Implement free and cofree Traversing functors

This commit is contained in:
Kiana Sheibani 2023-03-06 16:37:43 -05:00
parent 81c9486124
commit 20c3ce2ee8
Signed by: toki
GPG key ID: 6CB106C25E86A9F7

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@ -2,6 +2,7 @@ module Data.Profunctor.Traversing
import Control.Monad.Identity
import Data.Morphisms
import Data.Tensor
import Data.Profunctor.Types
import Data.Profunctor.Functor
import Data.Profunctor.Strong
@ -9,6 +10,24 @@ import Data.Profunctor.Closed
%default total
[FoldablePair] Foldable (Pair c) where
foldr op init (_, x) = x `op` init
foldl op init (_, x) = init `op` x
null _ = False
[TraversablePair] Traversable (Pair c) using FoldablePair where
traverse f (l, r) = (l,) <$> f r
[FoldableIdentity] Foldable Identity where
foldr f i (Id x) = f x i
foldl f i (Id x) = f i x
null _ = False
[TraversableIdentity] Traversable Identity using FoldableIdentity where
traverse f (Id x) = map Id (f x)
record Bazaar a b t where
constructor MkBazaar
getBazaar : forall f. Applicative f => (a -> f b) -> f t
@ -52,3 +71,98 @@ interface (Strong p, Choice p) => Traversing p where
wander : (forall f. Applicative f => (a -> f b) -> s -> f t) -> p a b -> p s t
wander f = dimap (\s => MkBaz $ \afb => f afb s) sold . traverse'
-- CofreeTraversing
public export
record CofreeTraversing p a b where
constructor MkCFT
getCFT : forall f. Traversable f => p (f a) (f b)
export
Profunctor p => Profunctor (CofreeTraversing p) where
lmap f (MkCFT p) = MkCFT (lmap (map f) p)
rmap g (MkCFT p) = MkCFT (rmap (map g) p)
dimap f g (MkCFT p) = MkCFT (dimap (map f) (map g) p)
export
Profunctor p => GenStrong Pair (CofreeTraversing p) where
strongr (MkCFT p) = MkCFT (p @{Compose @{%search} @{TraversablePair}})
strongl = dimap Builtin.swap Builtin.swap . strongr {p=CofreeTraversing p}
export
Profunctor p => GenStrong Either (CofreeTraversing p) where
strongr (MkCFT p) = MkCFT (p @{Compose {f=Either c}})
strongl = dimap swap swap . strongr {p=CofreeTraversing p}
export
Profunctor p => Traversing (CofreeTraversing p) where
traverse' (MkCFT p) = MkCFT (p @{Compose})
export
ProfunctorFunctor CofreeTraversing where
promap f (MkCFT p) = MkCFT (f p)
export
ProfunctorComonad CofreeTraversing where
proextract (MkCFT p) = dimap Id runIdentity $ p @{TraversableIdentity}
produplicate (MkCFT p) = MkCFT $ MkCFT $ p @{Compose}
export
Profunctor p => Functor (CofreeTraversing p a) where
map = rmap
export
cofreeTraversing : Traversing p => p :-> q -> p :-> CofreeTraversing q
cofreeTraversing f p = MkCFT $ f $ traverse' p
export
uncofreeTraversing : Profunctor q => p :-> CofreeTraversing q -> p :-> q
uncofreeTraversing f p = proextract $ f p
-- FreeTraversing
public export
data FreeTraversing : (p : Type -> Type -> Type) -> Type -> Type -> Type where
MkFT : Traversable f => (f y -> b) -> p x y -> (a -> f x) -> FreeTraversing p a b
export
Profunctor (FreeTraversing p) where
lmap f (MkFT l m r) = MkFT l m (r . f)
rmap f (MkFT l m r) = MkFT (f . l) m r
dimap f g (MkFT l m r) = MkFT (g . l) m (r . f)
export
GenStrong Pair (FreeTraversing p) where
strongr (MkFT l m r) = MkFT @{Compose @{TraversablePair}} (map l) m (map r)
strongl = dimap Builtin.swap Builtin.swap . strongr {p=FreeTraversing p}
export
GenStrong Either (FreeTraversing p) where
strongr (MkFT l m r) = MkFT @{Compose {t=Either c}} (map l) m (map r)
strongl = dimap swap swap . strongr {p=FreeTraversing p}
export
Traversing (FreeTraversing p) where
traverse' (MkFT l m r) = MkFT @{Compose} (map l) m (map r)
export
ProfunctorFunctor FreeTraversing where
promap f (MkFT l m r) = MkFT l (f m) r
export
ProfunctorMonad FreeTraversing where
propure p = MkFT @{TraversableIdentity} runIdentity p Id
projoin (MkFT l' (MkFT l m r) r') = MkFT @{Compose} (l' . map l) m (map r . r')
export
freeTraversing : Traversing q => p :-> q -> FreeTraversing p :-> q
freeTraversing fn (MkFT {f} l m r) = dimap r l (traverse' {f} (fn m))
export
unfreeTraversing : FreeTraversing p :-> q -> p :-> q
unfreeTraversing f p = f (MkFT @{TraversableIdentity} runIdentity p Id)