32 < /dev/zero

    PractRand should immediately show a large number of test failures. Don’t use /dev/zero as a source of random numbers!

    PRNGs

    While this post is about testing Legacy and SplitMix, the environment we created can test any PRNG written in any language. To demonstrate this, we have included programs in C, Python, Perl and Lua, each using the language’s standard PRNG to output a stream of unsigned 32-bit integers2. To see the source code of the generator scripts, run e.g. cat $(which generate.pl).

    You can run these programs as generate.c, generate.py, 坚果加速器下载官网 and 快喵ⅴpn破解版 within the Nix environment.

    All the statistical tests in this environment consume binary input. To convert the hexadecimal 32-bit numbers to binary, pipe them through 狸猫加速器安卓版百度云, e.g. $ generate.lua | xxd -r -p.

    Test batteries

    The environment contains a collection of PRNG test batteries. All of them either support reading from standard input or were wrapped to support this. As a result, all the tests can be run as follows:

    • To test a system-provided randomness source, run $ $TEST < $SOURCE, e.g. 狸猫突击队app免费下载_狸猫突击队安卓最新版1.3.0.0下载 ...:2021-1-4 · 多特安卓下载为您提供狸猫突击队 1.3.0.0安卓版,手机版下载,狸猫突击队 1.3.0.0apk免费下载安装到手机.同时支持便捷的二维码扫描下载功能!
    • To test a program that generates pseudo-random numbers, run 狸猫加速器安卓版安装包, e.g. $ generate.py | xxd -r -p | RNG_test stdin32

    The test batteries include:

    • 狸猫加速速器, the most recent PRNG test in the collection. It is adaptive: by default, it will consume random numbers until a significant test failure occurs.

      Example invocation: $ RNG_test stdin32

      Help: 狸猫加速器安卓版下载在哪里

    • 狸猫加速器安卓版下载在哪里, containing the test batteries SmallCrush (-s), Crush (-c) and BigCrush (-b). We have wrapped it in the executable TestU01_stdin, which accepts input from standard input.

      Example invocation: 狸猫加速速器

      Help: $ TestU01_stdin -h

    For a full list, see the README.

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    These test batteries test the randomness of individual sequences. But we want to test whether sequences generated by splits are independent or not, which involves at least two sequences at a time.

    Rather than coming up with new test batteries dedicated to split, 狸猫加速器安卓版 proposes four sequences built of a combination of next and 狸猫加速器安卓版. These “split sequences” are traditional (non-splittable) PRNGs built off next and split. The split sequences are then fed into regular PRNG tests.

    Here is the API for splittable PRNGs again:

    init :: Seed -> State
    next :: State -> (Output, 狸猫加速器安卓版下载)
    split :: State -> (State, State)

    A naming convention for the result of 狸猫加速器安卓版下载在哪里 will come in handy. Let’s say that a generator g is split into gL and gR (for “left” and “right”), that is, (gL, gR) = split g. Then we get gLL and gLR by applying split to gL via (gLL, gLR) = split gL, etc. Let’s also call rX the output of next gX, i.e. (rLL, _) = next gLL.

    This lets us express concisely the first of the sequences proposed by Schaathun:

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    This sequence recurses into the right generator returned by split while outputting a number generated by the left generator. We can visualise the sequence as a binary tree where the nodes are split operations. Asterisk (*) stands for a generated output, ellipsis (…) is where the next iteration of the sequence continues:

         split
         /  \
        *  split
           /  \
          *    …

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    Sequence S_R: given g, output rR; repeat for g = gL
    
         split
         /  \
       split *
       /  \
      …    *
    Sequence S_A: given g, output rR, rLL; repeat for g = gLR
    
         split
         /  \
       split *
       /  \
      *    …
    Sequence S: given g, output rRLL, rRLR, rRRL, rRRR; repeat for g = gL
    
              split
             /     \
           …      split
                 /     \
            split      split
            /  \       /  \
           *    *     *    *

    We implemented these sequences in a 狸猫加速器安卓版百度云 which uses Legacy or SplitMix as the underlying PRNG implementation and outputs the random numbers on stdout.

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    The following table shows our test results. We tested with PractRand and TestU01. The sequences S, S_A, S_L and S_R are those discussed above.

    The test battery output is usually a p-value per test indicating the probability of the input being random. We summarise the results as “Fail” or “Pass” here. Each table cell links to the full result, which includes the full command used to run them. Since the seeds of the sequences are fixed, you should be able to reproduce the results exactly.

