mirror of
https://github.com/idris-lang/Idris2.git
synced 2024-12-23 19:54:50 +03:00
110 lines
2.8 KiB
Idris
110 lines
2.8 KiB
Idris
module Data.Stream
|
|
|
|
import Data.List
|
|
import public Data.Zippable
|
|
|
|
%default total
|
|
|
|
||| Drop the first n elements from the stream
|
|
||| @ n how many elements to drop
|
|
public export
|
|
drop : (n : Nat) -> Stream a -> Stream a
|
|
drop Z xs = xs
|
|
drop (S k) (x::xs) = drop k xs
|
|
|
|
||| An infinite stream of repetitions of the same thing
|
|
public export
|
|
repeat : a -> Stream a
|
|
repeat x = x :: repeat x
|
|
|
|
||| Generate an infinite stream by repeatedly applying a function
|
|
||| @ f the function to iterate
|
|
||| @ x the initial value that will be the head of the stream
|
|
public export
|
|
iterate : (f : a -> a) -> (x : a) -> Stream a
|
|
iterate f x = x :: iterate f (f x)
|
|
|
|
public export
|
|
unfoldr : (b -> (a, b)) -> b -> Stream a
|
|
unfoldr f c = let (a, n) = f c in a :: unfoldr f n
|
|
|
|
||| Get the nth element of a stream
|
|
public export
|
|
index : Nat -> Stream a -> a
|
|
index Z (x::xs) = x
|
|
index (S k) (x::xs) = index k xs
|
|
|
|
---------------------------
|
|
-- Zippable --
|
|
---------------------------
|
|
|
|
export
|
|
Zippable Stream where
|
|
zipWith f (x :: xs) (y :: ys) = f x y :: zipWith f xs ys
|
|
|
|
zipWith3 f (x :: xs) (y :: ys) (z :: zs) = f x y z :: zipWith3 f xs ys zs
|
|
|
|
unzipWith f xs = unzip (map f xs)
|
|
|
|
unzip xs = (map fst xs, map snd xs)
|
|
|
|
unzipWith3 f xs = unzip3 (map f xs)
|
|
|
|
unzip3 xs = (map (\(x, _, _) => x) xs, map (\(_, x, _) => x) xs, map (\(_, _, x) => x) xs)
|
|
|
|
||| Return the diagonal elements of a stream of streams
|
|
export
|
|
diag : Stream (Stream a) -> Stream a
|
|
diag ((x::xs)::xss) = x :: diag (map tail xss)
|
|
|
|
||| Produce a Stream of left folds of prefixes of the given Stream
|
|
||| @ f the combining function
|
|
||| @ acc the initial value
|
|
||| @ xs the Stream to process
|
|
export
|
|
scanl : (f : a -> b -> a) -> (acc : a) -> (xs : Stream b) -> Stream a
|
|
scanl f acc (x :: xs) = acc :: scanl f (f acc x) xs
|
|
|
|
||| Produce a Stream repeating a sequence
|
|
||| @ xs the sequence to repeat
|
|
||| @ ok proof that the list is non-empty
|
|
export
|
|
cycle : (xs : List a) -> {auto 0 ok : NonEmpty xs} -> Stream a
|
|
cycle (x :: xs) = x :: cycle' xs
|
|
where cycle' : List a -> Stream a
|
|
cycle' [] = x :: cycle' xs
|
|
cycle' (y :: ys) = y :: cycle' ys
|
|
|
|
public export
|
|
partial
|
|
takeUntil : (n -> Bool) -> Stream n -> List n
|
|
takeUntil p (x :: xs)
|
|
= if p x
|
|
then [x]
|
|
else x :: takeUntil p xs
|
|
|
|
public export
|
|
partial
|
|
takeBefore : (n -> Bool) -> Stream n -> List n
|
|
takeBefore p (x :: xs)
|
|
= if p x
|
|
then []
|
|
else x :: takeBefore p xs
|
|
|
|
export
|
|
Applicative Stream where
|
|
pure = repeat
|
|
(<*>) = zipWith apply
|
|
|
|
export
|
|
Monad Stream where
|
|
s >>= f = diag (map f s)
|
|
|
|
--------------------------------------------------------------------------------
|
|
-- Properties
|
|
--------------------------------------------------------------------------------
|
|
|
|
lengthTake : (n : Nat) -> (xs : Stream a) -> length (take n xs) = n
|
|
lengthTake Z _ = Refl
|
|
lengthTake (S n) (x :: xs) = cong S (lengthTake n xs)
|