Change visibility on everything to public export
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@ -18,50 +18,50 @@ record Cayley {0 k1,k2,k3 : Type} f (p : k1 -> k2 -> k3) a b where
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runCayley : f (p a b)
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runCayley : f (p a b)
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export
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public export
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Functor f => Profunctor p => Profunctor (Cayley f p) where
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Functor f => Profunctor p => Profunctor (Cayley f p) where
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dimap f g (MkCayley p) = MkCayley (dimap f g <$> p)
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dimap f g (MkCayley p) = MkCayley (dimap f g <$> p)
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lmap f (MkCayley p) = MkCayley (lmap f <$> p)
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lmap f (MkCayley p) = MkCayley (lmap f <$> p)
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rmap g (MkCayley p) = MkCayley (rmap g <$> p)
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rmap g (MkCayley p) = MkCayley (rmap g <$> p)
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export
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public export
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Functor f => ProfunctorFunctor (Cayley f) where
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Functor f => ProfunctorFunctor (Cayley f) where
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promap f (MkCayley p) = MkCayley (map f p)
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promap f (MkCayley p) = MkCayley (map f p)
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export
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public export
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Monad m => ProfunctorMonad (Cayley m) where
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Monad m => ProfunctorMonad (Cayley m) where
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propure = MkCayley . pure
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propure = MkCayley . pure
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projoin (MkCayley p) = MkCayley $ p >>= runCayley
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projoin (MkCayley p) = MkCayley $ p >>= runCayley
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export
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public export
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Functor f => GenStrong ten p => GenStrong ten (Cayley f p) where
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Functor f => GenStrong ten p => GenStrong ten (Cayley f p) where
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strongl (MkCayley p) = MkCayley (strongl {ten} <$> p)
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strongl (MkCayley p) = MkCayley (strongl {ten} <$> p)
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strongr (MkCayley p) = MkCayley (strongr {ten} <$> p)
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strongr (MkCayley p) = MkCayley (strongr {ten} <$> p)
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export
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public export
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Functor f => GenCostrong ten p => GenCostrong ten (Cayley f p) where
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Functor f => GenCostrong ten p => GenCostrong ten (Cayley f p) where
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costrongl (MkCayley p) = MkCayley (costrongl {ten} <$> p)
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costrongl (MkCayley p) = MkCayley (costrongl {ten} <$> p)
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costrongr (MkCayley p) = MkCayley (costrongr {ten} <$> p)
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costrongr (MkCayley p) = MkCayley (costrongr {ten} <$> p)
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export
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public export
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Functor f => Closed p => Closed (Cayley f p) where
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Functor f => Closed p => Closed (Cayley f p) where
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closed (MkCayley p) = MkCayley (closed <$> p)
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closed (MkCayley p) = MkCayley (closed <$> p)
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export
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public export
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Functor f => Traversing p => Traversing (Cayley f p) where
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Functor f => Traversing p => Traversing (Cayley f p) where
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traverse' (MkCayley p) = MkCayley (traverse' <$> p)
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traverse' (MkCayley p) = MkCayley (traverse' <$> p)
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wander f (MkCayley p) = MkCayley (wander f <$> p)
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wander f (MkCayley p) = MkCayley (wander f <$> p)
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export
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public export
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Functor f => Mapping p => Mapping (Cayley f p) where
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Functor f => Mapping p => Mapping (Cayley f p) where
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map' (MkCayley p) = MkCayley (map' <$> p)
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map' (MkCayley p) = MkCayley (map' <$> p)
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roam f (MkCayley p) = MkCayley (roam f <$> p)
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roam f (MkCayley p) = MkCayley (roam f <$> p)
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export
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public export
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Functor g => Sieve p f => Sieve (Cayley g p) (g . f) using Functor.Compose where
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Functor g => Sieve p f => Sieve (Cayley g p) (g . f) using Functor.Compose where
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sieve (MkCayley p) x = ($ x) . sieve <$> p
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sieve (MkCayley p) x = ($ x) . sieve <$> p
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export
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public export
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mapCayley : (forall x. f x -> g x) -> Cayley f p :-> Cayley g p
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mapCayley : (forall x. f x -> g x) -> Cayley f p :-> Cayley g p
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mapCayley f (MkCayley p) = MkCayley (f p)
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mapCayley f (MkCayley p) = MkCayley (f p)
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@ -30,22 +30,22 @@ interface Profunctor p => Closed p where
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------------------------------------------------------------------------------
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------------------------------------------------------------------------------
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export
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public export
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Closed Morphism where
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Closed Morphism where
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closed (Mor f) = Mor (f .)
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closed (Mor f) = Mor (f .)
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||| A named implementation of `Closed` for function types.
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||| A named implementation of `Closed` for function types.
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||| Use this to avoid having to use a type wrapper like `Morphism`.
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||| Use this to avoid having to use a type wrapper like `Morphism`.
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export
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public export
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[Function] Closed (\a,b => a -> b) using Profunctor.Function where
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[Function] Closed (\a,b => a -> b) using Profunctor.Function where
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closed = (.)
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closed = (.)
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export
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public export
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Functor f => Closed (Costar f) where
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Functor f => Closed (Costar f) where
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closed (MkCostar p) = MkCostar $ \f,x => p (map ($ x) f)
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closed (MkCostar p) = MkCostar $ \f,x => p (map ($ x) f)
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export
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public export
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curry' : Closed p => p (a, b) c -> p a (b -> c)
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curry' : Closed p => p (a, b) c -> p a (b -> c)
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curry' = lmap (,) . closed
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curry' = lmap (,) . closed
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@ -71,40 +71,40 @@ record Closure p a b where
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runClosure : forall x. p (x -> a) (x -> b)
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runClosure : forall x. p (x -> a) (x -> b)
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export
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public export
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Profunctor p => Profunctor (Closure p) where
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Profunctor p => Profunctor (Closure p) where
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dimap f g (MkClosure p) = MkClosure $ dimap (f .) (g .) p
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dimap f g (MkClosure p) = MkClosure $ dimap (f .) (g .) p
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lmap f (MkClosure p) = MkClosure $ lmap (f .) p
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lmap f (MkClosure p) = MkClosure $ lmap (f .) p
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rmap f (MkClosure p) = MkClosure $ rmap (f .) p
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rmap f (MkClosure p) = MkClosure $ rmap (f .) p