    PRNG / sequence PractRand result TestU01 result
    Legacy / S Fail (8 MiB) Fail (SmallCrush)
    SplitMix / S Pass (2 TiB) 蚂蚁ant加速器安卓下载 (Crush)
    Legacy / S_A Pass (1 TiB) Pass (Crush)
    SplitMix / S_A Pass (2 TiB) Pass (BigCrush)
    Legacy / S_L Fail (8 GiB) Fail (Crush)
    SplitMix / S_L Pass (2 TiB) 狸猫Ⅴpn安卓 (BigCrush)
    Legacy / S_R Fail (64 GiB) Fail (Crush)
    SplitMix / S_R 狸猫Ⅴpn安卓 (2 TiB) Pass (BigCrush)

    Conclusion

    In this post, I’ve described how we’ve made sure that the PRNG used in the newly released version 1.2 of the random library is of high quality. The legacy PRNG used up to version 1.1 had a poor quality implementation of the split primitive, which we wanted to fix.

    To this effect, we created a general-purpose reproducible PRNG testing environment, which makes it easy to run the most commonly used PRNG tests using Nix with a minimal amount of setup work. For testing, we used split sequences to reduce the quality of split to the quality of a traditional PRNG.

    For further details, check the reddit announcement for random 1.2. And don’t hesitate to use our repository to setup your own PRNG testing.

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    Melissa O’Neill’s website on PCG, a family of PRNGs, contains a wealth of information on PRNGs and PRNG testing in general.

    Peter Occil’s website is also a great starting point for further reading on PRNGs and PRNG testing, in particular the pages 极光加速器官方网站 and on PRNG functions.


    1. Security-relevant applications also often require random data. They should not rely on the kinds of PRNGs discussed in this blog post. Instead, security-relevant applications should use cryptographically-secure pseudo-random number generators that have been vetted by the cryptographic community for this purpose.

    2. In the case of C, if RAND_MAX is not equal to 2^32, the program will not output the full 32-bit range and will thus fail statistical tests. The other programs should in theory output numbers in the correct range.

    June 29, 2024 12:00 AM

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    Rust at FP Complete, 2024 update

    At FP Complete, we have long spoken about the three pillars of a software development language: productivity, robustness, and performance. Often times, these three pillars are in conflict with each other, or at least appear to be. Getting to market quickly (productivity) often involves skimping on quality assurance (robustness), or writing inefficient code (performance). Or you can write simple code which is easy to test and validate (productivity and robustness), but end up with a slow algorithm (performance). Optimizing the code takes time and may introduce new bugs.

    For the entire history of our company, our contention has been that while some level of trade-off here is inevitable, we can leverage better tools, languages, and methodologies to improve our standing on all of these pillars. We initially focused on Haskell, a functional programming language that uses a strong type system and offers decent performance. We still love and continue to use Haskell. However, realizing that code was only half the battle, we then began adopting DevOps methodologies and tools.

    We've watched with great interest as the Rust programming language has developed, matured, and been adopted in industry. Virtually all major technology companies are now putting significant effort behind Rust. Most recently, Microsoft has been quite publicly embracing Rust.

    In this post, I wanted to share some thoughts on why we're thrilled to see Rust's adoption in industry, what we're using Rust for at FP Complete, and give some advice to interested companies in how they can begin adopting this language.

    Why Rust?

    We're big believers in using the computer itself to help us write better code. Some of this can be done with methodologies like test-driven development (TDD). But there are two weak links in the chain of techniques like TDD:

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    • It's possible to ignore these test failures and ship broken code

    The latter might sound contrived, but we've seen it happen in industry. The limitations of testing are well known, and we've 蓝灯vp:1 天前 · 蓝灯lantern破解版vip无限流量及各版本下载 | 路由器博客 [图文] 网站首页 >游戏助手>蓝灯VIP破解版v3.6.6破解内购专业版 蓝灯VIP破解版v3.6.6破解内购专业版 蓝灯的Android版本怎么用_ 点中间的按钮.选择确定.翻墙成功的话会在通知栏有一个小钥匙的标志.. And don't get me wrong: testing is an absolutely vital part of software development, and you should be doing more of it!

    But industry experience has shown us that many bugs slip through testing. Perhaps the most common and dangerous class of bug is memory safety issues. These include buffer overruns, use-after-free and double-free. What is especially worrying about these classes of bugs is that, typically, the best case scenario is your program crashing. Worst case scenario includes major security and privacy breaches.

    The industry standard approach has been to bypass these bugs by using managed languages. Managed languages bypass explicit memory management and instead rely on garbage collection. This introduces some downsides, latency being the biggest one. Typically, garbage collected languages are more memory hungry as well. This is the typical efficiency-vs-correctness trade-off mentioned above. We've been quite happy to make that trade-off ourselves, using languages like Haskell and accepting some level of performance hit.

    Rust took a different approach, one we admire deeply. By introducing concepts around ownership and borrowing, Rust seeks to drastically reduce the presence of memory safety errors, without introducing the overhead of garbage collection. This fits completely with FP Complete's mindset of using better tools when possible.

