mirror of
https://github.com/idris-lang/Idris2.git
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1d4c84171d
Main change
===========
The main change is to the type of function dealing with an untouched
segment of the local scope. e.g.
```
weak : {outer, vars : _} -> (ns : List Name) ->
tm (outer ++ inner) -> tm (outer ++ ns ++ inner)
```
Instead we now write
```
weak : SizeOf ns -> tm (outer ++ inner) -> tm (outer ++ ns ++ inner)
```
meaning that we do not need the values of `outer`, `inner` and `ns`
at runtime. Instead we only demand a `SizeOf ns` which is a `Nat`
together with an (erased) proof that `ns` is of that length.
Other modifications
===================
Quadratic behaviour
-------------------
A side effect of this refactor is the removal of two sources of
quadratic behaviour. They typically arise in a situation where
work is done on a scope of the form
```
outer ++ done ++ ns ++ inner
```
When `ns` is non-empty, some work is performed and then the variable
is moved to the pile of things we are `done` with. This leads to
recursive calls of the form `f done` -> `f (done ++ [v])` leading
to a cost quadratic in the size of `ns`.
Now that we only care about `SizeOf done`, the recursive call is
(once all the runtime irrelevant content is erased) for the form
`f n` -> `f (S n)`!
More runtime irrelevance
------------------------
In some places we used to rely on a list of names `vars` being
available. However once we only care about the length of `vars`,
the fact it is not available is not a limitation.
For instance a `SizeOf vars` can be reconstructed from an environment
assigning values to `vars` even if `vars` is irrelevant. Indeed the
size of the environment is the same as that of `vars`.
124 lines
3.5 KiB
Idris
124 lines
3.5 KiB
Idris
module Data.Stream
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import Data.List
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||| The first element of an infinite stream
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public export
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head : Stream a -> a
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head (x::xs) = x
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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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||| 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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||| Combine two streams element-wise using a function.
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||| @ f the function to combine elements with
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||| @ xs the first stream of elements
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||| @ ys the second stream of elements
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export
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zipWith : (f : a -> b -> c) -> (xs : Stream a) -> (ys : Stream b) -> Stream c
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zipWith f (x::xs) (y::ys) = f x y :: zipWith f xs ys
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||| Combine three streams by applying a function element-wise along them
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export
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zipWith3 : (a -> b -> c -> d) -> Stream a -> Stream b -> Stream c -> Stream d
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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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||| Create a stream of pairs from two streams
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export
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zip : Stream a -> Stream b -> Stream (a, b)
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zip = zipWith (\x,y => (x,y))
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||| Combine three streams into a stream of tuples elementwise
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export
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zip3 : Stream a -> Stream b -> Stream c -> Stream (a, b, c)
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zip3 = zipWith3 (\x,y,z => (x,y,z))
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||| Create a pair of streams from a stream of pairs
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export
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unzip : Stream (a, b) -> (Stream a, Stream b)
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unzip xs = (map fst xs, map snd xs)
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||| Split a stream of three-element tuples into three streams
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export
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unzip3 : Stream (a, b, c) -> (Stream a, Stream b, Stream c)
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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 : (1 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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