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export
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public export
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ProfunctorFunctor Closure where
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ProfunctorFunctor Closure where
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promap f (MkClosure p) = MkClosure (f p)
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promap f (MkClosure p) = MkClosure (f p)
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export
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public export
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ProfunctorComonad Closure where
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ProfunctorComonad Closure where
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proextract (MkClosure p) = dimap const ($ ()) p
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proextract (MkClosure p) = dimap const ($ ()) p
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produplicate (MkClosure p) = MkClosure $ MkClosure $ dimap uncurry curry p
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produplicate (MkClosure p) = MkClosure $ MkClosure $ dimap uncurry curry p
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export
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public export
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Strong p => GenStrong Pair (Closure p) where
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Strong p => GenStrong Pair (Closure p) where
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strongl (MkClosure p) = MkClosure $ dimap hither yon $ first p
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strongl (MkClosure p) = MkClosure $ dimap hither yon $ first p
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strongr (MkClosure p) = MkClosure $ dimap hither yon $ second p
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strongr (MkClosure p) = MkClosure $ dimap hither yon $ second p
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export
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public export
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Profunctor p => Closed (Closure p) where
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Profunctor p => Closed (Closure p) where
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closed p = runClosure $ produplicate p
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closed p = runClosure $ produplicate p
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export
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public export
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Profunctor p => Functor (Closure p a) where
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Profunctor p => Functor (Closure p a) where
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map = rmap
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map = rmap
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export
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public export
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close : Closed p => p :-> q -> p :-> Closure q
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close : Closed p => p :-> q -> p :-> Closure q
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close f p = MkClosure $ f $ closed p
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close f p = MkClosure $ f $ closed p
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export
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public export
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unclose : Profunctor q => p :-> Closure q -> p :-> q
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unclose : Profunctor q => p :-> Closure q -> p :-> q
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unclose f p = dimap const ($ ()) $ runClosure $ f p
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unclose f p = dimap const ($ ()) $ runClosure $ f p
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@ -121,17 +121,17 @@ data Environment : (p : Type -> Type -> Type) -> Type -> Type -> Type where
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MkEnv : ((z -> y) -> b) -> p x y -> (a -> z -> x) -> Environment p a b
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MkEnv : ((z -> y) -> b) -> p x y -> (a -> z -> x) -> Environment p a b
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export
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public export
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Profunctor (Environment p) where
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Profunctor (Environment p) where
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dimap f g (MkEnv l m r) = MkEnv (g . l) m (r . f)
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dimap f g (MkEnv l m r) = MkEnv (g . l) m (r . f)
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lmap f (MkEnv l m r) = MkEnv l m (r . f)
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lmap f (MkEnv l m r) = MkEnv l m (r . f)
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rmap g (MkEnv l m r) = MkEnv (g . l) m r
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rmap g (MkEnv l m r) = MkEnv (g . l) m r
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export
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public export
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ProfunctorFunctor Environment where
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ProfunctorFunctor Environment where
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promap f (MkEnv l m r) = MkEnv l (f m) r
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promap f (MkEnv l m r) = MkEnv l (f m) r
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export
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public export
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ProfunctorMonad Environment where
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ProfunctorMonad Environment where
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propure p = MkEnv ($ ()) p const
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propure p = MkEnv ($ ()) p const
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projoin (MkEnv {x=x',y=y',z=z'} l' (MkEnv {x,y,z} l m r) r') = MkEnv (ll . curry) m rr
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projoin (MkEnv {x=x',y=y',z=z'} l' (MkEnv {x,y,z} l m r) r') = MkEnv (ll . curry) m rr
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@ -141,12 +141,12 @@ ProfunctorMonad Environment where
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rr : a -> (z', z) -> x
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rr : a -> (z', z) -> x
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rr a (b, c) = r (r' a b) c
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rr a (b, c) = r (r' a b) c
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export
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public export
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ProfunctorAdjunction Environment Closure where
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ProfunctorAdjunction Environment Closure where
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prounit p = MkClosure (MkEnv id p id)
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prounit p = MkClosure (MkEnv id p id)
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procounit (MkEnv l (MkClosure x) r) = dimap r l x
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procounit (MkEnv l (MkClosure x) r) = dimap r l x
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export
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public export
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Closed (Environment p) where
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Closed (Environment p) where
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closed {x=x'} (MkEnv {x,y,z} l m r) = MkEnv l' m r'
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closed {x=x'} (MkEnv {x,y,z} l m r) = MkEnv l' m r'
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where
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where
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@ -155,15 +155,15 @@ Closed (Environment p) where
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r' : (x' -> a) -> (z, x') -> x
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r' : (x' -> a) -> (z, x') -> x
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r' f (z,x) = r (f x) z
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r' f (z,x) = r (f x) z
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export
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public export
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Profunctor p => Functor (Environment p a) where
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Profunctor p => Functor (Environment p a) where
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map = rmap
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map = rmap
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export
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public export
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environment : Closed q => p :-> q -> Environment p :-> q
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environment : Closed q => p :-> q -> Environment p :-> q
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environment f (MkEnv l m r) = dimap r l $ closed (f m)
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environment f (MkEnv l m r) = dimap r l $ closed (f m)
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export
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public export
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unenvironment : Environment p :-> q -> p :-> q
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unenvironment : Environment p :-> q -> p :-> q
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unenvironment f p = f (MkEnv ($ ()) p const)
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unenvironment f p = f (MkEnv ($ ()) p const)
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@ -84,17 +84,17 @@ unright = costrongr {ten=Either}
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------------------------------------------------------------------------------
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------------------------------------------------------------------------------
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export
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public export
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GenCostrong Pair Tagged where
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GenCostrong Pair Tagged where
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costrongl (Tag (x,_)) = Tag x
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costrongl (Tag (x,_)) = Tag x
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costrongr (Tag (_,x)) = Tag x
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costrongr (Tag (_,x)) = Tag x
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export