    The downside to this is complexity. Understanding ownership can be a challenge. But see below for information on how to get started with Rust. This is an area where FP Complete as a company, and I personally, have taken a lot of interest.

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    • Strong typing
    • Sum types (aka enums) and pattern matching
    • Explicit error handling, but with a beautiful syntax
    • Async syntax
    • Functional style via closures and Iterator pipelines

    In other words: Rust has fully embraced the concepts of using better approaches to solve problems, and to steal great ideas that have been tried and tested. We believe Rust has the potential to drastically improve software quality in the world, and lead to more maintainable solutions. We think Rust can be instrumental in solving the global software crisis.

    Rust at FP Complete

    We've taken a three-pronged approach to Rust at FP Complete until now. This has included:

    • Producing educational material for both internal and external audiences
    • Using Rust for internal tooling
    • Writing product code with Rust

    The primary educational offering we've created is our Rust Crash Course, which we'll provide at the end of this post. This course has been honed to address the most common pitfalls we've seen developers hit when onboarding with Rust.

    Also, as a personal project, I decided to see if Rust could be taught as a first programming language, and I think it can.

    For internal tooling and product code, we always have the debate: should we use Rust or Haskell. We've been giving our engineers more freedom to make that decision themselves in the past year. Personally, I'm still more comfortable with Haskell, which isn't really surprising: I've been using Haskell professionally longer than Rust has existed. But the progress we're seeing in Rust—both in the library ecosystem and the language itself—means that Rust becomes more competitive on an almost monthly basis.

    At this point, we have some specific times when Rust is a clear winner:

    • When performance is critical, we prefer Rust. Haskell is usually fast enough, but microoptimizing Haskell code ends up taking more time than writing it in Rust.
    • For client-side code (e.g., command line tooling) we've been leaning towards Rust. Overall, it has better cross-OS support than Haskell.
    • There are some domains that have much better library coverage in Rust than in Haskell, and then we'll gravitate towards them. (The same applies in the other direction too.)
    • And as we're engineers who like playing with shiny tools, if someone wants to have extra fun, Rust is usually it. In most places in the world, Haskell would probably be considered the shiny toy. FP Complete is pretty exceptional there.

    We're beginning to expand to a fourth area of Rust at FP Complete: consulting services. The market for Rust has been steadily growing over the past few years. We believe at this point Rust is ready for much broader adoption, and we're eager to help companies adopt this wonderful language. If you're interested in learning more, please contact our consulting team for more information.

    Getting started

    How do you get started with a language like Rust? Fortunately, the tooling and documentation for Rust is top notch. We can strongly recommend checking out the Rust homepage for guidance on installing Rust and getting started. The freely available Rust book is great too, covering many aspects of the language.

    That said, my recommendation is to check out our Rust Crash Course eBook (linked below). We've tried to focus this book on answering the most common questions about Rust first, and get you up and running quickly.

    If you're interested in getting your team started with Rust, you may also want to reach out to us for information on our training programs.

    Want to read more about Rust? Check out the FP Complete Rust homepage.

    Want to learn more about FP Complete offerings? Please reach out to us any time.

    June 29, 2024 12:00 AM

    快喵ⅴpn破解版

    Ken T Takusagawa

    [orfveorb] More Generalized Fermat Primes

    Consider numbers of the form a^2^n + b^2^n.  For each exponent n, we give the first 20 prime numbers of that form in ascending order.  Primes of this form is known as Generalized Fermat Primes, which is confusingly a generalization of another form (b restricted to 1) also known as Generalized Fermat Primes.

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    a^2^1 + b^2^1 : [1,1] [2,1] [3,2] [4,1] [5,2] [6,1] [5,4] [7,2] [6,5] [8,3] [8,5] [9,4] [10,1] [10,3] [8,7] [11,4] [10,7] [11,6] [13,2] [10,9] [12,7]

    a^2^2 + b^2^2 : [1,1] [2,1] [3,2] [4,1] [4,3] [5,2] [5,4] [6,1] [7,2] [7,4] [7,6] [8,3] [8,5] [9,2] [9,8] [10,7] [11,2] [11,4] [11,6] [10,9] [13,4]

    a^2^3 + b^2^3 : [1,1] [2,1] [4,1] [6,5] [10,3] [12,7] [13,2] [13,8] [14,3] [15,8] [16,9] [16,13] [17,4] [19,4] [18,17] [20,7] [20,17] [21,2] [21,8] [22,3] [22,5]

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    蓝灯vp:1 天前 · 蓝灯lantern破解版vip无限流量及各版本下载 | 路由器博客 [图文] 网站首页 >游戏助手>蓝灯VIP破解版v3.6.6破解内购专业版 蓝灯VIP破解版v3.6.6破解内购专业版 蓝灯的Android版本怎么用_ 点中间的按钮.选择确定.翻墙成功的话会在通知栏有一个小钥匙的标志.

