In the ``Kan Extensions for Program Optimisation'' by Ralf Hinze there is the definition of List type based on right Kan extension of the forgetful functor from the category of monoids along itself (section 7.4). The paper gives Haskell implementation as follows:

```
newtype List a = Abstr {
apply :: forall z . (Monoid z) => (a -> z) -> z
}
```

I was able to define usual nil and cons constructors:

```
nil :: List a
nil = Abstr (\f -> mempty)
cons :: a -> List a -> List a
cons x (Abstr app) = Abstr (\f -> mappend (f x) (app f))
```

With the following instance of Monoid class for Maybe functor, I managed to define head function:

```
instance Monoid (Maybe a) where
mempty = Nothing
mappend Nothing m = m
mappend (Just a) m = Just a
head :: List a -> Maybe a
head (Abstr app) = app Just
```

**Question**: How can one define tail function?

Answer:

Here is a rather principled solution to implementing head and tail in one go (full gist):

First of all, we know how to append lists (it will be useful later on):

```
append :: List a -> List a -> List a
append (Abstr xs) (Abstr ys) = Abstr (\ f -> xs f <> ys f)
```

Then we introduce a new type `Split`

which we will use to detect whether a `List`

is empty or not (and get, in the case it's non empty, a head and a tail):

```
newtype Split a = Split { outSplit :: Maybe (a, List a) }
```

This new type forms a monoid: indeed we know how to append two lists.

```
instance Monoid (Split a) where
mempty = Split Nothing
mappend (Split Nothing) (Split nns) = Split nns
mappend (Split mms) (Split Nothing) = Split mms
mappend (Split (Just (m, ms))) (Split (Just (n, ns))) =
Split $ Just (m, append ms (cons n ns))
```

Which means that we can get a function from `List a`

to `Split a`

using `List a`

's `apply`

:

```
split :: List a -> Split a
split xs = apply xs $ \ a -> Split $ Just (a, nil)
```

`head`

and `tail`

can finally be trivially derived from `split`

:

```
head :: List a -> Maybe a
head = fmap fst . outSplit . split
tail :: List a -> Maybe (List a)
tail = fmap snd . outSplit . split
```

haskell,file-io,lazy-evaluation

Here I'm back again with a (for me) really strange behaviour of my newest masterpiece... This code should read a file, but it doesn't: readCsvContents :: String -> IO ( String ) readCsvContents fileName = do withFile fileName ReadMode (\handle -> do contents <- hGetContents handle return contents ) main...

list,haskell,functional-programming,idiomatic

I'm very new to Haskell and functional programming in general, so I don't really know how to make this code idiomatic: type Coord = Double data Point = Point Coord Coord Coord deriving Show type Polyline = [Point] -- Add a point to a polyline addPoint :: Polyline -> Point...

haskell

Consider the following IO code: ghci> let x = return 100 :: IO Int ghci> :t do { a <- x; print a; return 500 } do { a <- x; print a; return 500 } :: Num b => IO b My understanding of do notation/bind is that the...

haskell,types

I'm just getting into my first real Haskell project of size (a web app), and I'm starting to run into issues with types from 3rd party libraries leaking all over my code. Here is a quick example: My Parser module imports Test.Parsec, and the exports a function (parseConfig) that returns...

haskell,types,binding,dependent-type

Haskell beginner here. I've defined the following types: data Nat = Z | S Nat data Vector a n where Nil :: Vector a Z (:-) :: a -> Vector a n -> Vector a (S n) infixl 5 :- I'm trying to write the function, takeWhileVector which behaves the...

haskell,lambda,instance,show,typeclass

So, I have already defined the lambda data type as such: data LExpr = Variable String -- variable | Apply LExpr LExpr -- function application | Lambda String LExpr -- Lambda abstraction deriving (Eq, Show) Now I want to implement an instance of Show myself. I have already the function...

haskell,tying-the-knot

Why isn't iterate defined like iterate :: (a -> a) -> a -> [a] iterate f x = xs where xs = x : map f xs in the Prelude?...