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public export
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GenCostrong Either (Forget r) where
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GenCostrong Either (Forget r) where
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costrongl (MkForget k) = MkForget (k . Left)
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costrongl (MkForget k) = MkForget (k . Left)
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costrongr (MkForget k) = MkForget (k . Right)
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costrongr (MkForget k) = MkForget (k . Right)
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export
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public export
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GenCostrong Pair (Coforget r) where
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GenCostrong Pair (Coforget r) where
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costrongl (MkCoforget k) = MkCoforget (fst . k)
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costrongl (MkCoforget k) = MkCoforget (fst . k)
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costrongr (MkCoforget k) = MkCoforget (snd . k)
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costrongr (MkCoforget k) = MkCoforget (snd . k)
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data GenCotambara : (ten, p : Type -> Type -> Type) -> Type -> Type -> Type where
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data GenCotambara : (ten, p : Type -> Type -> Type) -> Type -> Type -> Type where
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MkCotambara : GenCostrong ten q => q :-> p -> q a b -> GenCotambara ten p a b
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MkCotambara : GenCostrong ten q => q :-> p -> q a b -> GenCotambara ten p a b
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export
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public export
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Profunctor (GenCotambara ten p) where
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Profunctor (GenCotambara ten p) where
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lmap f (MkCotambara n p) = MkCotambara n (lmap f p)
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lmap f (MkCotambara n p) = MkCotambara n (lmap f p)
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rmap f (MkCotambara n p) = MkCotambara n (rmap f p)
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rmap f (MkCotambara n p) = MkCotambara n (rmap f p)
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dimap f g (MkCotambara n p) = MkCotambara n (dimap f g p)
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dimap f g (MkCotambara n p) = MkCotambara n (dimap f g p)
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export
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public export
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ProfunctorFunctor (GenCotambara ten) where
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ProfunctorFunctor (GenCotambara ten) where
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promap f (MkCotambara n p) = MkCotambara (f . n) p
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promap f (MkCotambara n p) = MkCotambara (f . n) p
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export
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public export
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GenCostrong ten (GenCotambara ten p) where
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GenCostrong ten (GenCotambara ten p) where
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costrongl (MkCotambara @{costr} n p) = MkCotambara n (costrongl @{costr} p)
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costrongl (MkCotambara @{costr} n p) = MkCotambara n (costrongl @{costr} p)
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costrongr (MkCotambara @{costr} n p) = MkCotambara n (costrongr @{costr} p)
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costrongr (MkCotambara @{costr} n p) = MkCotambara n (costrongr @{costr} p)
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export
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public export
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ProfunctorComonad (GenCotambara ten) where
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ProfunctorComonad (GenCotambara ten) where
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proextract (MkCotambara n p) = n p
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proextract (MkCotambara n p) = n p
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produplicate (MkCotambara n p) = MkCotambara id (MkCotambara n p)
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produplicate (MkCotambara n p) = MkCotambara id (MkCotambara n p)
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export
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public export
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Functor (GenCotambara ten p a) where
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Functor (GenCotambara ten p a) where
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map = rmap
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map = rmap
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@ -153,11 +153,11 @@ CotambaraSum : (p : Type -> Type -> Type) -> Type -> Type -> Type
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CotambaraSum = GenCotambara Either
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CotambaraSum = GenCotambara Either
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export
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public export
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cotambara : GenCostrong ten p => p :-> q -> p :-> GenCotambara ten q
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cotambara : GenCostrong ten p => p :-> q -> p :-> GenCotambara ten q
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cotambara f = MkCotambara f
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cotambara f = MkCotambara f
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export
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public export
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uncotambara : Tensor ten i => Profunctor q => p :-> GenCotambara ten q -> p :-> q
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uncotambara : Tensor ten i => Profunctor q => p :-> GenCotambara ten q -> p :-> q
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uncotambara f p = proextract (f p)
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uncotambara f p = proextract (f p)
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@ -174,27 +174,27 @@ record GenCopastro (ten, p : Type -> Type -> Type) a b where
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constructor MkCopastro
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constructor MkCopastro
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runCopastro : forall q. GenCostrong ten q => p :-> q -> q a b
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runCopastro : forall q. GenCostrong ten q => p :-> q -> q a b
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export
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public export
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Profunctor (GenCopastro ten p) where
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Profunctor (GenCopastro ten p) where
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dimap f g (MkCopastro h) = MkCopastro $ \n => dimap f g (h n)
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dimap f g (MkCopastro h) = MkCopastro $ \n => dimap f g (h n)
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lmap f (MkCopastro h) = MkCopastro $ \n => lmap f (h n)
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lmap f (MkCopastro h) = MkCopastro $ \n => lmap f (h n)
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rmap f (MkCopastro h) = MkCopastro $ \n => rmap f (h n)
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rmap f (MkCopastro h) = MkCopastro $ \n => rmap f (h n)
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export
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public export
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ProfunctorFunctor (GenCopastro ten) where
|
ProfunctorFunctor (GenCopastro ten) where
|
||||||
promap f (MkCopastro h) = MkCopastro $ \n => h (n . f)
|
promap f (MkCopastro h) = MkCopastro $ \n => h (n . f)
|
||||||
|
|
||||||
export
|
public export
|
||||||
ProfunctorMonad (GenCopastro ten) where
|
ProfunctorMonad (GenCopastro ten) where
|
||||||
propure p = MkCopastro ($ p)
|
propure p = MkCopastro ($ p)
|
||||||
projoin p = MkCopastro $ \x => runCopastro p (\y => runCopastro y x)
|
projoin p = MkCopastro $ \x => runCopastro p (\y => runCopastro y x)
|
||||||
|
|
||||||
export
|
public export
|
||||||
GenCostrong ten (GenCopastro ten p) where
|
GenCostrong ten (GenCopastro ten p) where
|
||||||
costrongl (MkCopastro h) = MkCopastro $ \n => costrongl {ten} (h n)
|
costrongl (MkCopastro h) = MkCopastro $ \n => costrongl {ten} (h n)
|
||||||
costrongr (MkCopastro h) = MkCopastro $ \n => costrongr {ten} (h n)
|
costrongr (MkCopastro h) = MkCopastro $ \n => costrongr {ten} (h n)
|
||||||
|
|
||||||
export
|
public export
|
||||||
ProfunctorAdjunction (GenCopastro ten) (GenCotambara ten) where
|
ProfunctorAdjunction (GenCopastro ten) (GenCotambara ten) where
|
||||||
prounit p = MkCotambara id (propure {t=GenCopastro ten} p)
|
prounit p = MkCotambara id (propure {t=GenCopastro ten} p)
|
||||||
procounit (MkCopastro h) = proextract (h id)
|
procounit (MkCopastro h) = proextract (h id)
|
||||||
|
@ -217,10 +217,10 @@ CopastroSum : (p : Type -> Type -> Type) -> Type -> Type -> Type
|
||||||
CopastroSum = GenCopastro Either
|
CopastroSum = GenCopastro Either
|
||||||
|
|
||||||
|
|
||||||
export
|
public export
|
||||||
copastro : GenCostrong ten q => p :-> q -> GenCopastro ten p :-> q
|
copastro : GenCostrong ten q => p :-> q -> GenCopastro ten p :-> q
|
||||||
copastro f (MkCopastro h) = h f
|
copastro f (MkCopastro h) = h f
|
||||||
|
|
||||||
export
|
public export
|
||||||
uncopastro : Tensor ten i => GenCopastro ten p :-> q -> p :-> q
|
uncopastro : Tensor ten i => GenCopastro ten p :-> q -> p :-> q
|
||||||
uncopastro f x = f (MkCopastro ($ x))
|
uncopastro f x = f (MkCopastro ($ x))
|
||||||
|
|
|
@ -38,14 +38,14 @@ interface (Traversing p, Closed p) => Mapping p where
|
||||||
------------------------------------------------------------------------------
|
------------------------------------------------------------------------------
|
||||||
|
|
||||||
|
|
||||||
export
|
public export
|
||||||
Mapping Morphism where
|
Mapping Morphism where
|
||||||
map' (Mor f) = Mor (map f)
|
map' (Mor f) = Mor (map f)
|
||||||
roam f (Mor x) = Mor (f x)
|
roam f (Mor x) = Mor (f x)
|
||||||
|
|
||||||
||| A named implementation of `Mapping` for function types.
|
||| A named implementation of `Mapping` for function types.
|
||||||
||| Use this to avoid having to use a type wrapper like `Morphism`.
|
||| Use this to avoid having to use a type wrapper like `Morphism`.