    a^2^6 + b^2^6 : [1,1] [11,8] [13,6] [16,7] [17,14] [29,12] [32,3] [32,27] [37,2] [38,7] [38,23] [39,4] [41,10] [49,6] [51,14] [52,3] [53,2] [55,4] [55,36] [58,21] [60,47]

    a^2^7 + b^2^7 : [1,1] [27,20] [32,31] [38,37] [44,25] [45,38] [47,10] [47,14] [47,24] [53,10] [54,47] [62,11] [66,65] [68,31] [69,40] [77,38] [78,53] [84,13] [85,6] [87,82] [88,21]

    a^2^8 + b^2^8 : [1,1] [14,5] [14,9] [16,3] [34,25] [38,13] [43,34] [50,17] [52,25] [54,31] [65,54] [68,49] [70,9] [73,44] [76,73] [77,12] [83,26] [83,48] [86,85] [87,86] [88,85]

    a^2^9 + b^2^9 : [1,1] [13,2] [29,22] [35,24] [38,35] [44,3] [46,1] [60,59] [68,61] [89,62] [92,89] [96,17] [99,94] [115,8] [115,18] [116,99] [117,10] [119,54] [124,19] [136,25] [143,68]

    a^2^10 + b^2^10 : [1,1] [47,26] [56,39] [67,28] [68,59] [72,47] [80,43] [82,79] [84,71] [103,32] [104,9] [114,97] [115,6] [119,86] [128,93] [134,49] [144,125] [146,107] [149,122] [157,22] [162,53]

    a^2^11 + b^2^11 : [1,1] [22,3] [43,2] [78,41] [82,9] [101,18] [106,29] [109,18] [150,1] [150,7] [163,78] [188,15] [209,142] [211,190] [236,101] [254,109] [259,76] [263,88] [264,71] [271,2] [281,52]

    a^2^12 + b^2^12 : [1,1] [53,2] [53,48] [122,69] [137,10] [153,40] [155,66] [215,98] [221,198] [228,211] [251,174] [260,77] [269,142] [281,188] [310,169] [311,30] [312,311] [317,74] [330,47]

    a^2^13 + b^2^13 : [1,1] [72,43] ... [257,52]

    Exponents 0 through 11 took 2.5 hours total.  The largest prime in that batch, 281^2048 + 52^2048, has size 16660 bits.

    The short list for exponent 12 is the result of 24 hours of computing.  The largest prime on that line, 330^4096 + 47^4096, has size 34269 bits.

    The first two primes for exponent 13 took 12 hours to find.  72^8192 + 43^8192 has size 50545 bits.  The third listed prime, 257^8192 + 52^8192 (65583 bits), was found when we accidentally started searching at the wrong start point.  There is an unsearched gap indicated by ellipses.

    We also searched for primes of the form (a^2^n + b^2^n)/2.  For exponents greater than 0, this requires both a and b to be odd, a parity combination not possible above.

    (a^2^0 + b^2^0)/2 : [2,2] [3,1] [4,0] [3,3] [4,2] [5,1] [6,0] [5,5] [6,4] [7,3] [8,2] [9,1] [10,0] [7,7] [8,6] [9,5] [10,4] [11,3] [12,2] [13,1] [14,0]

    (a^2^1 + b^2^1)/2 : [2,0] [3,1] [5,1] [5,3] [7,3] [7,5] [9,1] [9,5] [11,1] [11,5] [13,3] [13,5] [11,9] [13,7] [15,1] [15,7] [17,3] [17,5] [15,11] [19,1] [19,5]

    (a^2^2 + b^2^2)/2 : [3,1] [5,1] [5,3] [7,1] [9,5] [9,7] [11,1] [11,7] [11,9] [13,1] [13,3] [13,5] [13,11] [15,7] [15,11] [17,1] [17,3] [17,5] [17,7] [17,11] [17,13]

    (a^2^3 + b^2^3)/2 : [5,3] [9,1] [11,3] [13,1] [13,9] [17,3] [19,17] [23,3] [25,19] [27,7] [27,11] [29,5] [29,17] [29,23] [29,27] [31,5] [31,7] [31,11] [31,27] [31,29] [33,1]

    (a^2^4 + b^2^4)/2 : [3,1] [7,5] [9,1] [11,7] [13,5] [15,13] [17,3] [19,3] [23,5] [23,19] [25,11] [25,13] [27,5] [27,25] [29,1] [31,23] [31,25] [31,27] [35,9] [35,13] [35,31]

