Create Control.Zipper

Most of this code is ported from the haskell `zippers` library.
This commit is contained in:
Kiana Sheibani 2023-04-22 23:45:00 -04:00
parent e0297af9f3
commit de087603bf
Signed by: toki
GPG key ID: 6CB106C25E86A9F7
2 changed files with 141 additions and 1 deletions

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@ -121,7 +121,7 @@ public export
(<.) l l' @{ind} = l @{Idxed} . runIndexed . l' . MkIndexed {p} . indexed @{ind}
||| Augment an optic with a constant index.
||| Augment an optic with an index that is constant for all inputs.
public export
constIndex : IsIso p => i -> Optic' p s t a b -> IndexedOptic' p i s t a b
constIndex i l @{MkIsIso _} @{ind} = l . lmap (i,) . indexed @{ind}

140
src/Control/Zipper.idr Normal file
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@ -0,0 +1,140 @@
||| A system for type-safe, traversal-based zippers into arbitrary datatypes.
module Control.Zipper
import Data.Maybe
import Data.List
import Control.Lens
%default total
------------------------------------------------------------------------------
-- Pointer
------------------------------------------------------------------------------
Pointer : (i, a : Type) -> Type
Pointer i a = (SnocList (i, a), List (i, a))
fromPointer : i -> a -> Pointer i a -> List (i, a)
fromPointer k x (l, r) = l <>> (k,x) :: r
------------------------------------------------------------------------------
-- Zipper
------------------------------------------------------------------------------
infix 9 @>
public export
data ZipLayer : Type where
(@>) : (i, a : Type) -> ZipLayer
public export
getTy : ZipLayer -> Type
getTy (_ @> a) = a
data Coil : List ZipLayer -> Type -> Type -> Type where
Nil : Coil [] i a
Cons : IndexedTraversal' i s a -> Pointer j s -> j -> (List (i, a) -> s) ->
Coil hs j s -> Coil (j @> s :: hs) i a
export
data Zipper : List ZipLayer -> Type -> Type -> Type where
MkZipper : Coil hs i a -> Pointer i a -> i -> a -> Zipper hs i a
export
zipper : a -> Zipper [] () a
zipper x = MkZipper Nil ([<], []) () x
export
focus : IndexedLens' i (Zipper hs i a) a
focus = ilens (\(MkZipper _ _ i x) => (i, x))
(\(MkZipper coil p i _),x => MkZipper coil p i x)
------------------------------------------------------------------------------
-- Zipper movement
------------------------------------------------------------------------------
export
upward : Zipper (j @> s :: hs) i a -> Zipper hs j s
upward (MkZipper (Cons _ p j k coil) q i x) =
MkZipper coil p j $ k $ fromPointer i x q
export
tug : (a -> Maybe a) -> a -> a
tug f x = fromMaybe x (f x)
export
rightward : Alternative f => Zipper hs i a -> f (Zipper hs i a)
rightward (MkZipper _ (_, []) _ _) = empty
rightward (MkZipper coil (l, (j,y) :: r) i x) =
pure $ MkZipper coil (l :< (i,x), r) j y
export
leftward : Alternative f => Zipper hs i a -> f (Zipper hs i a)
leftward (MkZipper _ ([<], _) _ _) = empty
leftward (MkZipper coil (l :< (j,y), r) i x) =
pure $ MkZipper coil (l, (i,x) :: r) j y
export
leftmost : Zipper hs i a -> Zipper hs i a
leftmost (MkZipper coil p i x) =
case fromPointer i x p of
(j,y) :: xs => MkZipper coil ([<], xs) j y
-- Too lazy to prove this impossible for now
[] => assert_total $ idris_crash "Unreachable"
export
rightmost : Zipper hs i a -> Zipper hs i a
rightmost (MkZipper coil (l,r) i x) =
case l :< (i,x) <>< r of
xs :< (j,y) => MkZipper coil (xs, []) j y
-- Too lazy to prove this impossible for now
[<] => assert_total $ idris_crash "Unreachable"
export
idownward : IndexedLens' i s a -> Zipper hs j s -> Zipper (j @> s :: hs) i a
idownward l (MkZipper coil p j y) =
let (i,x) = iview l y
in MkZipper (Cons l p j (go . map snd) coil) ([<],[]) i x
where
go : List a -> s
go ls = set (partsOf l) ls y
export
downward : Lens' s a -> Zipper hs j s -> Zipper (j @> s :: hs) () a
downward l (MkZipper coil p i x) =
MkZipper (Cons (constIndex () l) p i (go . map snd) coil) ([<], []) () (x ^. l)
where
go : List a -> s
go ls = set (partsOf l) ls x
export
iwithin : Alternative f => IndexedTraversal' i s a -> Zipper hs j s -> f (Zipper (j @> s :: hs) i a)
iwithin l (MkZipper coil p j y) =
case itoListOf l y of
(i,x) :: xs => pure $ MkZipper (Cons l p j (go . map snd) coil) ([<], xs) i x
[] => empty
where
go : List a -> s
go ls = set (partsOf l) ls y
export
within : Alternative f => Traversal' s a -> Zipper hs j s -> f (Zipper (j @> s :: hs) Nat a)
within = iwithin . iordinal
recoil : Coil hs i a -> List (i, a) -> getTy $ last (i @> a :: hs)
recoil Nil xs = assert_total $ case xs of (_,x) :: _ => x
recoil (Cons _ p i f coil) xs = recoil coil $ fromPointer i (f xs) p
export
rezip : Zipper hs i a -> getTy $ last (i @> a :: hs)
rezip (MkZipper coil p i x) = recoil coil $ fromPointer i x p