|
||||||
export
|
public export
|
||||||
[Function] Mapping (\a,b => a -> b)
|
[Function] Mapping (\a,b => a -> b)
|
||||||
using Traversing.Function Closed.Function where
|
using Traversing.Function Closed.Function where
|
||||||
map' = map
|
map' = map
|
||||||
|
@ -64,31 +64,31 @@ record CofreeMapping p a b where
|
||||||
constructor MkCFM
|
constructor MkCFM
|
||||||
runCFM : forall f. Functor f => p (f a) (f b)
|
runCFM : forall f. Functor f => p (f a) (f b)
|
||||||
|
|
||||||
export
|
public export
|
||||||
Profunctor p => Profunctor (CofreeMapping p) where
|
Profunctor p => Profunctor (CofreeMapping p) where
|
||||||
lmap f (MkCFM p) = MkCFM (lmap (map f) p)
|
lmap f (MkCFM p) = MkCFM (lmap (map f) p)
|
||||||
rmap f (MkCFM p) = MkCFM (rmap (map f) p)
|
rmap f (MkCFM p) = MkCFM (rmap (map f) p)
|
||||||
dimap f g (MkCFM p) = MkCFM (dimap (map f) (map g) p)
|
dimap f g (MkCFM p) = MkCFM (dimap (map f) (map g) p)
|
||||||
|
|
||||||
export
|
public export
|
||||||
Profunctor p => Functor (CofreeMapping p a) where
|
Profunctor p => Functor (CofreeMapping p a) where
|
||||||
map = rmap
|
map = rmap
|
||||||
|
|
||||||
export
|
public export
|
||||||
ProfunctorFunctor CofreeMapping where
|
ProfunctorFunctor CofreeMapping where
|
||||||
promap f (MkCFM p) = MkCFM (f p)
|
promap f (MkCFM p) = MkCFM (f p)
|
||||||
|
|
||||||
export
|
public export
|
||||||
ProfunctorComonad CofreeMapping where
|
ProfunctorComonad CofreeMapping where
|
||||||
proextract (MkCFM p) = dimap Id runIdentity p
|
proextract (MkCFM p) = dimap Id runIdentity p
|
||||||
produplicate (MkCFM p) = MkCFM $ MkCFM $ p @{Compose}
|
produplicate (MkCFM p) = MkCFM $ MkCFM $ p @{Compose}
|
||||||
|
|
||||||
export
|
public export
|
||||||
Symmetric ten => Profunctor p => GenStrong ten (CofreeMapping p) where
|
Symmetric ten => Profunctor p => GenStrong ten (CofreeMapping p) where
|
||||||
strongr (MkCFM p) = MkCFM (p @{Compose {g=ten c} @{%search} @{MkFunctor mapSnd}})
|
strongr (MkCFM p) = MkCFM (p @{Compose {g=ten c} @{%search} @{MkFunctor mapSnd}})
|
||||||
strongl (MkCFM p) = MkCFM (p @{Compose {g=(`ten` c)} @{%search} @{MkFunctor mapFst}})
|
strongl (MkCFM p) = MkCFM (p @{Compose {g=(`ten` c)} @{%search} @{MkFunctor mapFst}})
|
||||||
|
|
||||||
export
|
public export
|
||||||
Profunctor p => Closed (CofreeMapping p) where
|
Profunctor p => Closed (CofreeMapping p) where
|
||||||
closed (MkCFM p) = MkCFM (p @{Compose {g = \b => x -> b} @{%search} @{MkFunctor (.)}})
|
closed (MkCFM p) = MkCFM (p @{Compose {g = \b => x -> b} @{%search} @{MkFunctor (.)}})
|
||||||
|
|
||||||
|
@ -99,12 +99,12 @@ roamCofree f (MkCFM p) = MkCFM $ dimap (map (flip f)) (map ($ id)) $
|
||||||
functor : Functor (\a => (a -> b) -> t)
|
functor : Functor (\a => (a -> b) -> t)
|
||||||
functor = MkFunctor (\f => (. (. f)))
|
functor = MkFunctor (\f => (. (. f)))
|
||||||
|
|
||||||
export
|
public export
|
||||||
Profunctor p => Traversing (CofreeMapping p) where
|
Profunctor p => Traversing (CofreeMapping p) where
|
||||||
traverse' (MkCFM p) = MkCFM (p @{Compose})
|
traverse' (MkCFM p) = MkCFM (p @{Compose})
|
||||||
wander f = roamCofree $ (runIdentity .) . f . (Id .)
|
wander f = roamCofree $ (runIdentity .) . f . (Id .)
|
||||||
|
|
||||||
export
|
public export
|
||||||
Profunctor p => Mapping (CofreeMapping p) where
|
Profunctor p => Mapping (CofreeMapping p) where
|
||||||
map' (MkCFM p) = MkCFM (p @{Compose})
|
map' (MkCFM p) = MkCFM (p @{Compose})
|
||||||
roam = roamCofree
|
roam = roamCofree
|
||||||
|
@ -119,36 +119,36 @@ public export
|
||||||
data FreeMapping : (p : Type -> Type -> Type) -> Type -> Type -> Type where
|
data FreeMapping : (p : Type -> Type -> Type) -> Type -> Type -> Type where
|
||||||
MkFM : Functor f => (f y -> b) -> p x y -> (a -> f x) -> FreeMapping p a b
|
MkFM : Functor f => (f y -> b) -> p x y -> (a -> f x) -> FreeMapping p a b
|
||||||
|
|
||||||
export
|
public export
|
||||||
Profunctor (FreeMapping p) where
|
Profunctor (FreeMapping p) where
|
||||||
lmap f (MkFM l m r) = MkFM l m (r . f)
|
lmap f (MkFM l m r) = MkFM l m (r . f)
|
||||||
rmap f (MkFM l m r) = MkFM (f . l) m r
|
rmap f (MkFM l m r) = MkFM (f . l) m r
|
||||||
dimap f g (MkFM l m r) = MkFM (g . l) m (r . f)
|
dimap f g (MkFM l m r) = MkFM (g . l) m (r . f)
|
||||||
|
|
||||||
export
|
public export
|
||||||
ProfunctorFunctor FreeMapping where
|
ProfunctorFunctor FreeMapping where
|
||||||
promap f (MkFM l m r) = MkFM l (f m) r
|
promap f (MkFM l m r) = MkFM l (f m) r
|
||||||
|
|
||||||
export
|
public export
|
||||||
ProfunctorMonad FreeMapping where
|
ProfunctorMonad FreeMapping where
|
||||||
propure p = MkFM runIdentity p Id
|
propure p = MkFM runIdentity p Id
|
||||||
projoin (MkFM l' (MkFM l m r) r') = MkFM @{Compose} (l' . map l) m (map r . r')
|
projoin (MkFM l' (MkFM l m r) r') = MkFM @{Compose} (l' . map l) m (map r . r')
|
||||||
|
|
||||||
export
|
public export
|
||||||
Functor (FreeMapping p a) where
|
Functor (FreeMapping p a) where
|
||||||
map = rmap
|
map = rmap
|
||||||
|
|
||||||
export
|
public export
|
||||||
GenStrong Pair (FreeMapping p) where
|
GenStrong Pair (FreeMapping p) where
|
||||||
strongr (MkFM l m r) = MkFM @{Compose} (map l) m (map r)
|
strongr (MkFM l m r) = MkFM @{Compose} (map l) m (map r)
|
||||||
strongl = dimap swap' swap' . strongr {p=FreeMapping p}
|
strongl = dimap swap' swap' . strongr {p=FreeMapping p}
|
||||||
|
|
||||||
export
|
public export
|
||||||
GenStrong Either (FreeMapping p) where
|
GenStrong Either (FreeMapping p) where
|
||||||
strongr (MkFM l m r) = MkFM @{Compose} (map l) m (map r)
|
strongr (MkFM l m r) = MkFM @{Compose} (map l) m (map r)
|
||||||
strongl = dimap swap' swap' . strongr {p=FreeMapping p}
|
strongl = dimap swap' swap' . strongr {p=FreeMapping p}
|
||||||
|
|
||||||
export
|
public export
|
||||||
Closed (FreeMapping p) where
|
Closed (FreeMapping p) where
|
||||||
closed (MkFM l m r) = dimap Mor applyMor $ MkFM @{Compose} (map l) m (map r)
|
closed (MkFM l m r) = dimap Mor applyMor $ MkFM @{Compose} (map l) m (map r)
|
||||||
|
|
||||||
|
@ -158,12 +158,12 @@ roamFree f (MkFM l m r) = MkFM @{Compose @{functor}} (($ id) . map @{functor} l)
|
||||||
functor : Functor (\a => (a -> b) -> t)
|
functor : Functor (\a => (a -> b) -> t)
|
||||||
functor = MkFunctor (\f => (. (. f)))
|
functor = MkFunctor (\f => (. (. f)))
|
||||||
|
|
||||||
export
|
public export
|
||||||
Traversing (FreeMapping p) where
|
Traversing (FreeMapping p) where
|
||||||
traverse' (MkFM l m r) = MkFM @{Compose} (map l) m (map r)
|
traverse' (MkFM l m r) = MkFM @{Compose} (map l) m (map r)
|
||||||
wander f = roamFree $ (runIdentity .) . f . (Id .)