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    (a^2^6 + b^2^6)/2 : [3,1] [19,11] [33,19] [35,1] [41,17] [41,37] [43,29] [51,1] [51,49] [55,27] [59,51] [61,19] [65,17] [71,23] [75,23] [75,37] [81,67] [83,61] [85,1] [89,49] [91,81]

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    (a^2^9 + b^2^9)/2 : [35,9] [41,17] [51,13] [67,15] [81,37] [83,37] [89,83] [101,3] [113,91] [115,79] [123,47] [123,85] [127,51] [127,107] [131,51] [135,79] [137,31] [149,87] [155,39] [155,43] [159,13]

    (a^2^10 + b^2^10)/2 : [67,57] [77,15] [79,7] [93,85] [95,61] [117,29] [151,33] [181,71] [181,155] [183,37] [185,147] [191,111] [193,11] [199,55] [211,29] [211,113] [215,21] [223,73] [223,83] [229,93] [229,185]

    (a^2^11 + b^2^11)/2 : [75,49] [109,69] [109,81] [167,75] [193,155] [195,41] [227,53] [249,107] [259,223] [275,39] [281,107] [299,35] [311,117] [333,287] [335,239] [349,259] [351,239] [353,125] [409,357] [431,39] [431,167]

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    Haskell source code here.  We use Data.List.Ordered.mergeBy to merge infinite lists to generate numbers in order for primality testing.  The code is generalized to handle an arbitrary number of terms, a^2^n + b^2^n + c^2^n + ..., though we only investigated 2 terms.  The tricky bit of code, in the cchildren function, avoids generating the same number multiple times.  This saves an exponential amount of work.

    Update (2024-06-28): minor wordsmithing.

    by Unknown (noreply@blogger.com) at June 28, 2024 07:22 AM

    June 27, 2024

    Chris Smith 2

    深渊冒险安卓版下载- 全方位下载:2021-2-17 · 熊猫加速器安卓版 熊猫加速器 最新版 小米运动app 小米运动官方下载 小米运动手机版 小米运动安卓版 ... 睡你妹闹钟手机版 win7 语言包下载 win7中文语言包 win7系统语言包 狸猫转换器官方免费版 狸猫 ...

    I’ve made another change to make the CodeWorld environment more useful for general Haskell programming.

    What?

    Here is the calculator from http://reflex-frp.org/tutorial:

    Here is the calculator running inside CodeWorld:

    极光加速器官方网站

    You can also use Miso from CodeWorld:

    CodeWorld

    You can even build your own HTML with ghcjs-dom, jsaddle, or even just the JavaScript FFI. For example, here’s how you can incorporate the diagrams library into CodeWorld:

    CodeWorld

    I’d love to add anything else that’s useful. The framework must be usable in an otherwise blank page, so frameworks that expect lost of preexisting HTML, CSS, images, etc. won’t work out so well. If you would like to use CodeWorld with a different client-side web framework or library that meets this description, just leave a comment and let me know, or send a GitHub pull request to modify this file and add it.

    蚂蚁vp(永久免费)

    Setting up a development environment with GHCJS can be a real pain. For serious work, nix is emerging as the standard tooling, but nix is the most complex build tool available for Haskell. Building GHCJS with cabal or stack is possible, but the setup takes hours. Entire tooling projects (see Obelisk) have been born out of the goal of helping make it easier to get up and running with a GHCJS client-side web project.

    But what if you’re visiting a friend and want to show them what Haskell can do? They don’t have GHC installed, and you don’t want to start your pitch by walking them through an hour of software setup. Or maybe you’re teaching a survey class on different applications of functional programming. Maybe you want to post something to Twitter, or your blog, and let readers tinker and experiment with it easily?

    CodeWorld is the answer. Just write code, click Run, and voila! Want to share your code? Just copy and paste the URL and the people you share it with can see, edit, and run their modified versions of your code. Zero installation, no down time.

    How?

    This was actually a pretty easy change to make, once I realized I should do it. It used to be that the CodeWorld environment ran applications in an HTML page with a giant Canvas, and the codeworld-api package looked up that canvas and drew onto it. After this change, the CodeWorld environment runs applications in a document with an empty body. Any client-side framework, whether it’s codeworld-api, reflex-dom, etc., can add its own elements to the document. The codeworld-api package now dynamically adds its canvas to the document before drawing to it.

    There were a few more details to work out. I don’t want the output page to pop up when you’re only running console-mode code in the CodeWorld environment, so there’s a trick with MutationObserver to detect when the running app modifies its own document, and change the parent UI to show it if so.

    Implementation details are documented at http://github.com/google/codeworld/issues/1362, if you’re excessively curious.

    by Chris Smith at June 27, 2024 01:23 AM

    Thanks, Paul.

