Data.List.Infinite

Type of infinite lists.

In terms of recursion schemes, Infinite a is a fix point of the base functor (a,), foldr is a catamorphism and unfoldr is an anamorphism.

Get the first elements of an infinite list.

Get the elements of an infinite list after the first one.

Split an infinite list into its head and tail.

Convert to a list. Use cycle to go in the opposite direction.

Right-associative fold of an infinite list, necessarily lazy in the accumulator. Any unconditional attempt to force the accumulator even to the weak head normal form (WHNF) will hang the computation. E. g., the following definition isn't productive:

import Data.List.NonEmpty (NonEmpty(..))
toNonEmpty = foldr (\a (x :| xs) -> a :| x : xs) :: Infinite a -> NonEmpty a

One should use lazy patterns, e. g.,

toNonEmpty = foldr (\a ~(x :| xs) -> a :| x : xs)

This is a catamorphism on infinite lists.

Apply a function to every element of an infinite list.

Fold an infinite list from the left and return a list of successive reductions, starting from the initial accumulator:

scanl f acc (x1 :< x2 :< ...) = acc :< f acc x1 :< f (f acc x1) x2 :< ...

Same as scanl, but strict in accumulator.

Fold an infinite list from the left and return a list of successive reductions, starting from the first element:

scanl1 f (x0 :< x1 :< x2 :< ...) = x0 :< f x0 x1 :< f (f x0 x1) x2 :< ...

Fold an infinite list from the left and return a list of successive reductions, keeping accumulator in a state:

mapAccumL f acc0 (x1 :< x2 :< ...) =
  let (acc1, y1) = f acc0 x1 in
    let (acc2, y2) = f acc1 x2 in
      ...
        y1 :< y2 :< ...

If you are looking how to traverse with a state, look no further.

Same as mapAccumL, but strict in accumulator.

Map each element to an action, evaluate these actions from left to right and ignore the results. Note that the return type is Void instead of usual ().

>>> traverse_ print (0...) -- hit Ctrl+C to terminate012Interrupted

traverse_ could be productive for some short-circuiting f:

>>> traverse_ (\x -> if x > 10 then Left x else Right ()) (0...)Left 11

Flipped traverse_.

Flatten out an infinite list of non-empty lists.

The peculiar type with NonEmpty is to guarantee that concat is productive and results in an infinite list. Otherwise the concatenation of infinitely many [a] could still be a finite list.

First map every element, then concat.

The peculiar type with NonEmpty is to guarantee that concatMap is productive and results in an infinite list. Otherwise the concatenation of infinitely many [b] could still be a finite list.

Insert an element between adjacent elements of an infinite list.

Insert a non-empty list between adjacent elements of an infinite list, and subsequently flatten it out.

The peculiar type with NonEmpty is to guarantee that intercalate is productive and results in an infinite list. If separator is an empty list, concatenation of infinitely many [a] could still be a finite list.

Interleave two infinite lists.

Transpose rows and columns of an argument.

This is actually distribute from Distributive type class in disguise.

Generate an infinite list of all finite subsequences of the argument.

>>> take 8 (subsequences (0...))[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2]]

Generate an infinite list of all non-empty finite subsequences of the argument.

>>> take 7 (subsequences1 (0...))[0 :| [],1 :| [],0 :| [1],2 :| [],0 :| [2],1 :| [2],0 :| [1,2]]

Generate an infinite list of all finite (such that only finite number of elements change their positions) permutations of the argument.

>>> take 6 (fmap (take 3) (permutations (0...)))[[0,1,2],[1,0,2],[2,1,0],[1,2,0],[2,0,1],[0,2,1]]

Generate an infinite progression, starting from a given element, similar to [x..]. For better user experience consider enabling {-# LANGUAGE PostfixOperators #-}:

>>> :set -XPostfixOperators>>> Data.List.Infinite.take 10 (0...)[0,1,2,3,4,5,6,7,8,9]

Beware that for finite types (...) applies cycle atop of [x..]:

>>> :set -XPostfixOperators>>> Data.List.Infinite.take 10 (EQ...)[EQ,GT,EQ,GT,EQ,GT,EQ,GT,EQ,GT]

Remember that Int is a finite type as well. One is unlikely to hit this on a 64-bit architecture, but on a 32-bit machine it's fairly possible to traverse ((0 :: Int) ...) far enough to encounter 0 again.