|
wander f = roamFree $ (runIdentity .) . f . (Id .)
|
||||||
|
|
||||||
export
|
public export
|
||||||
Mapping (FreeMapping p) where
|
Mapping (FreeMapping p) where
|
||||||
map' (MkFM l m r) = MkFM @{Compose} (map l) m (map r)
|
map' (MkFM l m r) = MkFM @{Compose} (map l) m (map r)
|
||||||
roam = roamFree
|
roam = roamFree
|
||||||
|
|
|
@ -21,7 +21,7 @@ interface (Sieve p f, Strong p) => Representable p f | p where
|
||||||
tabulate : (a -> f b) -> p a b
|
tabulate : (a -> f b) -> p a b
|
||||||
|
|
||||||
|
|
||||||
||| A profunctor `p` is representable if it is isomorphic to `Costar f` for some `f`.
|
||| A profunctor `p` is corepresentable if it is isomorphic to `Costar f` for some `f`.
|
||||||
public export
|
public export
|
||||||
interface Cosieve p f => Corepresentable p f | p where
|
interface Cosieve p f => Corepresentable p f | p where
|
||||||
cotabulate : (f a -> b) -> p a b
|
cotabulate : (f a -> b) -> p a b
|
||||||
|
|
|
@ -30,44 +30,44 @@ interface (Profunctor p, Functor f) => Cosieve p f | p where
|
||||||
------------------------------------------------------------------------------
|
------------------------------------------------------------------------------
|
||||||
|
|
||||||
|
|
||||||
export
|
public export
|
||||||
Sieve Morphism Identity where
|
Sieve Morphism Identity where
|
||||||
sieve (Mor f) = Id . f
|
sieve (Mor f) = Id . f
|
||||||
|
|
||||||
||| A named implementation of `Sieve` for function types.
|
||| A named implementation of `Sieve` for function types.
|
||||||
||| Use this to avoid having to use a type wrapper like `Morphism`.
|
||| Use this to avoid having to use a type wrapper like `Morphism`.
|
||||||
export
|
public export
|
||||||
[Function] Sieve (\a,b => a -> b) Identity using Profunctor.Function where
|
[Function] Sieve (\a,b => a -> b) Identity using Profunctor.Function where
|
||||||
sieve = (Id .)
|
sieve = (Id .)
|
||||||
|
|
||||||
export
|
public export
|
||||||
Functor f => Sieve (Kleislimorphism f) f where
|
Functor f => Sieve (Kleislimorphism f) f where
|
||||||
sieve = applyKleisli
|
sieve = applyKleisli
|
||||||
|
|
||||||
export
|
public export
|
||||||
Functor f => Sieve (Star f) f where
|
Functor f => Sieve (Star f) f where
|
||||||
sieve = applyStar
|
sieve = applyStar
|
||||||
|
|
||||||
export
|
public export
|
||||||
Sieve (Forget r) (Const r) where
|
Sieve (Forget r) (Const r) where
|
||||||
sieve (MkForget k) = MkConst . k
|
sieve (MkForget k) = MkConst . k
|
||||||
|
|
||||||
|
|
||||||
export
|
public export
|
||||||
Cosieve Morphism Identity where
|
Cosieve Morphism Identity where
|
||||||
cosieve (Mor f) = f . runIdentity
|
cosieve (Mor f) = f . runIdentity
|
||||||
|
|
||||||
namespace Cosieve
|
namespace Cosieve
|
||||||
||| A named implementation of `Cosieve` for function types.
|
||| A named implementation of `Cosieve` for function types.
|
||||||
||| Use this to avoid having to use a type wrapper like `Morphism`.
|
||| Use this to avoid having to use a type wrapper like `Morphism`.
|
||||||
export
|
public export
|
||||||
[Function] Cosieve (\a,b => a -> b) Identity using Profunctor.Function where
|
[Function] Cosieve (\a,b => a -> b) Identity using Profunctor.Function where
|
||||||
cosieve = (. runIdentity)
|
cosieve = (. runIdentity)
|
||||||
|
|
||||||
export
|
public export
|
||||||
Functor f => Cosieve (Costar f) f where
|
Functor f => Cosieve (Costar f) f where
|
||||||
cosieve = applyCostar
|
cosieve = applyCostar
|
||||||
|
|
||||||
export
|
public export
|
||||||
Cosieve (Coforget r) (Const r) where
|
Cosieve (Coforget r) (Const r) where
|
||||||
cosieve (MkCoforget k) = k . runConst
|
cosieve (MkCoforget k) = k . runConst
|
||||||
|
|
|
@ -80,11 +80,11 @@ right : Choice p => p a b -> p (Either c a) (Either c b)
|
||||||
right = strongr {ten=Either}
|
right = strongr {ten=Either}
|
||||||
|
|
||||||
|
|
||||||
export
|
public export
|
||||||
uncurry' : Strong p => p a (b -> c) -> p (a, b) c
|
uncurry' : Strong p => p a (b -> c) -> p (a, b) c
|
||||||
uncurry' = rmap (uncurry id) . first
|
uncurry' = rmap (uncurry id) . first
|
||||||
|
|
||||||
export
|
public export
|
||||||
strong : Strong p => (a -> b -> c) -> p a b -> p a c
|
strong : Strong p => (a -> b -> c) -> p a b -> p a c
|
||||||
strong f = dimap dup (uncurry $ flip f) . first
|
strong f = dimap dup (uncurry $ flip f) . first
|
||||||
|
|
||||||
|
@ -94,55 +94,55 @@ strong f = dimap dup (uncurry $ flip f) . first
|
||||||
------------------------------------------------------------------------------
|
------------------------------------------------------------------------------
|
||||||
|
|
||||||
|
|
||||||
export
|
public export
|
||||||
Bifunctor ten => GenStrong ten Morphism where
|
Bifunctor ten => GenStrong ten Morphism where
|
||||||
strongl (Mor f) = Mor (mapFst f)
|
strongl (Mor f) = Mor (mapFst f)
|
||||||
strongr (Mor f) = Mor (mapSnd f)
|
strongr (Mor f) = Mor (mapSnd f)
|
||||||
|
|
||||||
||| A named implementation of `GenStrong` for function types.
|
||| A named implementation of `GenStrong` for function types.
|
||||||
||| Use this to avoid having to use a type wrapper like `Morphism`.
|
||| Use this to avoid having to use a type wrapper like `Morphism`.