    Thanks, Paul. Glad you've found it useful. Good news: I added smallcheck to the available package list.

    by Chris Smith at June 27, 2024 12:33 AM

    June 26, 2024

    狸猫Ⅴpn安卓

    Teaching quadratic functions

    Teaching quadratic expressions

    Quadratic expressions are the first category of non-linear expressions that algebra students typically study in detail. How do you motivate quadratics as an interesting object of study?

    There are a few answers to this question. For example:

    • Khan Academy starts with parabolas. After a hint that the shape of a parabola has to do with ballistics and the path of a thrown object, they go on to describe the shape of the graph in detail, including the vertex, the axis of symmetry, and the x and y intercepts.
    • EngageNY starts with algebraic techniques. Specifically, it is concerned with distributing and factoring. Engage goes out of its way to avoid giving any early significance to quadratics, instead focusing on the more general category of polynomials, and solving problems with polynomials using factoring. Quadratics are presented as a special case, and associated set of tricks, for that general problem.

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    Reviewing linear expressions

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    First, they must understand that an expression represents a number. The specific number that it represents, though, may change depending on the values of the variables used in that expression.

    I find students often get confused about the meaning of what they are doing as soon as x and y coordinates get involved. Suddenly they think the meaning of a linear expression is a line. (It’s the other way around: a line is one of several ways to represent a linear relationship!) This confusion is reinforced by terms like slope and especially y-intercept, which talk about the graph instead of the relationship between quantities. This has consequences: students who learn this way can answer questions about graphs, but don’t transfer that understanding to other changing values.

    For this reason, I prefer to leave x and y out of it, and talk in terms of t, which can represent either time or just a generic parameter, instead. An expression like mt + b represents a number, m represents the rate of change of that number (relative to change in t), and b represents the starting value of that number (when t = 0). That m is also the slope a a graph, and b the y-intercept of the graph, is a secondary meaning.

    Students should also understand that the defining characteristic of a linear expression is that it changes at a constant rate. (Specifically, that rate is m.)

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    To reach non-linear functions, one simply changes the assumption of the constant rate of change, instead using another linear expression for the rate of change.

    The resulting expression looks like: (m t + v) t + b. The rate of change is now the entire linear expression: m t + b. Now students can dig into the rate of change, and they will see that it has its own initial value and its own rate of change. (There’s one important caveat, though, discussed in the next paragraph.) There’s also just one quick application of the distributive property between this form and the more popular m t² + v t + b. But this time, the meanings of the coefficients are front and center.

    Here’s the caveat: m does not represent the acceleration, or change in the instantaneous rate. Instead, it represents the change in the 安卓永久免费网络加速器 rate so far. A bit of guided exploration can clarify that this must be the case: to decide how far something has traveled, you need to know its average speed, not its speed right this moment. The starting rate is v. The rate at time t is a t + v (where a is the acceleration). That means the average rate so far is the sum of these, divided by 2, or 0.5 a t + v, so m is only half of the instantaneous acceleration.

    If a vehicle is accelerating, the distance it travels is related to its average speed.

    The upshot of this is that if students accept that a linear expression is the simplest kind of smooth change, then a quadratic expression is the simplest kind of smooth non-linear change!

    What next?

    Of course, once the importance of quadratic expressions is established, it’s still important to talk about the parabolas that appear in their graphs. It’s still important to talk about techniques for solving them. It’s important to talk about situations, such as trajectories of thrown objects, where they come up a lot. But as you do this, students will hopefully understand this as talking 狸猫加速器安卓版安装包 an idea that has a fundamentally important meaning. They aren’t studying quadratics because parabolas are an interesting shape or because the quadratic formula is so cool; they are studying them because once you need to talk about non-linear change, quadratics are the simplest model for doing that.

    If you are the whimsical sort, though, you might notice one more connection. The choice of inserting a linear expression for rate of change was the simplest option, but ultimately arbitrary. In fact, any continuous non-linear function can be written as f(t) = a(t) 狸猫加速器安卓版百度云, if a(t) is a function giving the 蚂蚁ant加速器安卓下载 rate of change of f(t) over the range from t = 0 to its current value. How could one find such a value for a(t)?

    In calculus, students will learn that the derivative of a function gives the instantaneous rate of change of a function at any point in time. We want a(t), then to represent the average value of that derivative. That integrals are so closely related to average values of a function over a range of input is less well-understood by early calculus students. Again, it’s more popular to present these ideas in terminology about areas, that confuse the graph representation for the fundamental meaning. But in fact, a(t) t is precisely the integral (specifically: the definite integral evaluated from 0 to t) of the derivative. A constant factor is lost by taking the derivative, so b recovers that detail. Everything fits nicely together.