Generate an infinite arithmetic progression, starting from given elements, similar to [x,y..]. For better user experience consider enabling {-# LANGUAGE PostfixOperators #-}:

>>> :set -XPostfixOperators>>> Data.List.Infinite.take 10 ((1,3)....)[1,3,5,7,9,11,13,15,17,19]

Beware that for finite types (....) applies cycle atop of [x,y..]:

>>> :set -XPostfixOperators>>> Data.List.Infinite.take 10 ((EQ,GT)....)[EQ,GT,EQ,GT,EQ,GT,EQ,GT,EQ,GT]

Remember that Int is a finite type as well: for a sufficiently large step of progression y - x one may observe ((x :: Int, y)....) cycling back to emit x fairly soon.

Generate an infinite list of repeated applications.

Same as iterate, but strict in accumulator.

Build an infinite list from a seed value.

This is an anamorphism on infinite lists.

Generate an infinite list of f 0, f 1, f 2...

tabulate and (Data.List.Infinite.!!) witness that Infinite is Representable.

Repeat the same element ad infinitum.

Repeat a non-empty list ad infinitum. If you were looking for something like fromList :: [a] -> Infinite a, look no further.

It would be less annoying to take [a] instead of NonEmpty a, but we strive to avoid partial functions.

Prepend a list to an infinite list.

Take a prefix of given length.

Drop a prefix of given length.

Split an infinite list into a prefix of given length and the rest.

Take the longest prefix satisfying a predicate.

Drop the longest prefix satisfying a predicate.

This function isn't productive (e. g., head . dropWhile f won't terminate), if all elements of the input list satisfy the predicate.

Split an infinite list into the longest prefix satisfying a predicate and the rest.

This function isn't productive in the second component of the tuple (e. g., head . snd . span f won't terminate), if all elements of the input list satisfy the predicate.

Split an infinite list into the longest prefix not satisfying a predicate and the rest.

This function isn't productive in the second component of the tuple (e. g., head . snd . break f won't terminate), if no elements of the input list satisfy the predicate.

Group consecutive equal elements.

Generate all prefixes of an infinite list.

>>> :set -XPostfixOperators>>> Data.List.Infinite.take 5 $ Data.List.Infinite.inits (0...)[[],[0],[0,1],[0,1,2],[0,1,2,3]]

If you need reversed prefixes, they can be generated cheaper using scanl':

>>> :set -XPostfixOperators>>> Data.List.Infinite.take 5 $ Data.List.Infinite.scanl' (flip (:)) [] (0...)[[],[0],[1,0],[2,1,0],[3,2,1,0]]

Generate all non-empty prefixes of an infinite list.

Generate all suffixes of an infinite list.

Check whether a list is a prefix of an infinite list.

If a list is a prefix of an infinite list, strip it and return the rest. Otherwise return Nothing.

Filter an infinite list, removing elements which does not satisfy a predicate.

This function isn't productive (e. g., head . filter f won't terminate), if no elements of the input list satisfy the predicate.

A common objection is that since it could happen that no elements of the input satisfy the predicate, the return type should be [a] instead of Infinite a. This would not however make filter any more productive. Note that such hypothetical filter could not ever generate [] constructor, only (:), so we would just have a more lax type gaining nothing instead. Same reasoning applies to other filtering / partitioning / searching functions.

Find the first pair, whose first component is equal to the first argument, and return the second component. If there is nothing to be found, this function will hang indefinitely.

Find the first element, satisfying a predicate. If there is nothing to be found, this function will hang indefinitely.

Apply a function to every element of an infinite list and collect Just results.

This function isn't productive (e. g., head . mapMaybe f won't terminate), if no elements of the input list result in Just.

Keep only Just elements.

This function isn't productive (e. g., head . catMaybes won't terminate), if no elements of the input list are Just.

Split an infinite list into two infinite lists: the first one contains elements, satisfying a predicate, and the second one the rest.