|
||||||
export
|
public export
|
||||||
[Function] Bifunctor ten => GenStrong ten (\a,b => a -> b)
|
[Function] Bifunctor ten => GenStrong ten (\a,b => a -> b)
|
||||||
using Profunctor.Function where
|
using Profunctor.Function where
|
||||||
strongl = mapFst
|
strongl = mapFst
|
||||||
strongr = mapSnd
|
strongr = mapSnd
|
||||||
|
|
||||||
export
|
public export
|
||||||
Functor f => GenStrong Pair (Kleislimorphism f) where
|
Functor f => GenStrong Pair (Kleislimorphism f) where
|
||||||
strongl (Kleisli f) = Kleisli $ \(a,c) => (,c) <$> f a
|
strongl (Kleisli f) = Kleisli $ \(a,c) => (,c) <$> f a
|
||||||
strongr (Kleisli f) = Kleisli $ \(c,a) => (c,) <$> f a
|
strongr (Kleisli f) = Kleisli $ \(c,a) => (c,) <$> f a
|
||||||
|
|
||||||
export
|
public export
|
||||||
Applicative f => GenStrong Either (Kleislimorphism f) where
|
Applicative f => GenStrong Either (Kleislimorphism f) where
|
||||||
strongl (Kleisli f) = Kleisli $ either (map Left . f) (pure . Right)
|
strongl (Kleisli f) = Kleisli $ either (map Left . f) (pure . Right)
|
||||||
strongr (Kleisli f) = Kleisli $ either (pure . Left) (map Right . f)
|
strongr (Kleisli f) = Kleisli $ either (pure . Left) (map Right . f)
|
||||||
|
|
||||||
export
|
public export
|
||||||
Functor f => GenStrong Pair (Star f) where
|
Functor f => GenStrong Pair (Star f) where
|
||||||
strongl (MkStar f) = MkStar $ \(a,c) => (,c) <$> f a
|
strongl (MkStar f) = MkStar $ \(a,c) => (,c) <$> f a
|
||||||
strongr (MkStar f) = MkStar $ \(c,a) => (c,) <$> f a
|
strongr (MkStar f) = MkStar $ \(c,a) => (c,) <$> f a
|
||||||
|
|
||||||
export
|
public export
|
||||||
Applicative f => GenStrong Either (Star f) where
|
Applicative f => GenStrong Either (Star f) where
|
||||||
strongl (MkStar f) = MkStar $ either (map Left . f) (pure . Right)
|
strongl (MkStar f) = MkStar $ either (map Left . f) (pure . Right)
|
||||||
strongr (MkStar f) = MkStar $ either (pure . Left) (map Right . f)
|
strongr (MkStar f) = MkStar $ either (pure . Left) (map Right . f)
|
||||||
|
|
||||||
export
|
public export
|
||||||
GenStrong Either Tagged where
|
GenStrong Either Tagged where
|
||||||
strongl (Tag x) = Tag (Left x)
|
strongl (Tag x) = Tag (Left x)
|
||||||
strongr (Tag x) = Tag (Right x)
|
strongr (Tag x) = Tag (Right x)
|
||||||
|
|
||||||
export
|
public export
|
||||||
GenStrong Pair (Forget r) where
|
GenStrong Pair (Forget r) where
|
||||||
strongl (MkForget k) = MkForget (k . fst)
|
strongl (MkForget k) = MkForget (k . fst)
|
||||||
strongr (MkForget k) = MkForget (k . snd)
|
strongr (MkForget k) = MkForget (k . snd)
|
||||||
|
|
||||||
export
|
public export
|
||||||
Monoid r => GenStrong Either (Forget r) where
|
Monoid r => GenStrong Either (Forget r) where
|
||||||
strongl (MkForget k) = MkForget (either k (const neutral))
|
strongl (MkForget k) = MkForget (either k (const neutral))
|
||||||
strongr (MkForget k) = MkForget (either (const neutral) k)
|
strongr (MkForget k) = MkForget (either (const neutral) k)
|
||||||
|
|
||||||
export
|
public export
|
||||||
GenStrong Either (Coforget r) where
|
GenStrong Either (Coforget r) where
|
||||||
strongl (MkCoforget k) = MkCoforget (Left . k)
|
strongl (MkCoforget k) = MkCoforget (Left . k)
|
||||||
strongr (MkCoforget k) = MkCoforget (Right . k)
|
strongr (MkCoforget k) = MkCoforget (Right . k)
|
||||||
|
@ -160,26 +160,26 @@ record GenTambara (ten, p : Type -> Type -> Type) a b where
|
||||||
constructor MkTambara
|
constructor MkTambara
|
||||||
runTambara : forall c. p (a `ten` c) (b `ten` c)
|
runTambara : forall c. p (a `ten` c) (b `ten` c)
|
||||||
|
|
||||||
export
|
public export
|
||||||
Bifunctor ten => Profunctor p => Profunctor (GenTambara ten p) where
|
Bifunctor ten => Profunctor p => Profunctor (GenTambara ten p) where
|
||||||
dimap f g (MkTambara p) = MkTambara $ dimap (mapFst f) (mapFst g) p
|
dimap f g (MkTambara p) = MkTambara $ dimap (mapFst f) (mapFst g) p
|
||||||
|
|
||||||
export
|
public export
|
||||||
ProfunctorFunctor (GenTambara ten) where
|
ProfunctorFunctor (GenTambara ten) where
|
||||||
promap f (MkTambara p) = MkTambara (f p)
|
promap f (MkTambara p) = MkTambara (f p)
|
||||||
|
|
||||||
export
|
public export
|
||||||
Tensor ten i => ProfunctorComonad (GenTambara ten) where
|
Tensor ten i => ProfunctorComonad (GenTambara ten) where
|
||||||
proextract (MkTambara p) = dimap unitr.rightToLeft unitr.leftToRight p
|
proextract (MkTambara p) = dimap unitr.rightToLeft unitr.leftToRight p
|
||||||
produplicate (MkTambara p) = MkTambara $ MkTambara $ dimap assocr assocl p
|
produplicate (MkTambara p) = MkTambara $ MkTambara $ dimap assocr assocl p
|
||||||
|
|
||||||
export
|
public export
|
||||||
Associative ten => Symmetric ten => Profunctor p => GenStrong ten (GenTambara ten p) where
|
Associative ten => Symmetric ten => Profunctor p => GenStrong ten (GenTambara ten p) where
|
||||||
strongl (MkTambara p) = MkTambara $ dimap assocr assocl p
|
strongl (MkTambara p) = MkTambara $ dimap assocr assocl p
|
||||||
strongr (MkTambara p) = MkTambara $ dimap (assocr . mapFst swap')
|
strongr (MkTambara p) = MkTambara $ dimap (assocr . mapFst swap')
|
||||||
(mapFst swap' . assocl) p
|
(mapFst swap' . assocl) p
|
||||||
|
|
||||||
export
|
public export
|
||||||
Bifunctor ten => Profunctor p => Functor (GenTambara ten p a) where
|
Bifunctor ten => Profunctor p => Functor (GenTambara ten p a) where
|
||||||
map = rmap
|
map = rmap
|
||||||
|
|
||||||
|
@ -201,11 +201,11 @@ TambaraSum : (p : Type -> Type -> Type) -> Type -> Type -> Type
|
||||||
TambaraSum = GenTambara Either
|
TambaraSum = GenTambara Either
|
||||||
|