    You wouldn’t get into this with an algebra class, but it’s an interesting follow-on.

    by Chris Smith at June 26, 2024 09:41 PM

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    For the past 3 years I’ve been managing the Testing + Verification org at Facebook London, a group of teams that build bug finding tools, focusing on test infrastructure, dynamic analysis, automated test generation, type systems and static analysis.

    Now, I’m switching track to a software engineering role at Facebook, in the same organization. I’m interested in bug prevention strategies when you have a very large scale, highly automated CI system. Given all the great tools we have to find bugs, how do you best integrate them into development processes, particularly when there are thousands of engineers in the loop.

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    ZuriHac 2024 Advanced Track Materials

    We had a lot of fun at ZuriHac this year, and are very grateful for the many attendees of our two Advanced Track lectures on “Datatype-generic programming” and “Haskell and Infosec”.

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    The videos of our sessions as well as the materials used in them are available online, so those who could not attend during the event itself can still do so by following the links below.

    Datatype-Generic Programming (by 狸猫加速器安卓版安装包)

    Watch video on YouTubeRead lecture notes on GithubRepository with source code

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    In this workshop, we focus on the ideas at the core of two popular approaches to generic programming: 狸猫Ⅴpn安卓 and generics-sop. Both can be difficult to understand at first. We build simpler versions of both approaches to illustrate some of the design decisions taken. This exploration will lead to a better understanding of the trade-offs and ultimately also make using these libraries easier.

    This presentation involves various type-level programming concepts such as type families, data kinds, GADTs and higher-rank types. It’s not a requirement to be an expert in using these features, but I do not focus on explaining them in detail either; so having some basic familiarity with the syntax and semantics is helpful.

    Haskell and Infosec (by 坚果加速器下载官网)

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    In this workshop, we look at Haskell from an information security point of view. How do security vulnerabilities such as SQL Injection (SQLi) or Cross-Site Scripting (XSS) work? How does a hacker exploit them? What can we, as Haskell programmers, do to prevent them, and how can Haskell help us with that? And what principles can we extract from this to develop more security-aware coding habits?

    No knowledge of or experience with information security is required for this course, but participants are expected to have a working knowledge of practical Haskell. If you can write a simple web application with, e.g., Scotty, you should be fine.

    Other ZuriHac videos

    Of course, there was more to ZuriHac than just the Advanced Track. If you haven’t yet, you might want to have a look at the YouTube playlist, which also contains all the keynotes as well as the lectures of the GHC track.

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    If you are interested in our courses or other services, check our Training page, Services page, or just send us an email.

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    In my previous post (apologies it has been so long!) I challenged you to solve Vacuumba, which asks us to figure out where a robot ends up after following a sequence of instructions. Mathematically, this corresponds to adding up a bunch of vectors, but the interesting point is that the instructions are always relative to the robot’s current state, so robot programs are imperative programs.

    Vector basics

    The first order of business is to code up some primitives for dealing with (2D) vectors. I have accumulated a lot of library code for doing geometric stuff, but it’s kind of a mess; I’m using this as an opportunity to clean it up bit by bit. So there won’t be much code at first, but the library will grow as we do more geometry problems. The code so far (explained below) can be found in the comprog-hs repository.

    First, a basic representation for 2D vectors, the zero vector, and addition and subtraction of vectors.

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    module Geom where
    
    ------------------------------------------------------------
    -- 2D points and vectors
    
    data V2 s = V2 !s !s deriving (Eq, Ord, Show)
    type V2D  = V2 Double
    
    instance Foldable V2 where
      foldMap f (V2 x y) = f x <> f y
    
    zero :: Num s => V2 s
    zero = V2 0 0
    
    -- Adding and subtracting vectors
    (^+^), (^-^) :: Num s => V2 s -> V2 s -> V2 s
    V2 x1 y1 ^+^ V2 x2 y2 = V2 (x1+x2) (y1+y2)
    V2 x1 y1 ^-^ V2 x2 y2 = V2 (x1-x2) (y1-y2)

    A few things to point out:

    • The V2 type is parameterized over the type of scalars, but we define V2D as a synonym for V2 Double, which is very common. The reason for making V2 polymorphic in the first place, though, is that some problems require the use of exact integer arithmetic. It’s nice to be able to share code where we can, and have the type system enforce what we can and can’t do with vectors over various scalar types.

    • For a long time I just represented vectors as lists, type V2 s = [s]. This makes implementing addition and subtraction very convenient: for example, 狸猫加速器安卓版下载. Although this has worked just fine for solving many geometry problems, I have recently been reminded that having lots of small lists can be bad for performance. As long as we’re making a library anyway we might as well use a proper data type for vectors!

    • Elsewhere I have made a big deal out of the fact that vectors and points ought to be represented as separate types. But in a competitive programming context I have always just used a single type for both and it hasn’t bit me (yet!).

