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