|
||||||
|
|
||||||
export
|
public export
|
||||||
tambara : GenStrong ten p => p :-> q -> p :-> GenTambara ten q
|
tambara : GenStrong ten p => p :-> q -> p :-> GenTambara ten q
|
||||||
tambara @{gs} f x = MkTambara $ f $ strongl @{gs} x
|
tambara @{gs} f x = MkTambara $ f $ strongl @{gs} x
|
||||||
|
|
||||||
export
|
public export
|
||||||
untambara : Tensor ten i => Profunctor q => p :-> GenTambara ten q -> p :-> q
|
untambara : Tensor ten i => Profunctor q => p :-> GenTambara ten q -> p :-> q
|
||||||
untambara f x = dimap unitr.rightToLeft unitr.leftToRight $ runTambara $ f x
|
untambara f x = dimap unitr.rightToLeft unitr.leftToRight $ runTambara $ f x
|
||||||
|
|
||||||
|
@ -222,17 +222,17 @@ data GenPastro : (ten, p : Type -> Type -> Type) -> Type -> Type -> Type where
|
||||||
MkPastro : (y `ten` z -> b) -> p x y -> (a -> x `ten` z) -> GenPastro ten p a b
|
MkPastro : (y `ten` z -> b) -> p x y -> (a -> x `ten` z) -> GenPastro ten p a b
|
||||||
|
|
||||||
|
|
||||||
export
|
public export
|
||||||
Profunctor (GenPastro ten p) where
|
Profunctor (GenPastro ten p) where
|
||||||
dimap f g (MkPastro l m r) = MkPastro (g . l) m (r . f)
|
dimap f g (MkPastro l m r) = MkPastro (g . l) m (r . f)
|
||||||
lmap f (MkPastro l m r) = MkPastro l m (r . f)
|
lmap f (MkPastro l m r) = MkPastro l m (r . f)
|
||||||
rmap g (MkPastro l m r) = MkPastro (g . l) m r
|
rmap g (MkPastro l m r) = MkPastro (g . l) m r
|
||||||
|
|
||||||
export
|
public export
|
||||||
ProfunctorFunctor (GenPastro ten) where
|
ProfunctorFunctor (GenPastro ten) where
|
||||||
promap f (MkPastro l m r) = MkPastro l (f m) r
|
promap f (MkPastro l m r) = MkPastro l (f m) r
|
||||||
|
|
||||||
export
|
public export
|
||||||
(Tensor ten i, Symmetric ten) => ProfunctorMonad (GenPastro ten) where
|
(Tensor ten i, Symmetric ten) => ProfunctorMonad (GenPastro ten) where
|
||||||
propure x = MkPastro unitr.leftToRight x unitr.rightToLeft
|
propure x = MkPastro unitr.leftToRight x unitr.rightToLeft
|
||||||
projoin (MkPastro {x=x',y=y',z=z'} l' (MkPastro {x,y,z} l m r) r') = MkPastro ll m rr
|
projoin (MkPastro {x=x',y=y',z=z'} l' (MkPastro {x,y,z} l m r) r') = MkPastro ll m rr
|
||||||
|
@ -243,12 +243,12 @@ export
|
||||||
rr : a -> x `ten` (z' `ten` z)
|
rr : a -> x `ten` (z' `ten` z)
|
||||||
rr = mapSnd swap' . assocr . mapFst r . r'
|
rr = mapSnd swap' . assocr . mapFst r . r'
|
||||||
|
|
||||||
export
|
public export
|
||||||
ProfunctorAdjunction (GenPastro ten) (GenTambara ten) where
|
ProfunctorAdjunction (GenPastro ten) (GenTambara ten) where
|
||||||
prounit x = MkTambara (MkPastro id x id)
|
prounit x = MkTambara (MkPastro id x id)
|
||||||
procounit (MkPastro l (MkTambara x) r) = dimap r l x
|
procounit (MkPastro l (MkTambara x) r) = dimap r l x
|
||||||
|
|
||||||
export
|
public export
|
||||||
(Associative ten, Symmetric ten) => GenStrong ten (GenPastro ten p) where
|
(Associative ten, Symmetric ten) => GenStrong ten (GenPastro ten p) where
|
||||||
strongl (MkPastro {x,y,z} l m r) = MkPastro l' m r'
|
strongl (MkPastro {x,y,z} l m r) = MkPastro l' m r'
|
||||||
where
|
where
|
||||||
|
@ -281,11 +281,11 @@ PastroSum : (p : Type -> Type -> Type) -> Type -> Type -> Type
|
||||||
PastroSum = GenPastro Either
|
PastroSum = GenPastro Either
|
||||||
|
|
||||||
|
|
||||||
export
|
public export
|
||||||
pastro : GenStrong ten q => p :-> q -> GenPastro ten p :-> q
|
pastro : GenStrong ten q => p :-> q -> GenPastro ten p :-> q
|
||||||
pastro @{gs} f (MkPastro l m r) = dimap r l (strongl @{gs} (f m))
|
pastro @{gs} f (MkPastro l m r) = dimap r l (strongl @{gs} (f m))
|
||||||
|
|
||||||
export
|
public export
|
||||||
unpastro : Tensor ten i => GenPastro ten p :-> q -> p :-> q
|
unpastro : Tensor ten i => GenPastro ten p :-> q -> p :-> q
|
||||||
unpastro f x = f (MkPastro unitr.leftToRight x unitr.rightToLeft)
|
unpastro f x = f (MkPastro unitr.leftToRight x unitr.rightToLeft)
|
||||||
|
|
||||||
|
|
|
@ -66,7 +66,7 @@ Foldable (Baz t b) where
|
||||||
Traversable (Baz t b) where
|
Traversable (Baz t b) where
|
||||||
traverse f bz = map (\m => MkBaz (runBazaar m)) $ runBaz bz @{Compose} $ \x => sell <$> f x
|
traverse f bz = map (\m => MkBaz (runBazaar m)) $ runBaz bz @{Compose} $ \x => sell <$> f x
|
||||||
|
|
||||||
export
|
public export
|
||||||
wanderDef : Profunctor p => (forall f. Traversable f => p a b -> p (f a) (f b))
|
wanderDef : Profunctor p => (forall f. Traversable f => p a b -> p (f a) (f b))
|
||||||
-> (forall f. Applicative f => (a -> f b) -> s -> f t) -> p a b -> p s t
|
-> (forall f. Applicative f => (a -> f b) -> s -> f t) -> p a b -> p s t
|
||||||
wanderDef tr f = dimap (\s => MkBaz $ \afb => f afb s) sold . tr
|
wanderDef tr f = dimap (\s => MkBaz $ \afb => f afb s) sold . tr
|
||||||
|
@ -100,29 +100,29 @@ interface (Strong p, Choice p) => Traversing p where
|
||||||
------------------------------------------------------------------------------
|
------------------------------------------------------------------------------
|
||||||
|
|
||||||
|
|
||||||
export
|
public export
|
||||||
Traversing Morphism where
|
Traversing Morphism where
|
||||||
traverse' (Mor f) = Mor (map f)
|
traverse' (Mor f) = Mor (map f)
|
||||||
wander f (Mor p) = Mor (runIdentity . (f $ Id . p))
|
wander f (Mor p) = Mor (runIdentity . (f $ Id . p))
|
||||||
|
|
||||||
||| A named implementation of `Traversing` for function types.
|
||| A named implementation of `Traversing` for function types.
|
||||||
||| Use this to avoid having to use a type wrapper like `Morphism`.
|
||| Use this to avoid having to use a type wrapper like `Morphism`.