    • The Foldable instance for V2 gets us toList. It also gets us things like sum and maximum which could occasionally come in handy.

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    The other thing we are going to need for this problem is angles.

    ------------------------------------------------------------
    -- Angles
    
    newtype Angle = A Double  -- angle (radians)
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    fromDeg d = A (d * pi / 180)
    
    fromRad :: Double -> 狸猫加速器安卓版下载在哪里
    fromRad = A
    
    toDeg :: Angle -> Double
    toDeg (A r) = r * 180 / pi
    
    toRad :: Angle -> Double
    toRad (A r) = r
    
    -- Construct a vector in polar coordinates.
    fromPolar :: Double -> Angle -> V2D
    fromPolar r θ = rot θ (V2 r 0)
    
    -- Rotate a vector counterclockwise by a given angle.
    rot :: Angle -> V2D -> V2D
    rot (A θ) (V2 x y) = V2 (cos θ * x - sin θ * y) (sin θ * x + cos θ * y)
    

    Nothing too complicated going on here: we have a type to represent angles, conversions to and from degrees and radians, and then two uses for angles: a function to construct a vector in polar coordinates, and a function to perform rotation.

    Incidentally, one could of course define type Angle = Double, which would be simpler in some ways, but after getting bitten several times by forgetting to convert from degrees to radians, I decided it was much better to use a newtype and entirely prevent that class of error.

    Solving Vacuumba

    Now we just put the pieces together to solve the problem. First, some imports:

    {-# LANGUAGE FlexibleContexts #-}
    {-# LANGUAGE RecordWildCards  #-}
    
    import           Control.Arrow
    极光加速器官方网站           Control.Monad.State
    import qualified Data.Foldable       as F
    import           Text.Printf
    
    import           Geom
    狸猫加速器安卓版下载           Scanner

    We make a data type for representing robot instructions, and a corresponding Scanner. Notice how we are forced to use fromDeg to convert the raw input into an appropriate type.

    data Instr = I { turn :: Angle, dist :: Double }
    
    狸猫加速器安卓版百度云 :: Scanner Instr
    instr = I <$> (fromDeg <$> double) <*> double

    The high-level solution then reads the input via a 狸猫加速器安卓版百度云, solves each scenario, and formats the output. The output is a V2D, so we just convert it to a list with 快喵ⅴpn破解版 and use printf to format each coordinate.

    hi vph加速器下载 = interact $
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      map (solve >>> 坚果加速器下载官网 >>> map (printf "%.6f") >>> unwords) >>> unlines

    Our solve function needs to take a list of instructions, and output the final location of the robot. Since the instructions can be seen as an imperative program for updating the state of the robot, it’s entirely appropriate to use a localized State computation.

    First, a data type to represent the robot’s current state, consisting of a 2D vector recording the position, and an angle to record the current heading. initRS records the robot’s initial state (noting that it starts out facing north, corresponding to an angle of as measured clockwise from the positive -axis).

    data RobotState = RS { pos :: V2D, heading :: Angle }
    initRS = RS 狸猫加速器安卓版百度云 (fromDeg 90)

    Finally, the solve function itself executes each instruction in sequence as a State RobotState computation, uses 黑洞加速器破解版app to run the resulting overall computation and extract the final state, and then projects out the robot’s final position. Executing a single instruction is where the geometry happens: we look up the current robot state, calculate its new heading by adding the turn angle to the current heading, construct a movement vector in the direction of the new heading using polar coordinates, and add the movement to the current position.

    solve :: [安卓永久免费网络加速器] -> V2D
    solve = mapM_ exec >>> flip execState initRS >>> pos
      where
        exec :: Instr -> 狸猫加速器安卓版安装包 RobotState ()
        exec (I θ d) = do
          RS{..} <- get
          let heading' = 狸猫加速器安卓版下载 + θ
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    We’ll definitely be doing more geometry, but for the next post I feel like doing something different. I invite you to solve Checking Break.

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    Chris Smith 2

    Thanks. It's fixed now.

    Thanks. It's fixed now.

    by Chris Smith at June 24, 2024 04:20 PM

    Toy Machine Learning with Haskell

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    I’m going to try something different. Instead of writing in Medium, I’ve written up this post in comments inside of CodeWorld.

    Part 1: Model Structure

    In this part, I explain what a machine learning model is, define the Haskell types for the parts of the model, and write the code to make the model work. We end with a visualization of a pre-trained model to recognize which points are in a circle.

    Link: http://code.world/haskell#PisFfAHxvUXzYBjnDoeRmew

    Part 2: Training

    In this part, I show how to use automatic differentiation to train the model that we defined in the previous section.

    Link: http://code.world/haskell#PsgrIqxf3C_eFoRPqK3q0eQ

    by Chris Smith at June 24, 2024 04:20 PM

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