string,function,haskell,if-statement,recursion

So, I have this function which aims to align the text on the left without cutting words(only white spaces). However my problem is that I cannot find a stopping condition of the function and it goes infinitely. f n "" = "" --weak condition f n s = if n...

sockets,haskell,network-programming,io-monad

I writing a tcp server, and here's my main loop method: serverLoop :: Socket -> IO () serverLoop sock = do (conn, _) <- accept sock forkIO $ handleConn conn serverLoop sock (Note: handleConn :: Socket -> IO () is a function specific to my program.) I would like to...

haskell

Starting from a simple case of "fold" (I used (+) but can be anything else): Prelude.foldl (+) 0 [10,20,30] is it possible apply an inline transformation similar to (that doesn't work): Prelude.foldl ((+) . (\x -> read x :: Int)) 0 ["10","20","30"] In case not, is there an alternative to...

haskell

I have this: data Data1 = Data1 { field1 :: Int, field2 :: Int } data DataMain = DataMain { a :: String , b :: Bool , subData :: Data1 } And JSON { a: 'some value', b: 'some value2', c: 'some value3', d: 'some value4', } And here...

haskell,compiler-errors,instance,equality,typeclass

So, when I compile the following piece of code edited: instance (Eq a) => PartOrd a where [] == [] = True (x:xs) == (y:ys) = x==y && xs==ys _==_ = False xs /= ys = not (xs == ys) I get: `==' is not a (visible) method of class...

haskell,statistics,gsl

I am trying to find the best way to draw from a normal distribution. I want to be able to use the normal probability density function (and its cumulative) in Haskell. To put it simply, I want to use the functions on this page without using the GSL binding... I...

haskell,syntax,infix-notation,applicative,infix-operator

Why is f <$> g <$> x equivalent to (f . g) <$> x although <$> is not right-associative? (This kind of equivalence is valid in a popular idiom with plain $, but currently $ is right-associative!) <*> has the same associativity and precedence as <$>, but behaves differently! Example:...

haskell

Given the code below: import Data.List; main = (readLn :: IO [Integer]) >>= print . subsequences It takes a list of integers from standard input (for example [1,2,3]) and outputs something like: [[],[1],[2],[1,2],[3],[1,3],[2,3],[1,2,3]] I want it to be like this: {},{1},{2},{1,2},{3},{1,3},{2,3},{1,2,3}} so my goal is to replace every [ and...

haskell,svg,haskell-diagrams

I am working with the diagrams package for haskell, and I am using the SVG backend. I embed the SVG markup directly into an HTML document, so that the graph as a part of a web page. I have built a pretty cool looking bar graph, and I would like...

haskell,yesod,api-key

I'm trying out a yesod applications which I will eventually put up on github or similar. I will use oauth2 with google which means I have to provide an email and secret token. Which I obviously do not want up on github. What is a good place to store these...

linux,haskell,make,ghc,theorem-proving

I am trying to install the paradox theorem prover sourced from here. When I run the makefile this is the command that runs: ghc -optl -static -lstdc++ -I../instantiate -I../minisat/current-base ../minisat/current-base/Solver.or ../minisat/current-base/Prop.or ../instantiate/MiniSatWrapper.or ../instantiate/MiniSatInstantiateClause.or -fglasgow-exts -O2 -static -threaded -main-is Paradox.Main.main --make Paradox.Main -o paradox And it results in several errors like...

string,function,haskell,recursion,parameters

So, I have this function that aligns the text to the left for a given column width. I have already fixed some of its problems, but I am unable to make it not use the decremented parameter once it is called, but to return to the starting value of n....

haskell,applicative

I would like to write something as the following: (+) <$> Just 3 <*> Just 5 <*>' (+) <*> Just 6 However the problem is that I need to somehow flip <*>. What is the idiomatic way in Haskell to do the type of chaining I'm trying?...