This function isn't productive in the first component of the tuple (e. g., head . fst . partition f won't terminate), if no elements of the input list satisfy the predicate. Same for the second component, if all elements of the input list satisfy the predicate.

Apply a function to every element of an infinite list and separate Left and Right results.

This function isn't productive (e. g., head . fst . mapEither f won't terminate), if no elements of the input list result in Left or Right.

Separate Left and Right elements.

This function isn't productive (e. g., head . fst . partitionEithers won't terminate), if no elements of the input list are Left or Right.

Return n-th element of an infinite list. On contrary to Data.List.!!, this function takes Word instead of Int to avoid error on negative arguments.

If you are concerned that unsigned indices may accidentally underflow, compile with -fno-ignore-asserts: there is an assert checking that the index does not exceed fromIntegral (maxBound :: Int).

This is actually index from Representable type class in disguise.

Return an index of the first element, equal to a given. If there is nothing to be found, this function will hang indefinitely.

Return indices of all elements, equal to a given.

This function isn't productive (e. g., head . elemIndices f won't terminate), if no elements of the input list are equal the given one.

Return an index of the first element, satisfying a predicate. If there is nothing to be found, this function will hang indefinitely.

Return indices of all elements, satisfying a predicate.

This function isn't productive (e. g., head .' findIndices f won't terminate), if no elements of the input list satisfy the predicate.

Zip two infinite lists.

Zip two infinite lists with a given function.

Zip three infinite lists.

Zip three infinite lists with a given function.

Zip four infinite lists.

Zip four infinite lists with a given function.

Zip five infinite lists.

Zip five infinite lists with a given function.

Zip six infinite lists.

Zip six infinite lists with a given function.

Zip seven infinite lists.

Zip seven infinite lists with a given function.

Zip an Infinite with any Traversable, maintaining the shape of the latter.

>>> import Data.Functor.Compose (Compose(..))>>> heteroZip (0...) (Compose [Just 10, Nothing, Just 20])Compose [Just (0,10),Nothing,Just (1,20)]

Use a given function to zip an Infinite with any Traversable, maintaining the shape of the latter.

>>> import Data.Functor.Compose (Compose(..))>>> heteroZipWith (+) (0...) (Compose [Just 10, Nothing, Just 20])Compose [Just 10,Nothing,Just 21]

Unzip an infinite list of tuples.

Unzip an infinite list of triples.

Unzip an infinite list of quadruples.

Unzip an infinite list of quintuples.

Unzip an infinite list of sextuples.

Unzip an infinite list of septuples.

Split an infinite string into lines, by \n. Empty lines are preserved.

In contrast to their counterparts from Data.List, it holds that unlines . lines = id.

Split an infinite string into words, by any isSpace symbol. Leading spaces are removed and, as underlined by the return type, repeated spaces are treated as a single delimiter.

Concatenate lines together with \n.

In contrast to their counterparts from Data.List, it holds that unlines . lines = id.

Concatenate words together with a space.

The function is meant to be a counterpart of with words. If you need to concatenate together Infinite [Char], use intercalate (pure ' ').

Remove duplicate from a list, keeping only the first occurrence of each element. Because of a very weak constraint on a, this operation takes O(n²) time. Consider using nubOrd instead.

Same as nub, but asymptotically faster, taking only O(n log n) time.

Remove all occurrences of an element from an infinite list.

Take an infinite list and remove the first occurrence of every element of a finite list.

Union of a finite and an infinite list. It contains the finite list as a prefix and afterwards all non-duplicate elements of the infinite list, which are not members of the finite list.

Return all elements of an infinite list, which are simultaneously members of a finite list.

Insert an element at the first position where it is less than or equal to the next one. If the input was sorted, the output remains sorted as well.

Overloaded version of nub. Consider using nubOrdBy instead.

Overloaded version of nubOrd.

Overloaded version of delete.

Overloaded version of (Data.List.Infinite.\\).

Overloaded version of union.

Overloaded version of intersect.

Overloaded version of group.

Overloaded version of insert.

Take a prefix of given length.

Drop a prefix of given length.

Split an infinite list into a prefix of given length and the rest.