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https://github.com/idris-lang/Idris2.git
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97 lines
3.3 KiB
Idris
97 lines
3.3 KiB
Idris
module Data.List.Views
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import Control.WellFounded
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import Data.List
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import Data.Nat
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import Data.Nat.Views
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%default total
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lengthSuc : (xs : List a) -> (y : a) -> (ys : List a) ->
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length (xs ++ (y :: ys)) = S (length (xs ++ ys))
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lengthSuc [] _ _ = Refl
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lengthSuc (x :: xs) y ys = cong S (lengthSuc xs y ys)
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lengthLT : (xs : List a) -> (ys : List a) ->
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LTE (length xs) (length (ys ++ xs))
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lengthLT xs [] = lteRefl
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lengthLT xs (x :: ys) = lteSuccRight (lengthLT _ _)
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smallerLeft : (ys : List a) -> (y : a) -> (zs : List a) ->
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LTE (S (S (length ys))) (S (length (ys ++ (y :: zs))))
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smallerLeft [] y zs = LTESucc (LTESucc LTEZero)
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smallerLeft (z :: ys) y zs = LTESucc (smallerLeft ys _ _)
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smallerRight : (ys : List a) -> (zs : List a) ->
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LTE (S (S (length zs))) (S (length (ys ++ (y :: zs))))
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smallerRight ys zs = rewrite lengthSuc ys y zs in
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(LTESucc (LTESucc (lengthLT _ _)))
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||| View for splitting a list in half, non-recursively
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public export
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data Split : List a -> Type where
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SplitNil : Split []
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SplitOne : (x : a) -> Split [x]
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SplitPair : (x : a) -> (xs : List a) ->
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(y : a) -> (ys : List a) ->
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Split (x :: xs ++ y :: ys)
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splitHelp : (head : a) ->
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(xs : List a) ->
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(counter : List a) -> Split (head :: xs)
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splitHelp head [] counter = SplitOne _
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splitHelp head (x :: xs) [] = SplitPair head [] x xs
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splitHelp head (x :: xs) [y] = SplitPair head [] x xs
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splitHelp head (x :: xs) (_ :: _ :: ys)
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= case splitHelp head xs ys of
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SplitOne x => SplitPair x [] _ []
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SplitPair x' xs y' ys => SplitPair x' (x :: xs) y' ys
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||| Covering function for the `Split` view
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||| Constructs the view in linear time
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export
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split : (xs : List a) -> Split xs
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split [] = SplitNil
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split (x :: xs) = splitHelp x xs xs
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public export
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data SplitRec : List a -> Type where
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SplitRecNil : SplitRec []
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SplitRecOne : (x : a) -> SplitRec [x]
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SplitRecPair : (lefts, rights : List a) -> -- Explicit, don't erase
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(lrec : Lazy (SplitRec lefts)) ->
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(rrec : Lazy (SplitRec rights)) -> SplitRec (lefts ++ rights)
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||| Covering function for the `SplitRec` view
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||| Constructs the view in O(n lg n)
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public export
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splitRec : (xs : List a) -> SplitRec xs
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splitRec xs with (sizeAccessible xs)
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splitRec xs | acc with (split xs)
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splitRec [] | acc | SplitNil = SplitRecNil
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splitRec [x] | acc | SplitOne x = SplitRecOne x
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splitRec (y :: ys ++ z :: zs) | Access acc | SplitPair y ys z zs
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= SplitRecPair _ _
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(splitRec (y :: ys) | acc _ (smallerLeft ys z zs))
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(splitRec (z :: zs) | acc _ (smallerRight ys zs))
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||| View for traversing a list backwards
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public export
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data SnocList : List a -> Type where
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Empty : SnocList []
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Snoc : (x : a) -> (xs : List a) ->
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(rec : SnocList xs) -> SnocList (xs ++ [x])
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snocListHelp : {input : _} ->
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SnocList input -> (rest : List a) -> SnocList (input ++ rest)
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snocListHelp snoc [] = rewrite appendNilRightNeutral input in snoc
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snocListHelp snoc (x :: xs)
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= rewrite appendAssociative input [x] xs in
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snocListHelp (Snoc x input snoc) xs
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||| Covering function for the `SnocList` view
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||| Constructs the view in linear time
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export
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snocList : (xs : List a) -> SnocList xs
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snocList xs = snocListHelp Empty xs
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