haskell,frege

It appears that Frege can evaluate 1/2 to return the Double value 0.5. The literal 1 is of type Int. It seems to be promoted to Double, which is a type in the Real class and thus knows the / operator. How does this happen? Is it using the Haskell...

haskell,cabal,cabal-install,nix,haskell-ng

I have been reading this StackOverflow post in which we are advised to use the haskellng package set. I have also read this but I did not understand what haskellng is. I have read this too, but I still don't know what haskellng is. Could someone please explain what haskellng...

haskell,boilerplate

I run into this situation often enough for it to be annoying. Let's say I have a sum type which can hold an instance of x or a bunch of other things unrelated to x - data Foo x = X x | Y Int | Z String | ...(other...

ubuntu,haskell,vim,ubuntu-14.04,cabal

I would like to install this vim plugin: https://github.com/begriffs/haskell-vim-now When trying to run the suggested installation script: curl -o - https://raw.githubusercontent.com/begriffs/haskell-vim-now/master/install.sh | bash I get: --- Cabal version 1.18 or later is required. Aborting. I then try to install a newer version of cabal: [email protected]:~/Downloads/cabal-install-1.22.6.0$ ./bootstrap.sh The response I get:...

haskell

Haskell IO system is super hard to understand for me so i have question : How to read from standard input to list ? I know that there is function getLine :: IO String and interact. But i do not know how to convert the input to list so I...

haskell

Say, I got a list which length can be odd or even. Every iteration , I remove two items from the list. If there is one or no item at the end, I end the execution. If I store (length list)/2 every loop, I will get e.g. [5,4,3...] for a...

shell,haskell,command-line-arguments,executable

Say there's a C++ code that I've compiled into an executable using: g++ test.cpp -o testcpp I can run this using Terminal (I'm using OS X), and provide an input file for processing inside the C++ program, like: ./testcpp < input.txt I was wondering if doing this is possible, from...

haskell

I have a powerset implementation that I'm trying to run here: http://rextester.com/runcode. I'm still getting this error and can't figure out how to make it right. I'm trying to read as much as possible about IO in haskell but it is super hard for me. import Control.Monad (filterM) powerset =...

haskell,containers,sequence

Data.Sequence has takeWhileR and dropWhileR for efficient deconstruction of Seqs from the right. However, takeR, dropR and splitAtR are conspicuously absent. take and drop are implemented in terms of splitAt. So, do finger trees not admit an efficient splitAtR or was this functionality not included for some other reason? (Separate...

haskell,monads

I have the following code: data APNSIdentifier = NoIdentifier | Identifier Word32 deriving (Show, Eq) newtype APNSItem = Item Put createNotificationIdentifierItem :: APNSIdentifier -> APNSItem <--- here createNotificationIdentifierItem (Identifier identifier) = do putWord8 3 putWord16be 4 putWord32be identifier How can I "wrap" the Put monad with an APNSItem? Do I...

haskell,lazy-evaluation

When I tried the following code in cghi: take 1 $ take 1 $ repeat [1..] I was expecting the result of 1 instead of [[1,2,3,4,5,6,7,8,9,10,... printing on my terminal. Why is lazy evaluation not functioning as I'm hoping under such situation?...

haskell

I wrote the following logical expression evaluator. It works for simple 2-member expressions, and it runs but produces a fault for expression containing other expressions as the second/first member. Here's my code. data Expression = Literal Bool | Operation Operator Expression Expression data Operator = AND | OR eval ::...

scala,haskell

I am trying to implement a map using fold. I could do so in Haskell data Tree a = EmptyTree | Node a (Tree a) (Tree a) deriving (Show) foldTree :: Tree a -> b -> (b -> a -> b -> b) -> b foldTree EmptyTree d _ =...

haskell,concurrency,network-programming

I have been attempting to debug a problem when using multiple MVars, however to no luck. My code uses two MVars: one to store the servers current state, and another to pass network events to and from the client threads. However after connecting and disconnecting several times, the server stops...

haskell,fibonacci

I'm learning haskell and I have the following code: fib a b = a : fib b (a + b) findFibSum = sum [x | x <- fib 1 2, mod x 2 == 0 && x < 100] If I run findFibSum nothing happens, it just sits there. Shouldn't...

haskell,attoparsec

I have an attoparsec parser, and tests for it, what annoys me is that if I comment part of the parser and run the tests, the parser doesn't return Left "parse error at line ..." but instead I get Right []. Note that I'm using parseOnly to make it clear...

haskell,types,monoids,type-variables,foldable

I'm playing around with type-aligned sequences, and in particular I'm messing around with the idea of folding them. A foldable type-aligned sequence looks something like this: class FoldableTA fm where foldMapTA :: Category h => (forall b c . a b c -> h b c) -> fm a b...

haskell,monads

I'm using a graphic library in Haskell called ThreePennyUI. In this library the main function returns a UI monad object. This causes me much headache as when I attempt to unpack IO values into local variables I receive errors complaining of different monad types. Here's an example of my problem:...

haskell,recursion

In Haskell, I recently found the following function useful: listCase :: (a -> [a] -> b) -> [a] -> [b] listCase f [] = [] listCase f (x:xs) = f x xs : listCase f xs I used it to generate sliding windows of size 3 from a list, like...

haskell

I want to define a function, <-? to check whether an element is in a list/set/map. module Test where import qualified Data.Map as Map import qualified Data.Set as Set class Memberable a where (<-?) :: b -> a -> Bool instance Memberable [x] where (<-?) = elem instance Memberable (Map.Map...

haskell,travis-ci

I'd like to use travis-ci on my Haskell projects, but they require the latest version of GHC.

haskell

I'm writing this small program basically to identify each input tokens as operator/parenthesis/int. However, I encountered a problem stating that Not in scope: data constructor `Integer' Here's what I have so far (Data.Char only defines isDigit, nothing else) import Data.Char (isDigit) data Token = TPlus | TTimes | TParenLeft |...

list,haskell,io

I have a function that takes two filenames, and reads the contents of those two files into Strings, and then returns if they match or not. Here's the function: f :: String -> String -> IO Bool f fileName1 fileName2 = do str1 <- readFile fileName1 str2 <- readFile fileName2...

haskell,threepenny-gui

I have an Event String which I want to sink into a textarea. This works fine, but now I want to combine the current value of a checkbox selection to this string. First I did this by using checkedChange of the checkbox which works, but has a problem. If the...

haskell

I am very new to Haskell, and struggling a bit with a function here. The premise is simple enough: Run through a list, and combine each 3 items next to each other with another function and return a list with the results. The problem is to do it in a...

haskell,type-level-computation,hlist

I have a list of heterogeneous types (or at least that's what I have in mind): data Nul data Bits b otherBits where BitsLst :: b -> otherBits -> Bits b otherBits NoMoreBits :: Bits b Nul Now, given an input type b, I want to go through all the...

haskell,functional-programming,runtime,transactional-memory

I have been looking at how transactional memory is implemented in Haskell, and I am not sure I understand how the STM operations exposed to the programmer hook into the runtime system functions written in C. In ghc/libraries/base/GHC/Conc/Sync.hs of the git repo, I see the following definitions: -- |A monad...

haskell,cabal

According to the doc on Hackage, Data.Time.Format exposed defaultTimeLocal. However, when I try to use it, it doesn't exits. When I look at the code, it doesn't seems to be exposed either (if I generate the doc from the source, I don't see this defaultTimeLocale). Is it because it needs...

haskell,formatting,rational

I want to display some Rational values in their decimal expansion. That is, instead of displaying 3 % 4, I would rather display 0.75. I'd like this function to be of type Int -> Rational -> String. The first Int is to specify the maximum number of decimal places, since...

haskell,random

In Haskell, I'd like to generate a random list of Ints and use it throughout my program. My current solution causes the array to be created randomly each time I access/use it. How can I overcome this problem?...