|
||||||
export
|
public export
|
||||||
[Function] Traversing (\a,b => a -> b) using Strong.Function where
|
[Function] Traversing (\a,b => a -> b) using Strong.Function where
|
||||||
traverse' = map
|
traverse' = map
|
||||||
wander f g = runIdentity . (f $ Id . g)
|
wander f g = runIdentity . (f $ Id . g)
|
||||||
|
|
||||||
export
|
public export
|
||||||
Applicative f => Traversing (Kleislimorphism f) where
|
Applicative f => Traversing (Kleislimorphism f) where
|
||||||
traverse' (Kleisli p) = Kleisli (traverse p)
|
traverse' (Kleisli p) = Kleisli (traverse p)
|
||||||
wander f (Kleisli p) = Kleisli (f p)
|
wander f (Kleisli p) = Kleisli (f p)
|
||||||
|
|
||||||
export
|
public export
|
||||||
Applicative f => Traversing (Star f) where
|
Applicative f => Traversing (Star f) where
|
||||||
traverse' (MkStar p) = MkStar (traverse p)
|
traverse' (MkStar p) = MkStar (traverse p)
|
||||||
wander f (MkStar p) = MkStar (f p)
|
wander f (MkStar p) = MkStar (f p)
|
||||||
|
|
||||||
export
|
public export
|
||||||
Monoid r => Traversing (Forget r) where
|
Monoid r => Traversing (Forget r) where
|
||||||
traverse' (MkForget k) = MkForget (foldMap k)
|
traverse' (MkForget k) = MkForget (foldMap k)
|
||||||
wander f (MkForget k) = MkForget (runConst . f (MkConst . k))
|
wander f (MkForget k) = MkForget (runConst . f (MkConst . k))
|
||||||
|
@ -140,45 +140,45 @@ record CofreeTraversing p a b where
|
||||||
constructor MkCFT
|
constructor MkCFT
|
||||||
runCFT : forall f. Traversable f => p (f a) (f b)
|
runCFT : forall f. Traversable f => p (f a) (f b)
|
||||||
|
|
||||||
export
|
public export
|
||||||
Profunctor p => Profunctor (CofreeTraversing p) where
|
Profunctor p => Profunctor (CofreeTraversing p) where
|
||||||
lmap f (MkCFT p) = MkCFT (lmap (map f) p)
|
lmap f (MkCFT p) = MkCFT (lmap (map f) p)
|
||||||
rmap g (MkCFT p) = MkCFT (rmap (map g) p)
|
rmap g (MkCFT p) = MkCFT (rmap (map g) p)
|
||||||
dimap f g (MkCFT p) = MkCFT (dimap (map f) (map g) p)
|
dimap f g (MkCFT p) = MkCFT (dimap (map f) (map g) p)
|
||||||
|
|
||||||
export
|
public export
|
||||||
Profunctor p => GenStrong Pair (CofreeTraversing p) where
|
Profunctor p => GenStrong Pair (CofreeTraversing p) where
|
||||||
strongr (MkCFT p) = MkCFT (p @{Compose @{%search} @{TraversablePair}})
|
strongr (MkCFT p) = MkCFT (p @{Compose @{%search} @{TraversablePair}})
|
||||||
strongl = dimap swap' swap' . strongr {p=CofreeTraversing p}
|
strongl = dimap swap' swap' . strongr {p=CofreeTraversing p}
|
||||||
|
|
||||||
export
|
public export
|
||||||
Profunctor p => GenStrong Either (CofreeTraversing p) where
|
Profunctor p => GenStrong Either (CofreeTraversing p) where
|
||||||
strongr (MkCFT p) = MkCFT (p @{Compose {f=Either c}})
|
strongr (MkCFT p) = MkCFT (p @{Compose {f=Either c}})
|
||||||
strongl = dimap swap' swap' . strongr {p=CofreeTraversing p}
|
strongl = dimap swap' swap' . strongr {p=CofreeTraversing p}
|
||||||
|
|
||||||
export
|
public export
|
||||||
Profunctor p => Traversing (CofreeTraversing p) where
|
Profunctor p => Traversing (CofreeTraversing p) where
|
||||||
traverse' (MkCFT p) = MkCFT (p @{Compose})
|
traverse' (MkCFT p) = MkCFT (p @{Compose})
|
||||||
|
|
||||||
export
|
public export
|
||||||
ProfunctorFunctor CofreeTraversing where
|
ProfunctorFunctor CofreeTraversing where
|
||||||
promap f (MkCFT p) = MkCFT (f p)
|
promap f (MkCFT p) = MkCFT (f p)
|
||||||
|
|
||||||
export
|
public export
|
||||||
ProfunctorComonad CofreeTraversing where
|
ProfunctorComonad CofreeTraversing where
|
||||||
proextract (MkCFT p) = dimap Id runIdentity $ p @{TraversableIdentity}
|
proextract (MkCFT p) = dimap Id runIdentity $ p @{TraversableIdentity}
|
||||||
produplicate (MkCFT p) = MkCFT $ MkCFT $ p @{Compose}
|
produplicate (MkCFT p) = MkCFT $ MkCFT $ p @{Compose}
|
||||||
|
|
||||||
export
|
public export
|
||||||
Profunctor p => Functor (CofreeTraversing p a) where
|
Profunctor p => Functor (CofreeTraversing p a) where
|
||||||
map = rmap
|
map = rmap
|
||||||
|
|
||||||
|
|
||||||
export
|
public export
|
||||||
cofreeTraversing : Traversing p => p :-> q -> p :-> CofreeTraversing q
|
cofreeTraversing : Traversing p => p :-> q -> p :-> CofreeTraversing q
|
||||||
cofreeTraversing f p = MkCFT $ f $ traverse' p
|
cofreeTraversing f p = MkCFT $ f $ traverse' p
|
||||||
|
|
||||||
export
|
public export
|
||||||
uncofreeTraversing : Profunctor q => p :-> CofreeTraversing q -> p :-> q
|
uncofreeTraversing : Profunctor q => p :-> CofreeTraversing q -> p :-> q
|
||||||
uncofreeTraversing f p = proextract $ f p
|
uncofreeTraversing f p = proextract $ f p
|
||||||
|
|
||||||
|
@ -194,40 +194,40 @@ public export
|
||||||
data FreeTraversing : (p : Type -> Type -> Type) -> Type -> Type -> Type where
|
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
|
MkFT : Traversable f => (f y -> b) -> p x y -> (a -> f x) -> FreeTraversing p a b
|
||||||
|
|
||||||
export
|
public export
|
||||||
Profunctor (FreeTraversing p) where
|
Profunctor (FreeTraversing p) where
|
||||||
lmap f (MkFT l m r) = MkFT l m (r . f)
|
lmap f (MkFT l m r) = MkFT l m (r . f)
|
||||||
rmap f (MkFT l m r) = MkFT (f . l) m r
|
rmap f (MkFT l m r) = MkFT (f . l) m r
|
||||||
dimap f g (MkFT l m r) = MkFT (g . l) m (r . f)
|
dimap f g (MkFT l m r) = MkFT (g . l) m (r . f)
|
||||||
|
|
||||||
export
|
public export
|
||||||
GenStrong Pair (FreeTraversing p) where
|
GenStrong Pair (FreeTraversing p) where
|
||||||
strongr (MkFT l m r) = MkFT @{Compose @{TraversablePair}} (map l) m (map r)
|
strongr (MkFT l m r) = MkFT @{Compose @{TraversablePair}} (map l) m (map r)
|
||||||
strongl = dimap swap' swap' . strongr {p=FreeTraversing p}
|
strongl = dimap swap' swap' . strongr {p=FreeTraversing p}
|
||||||
|
|
||||||
export
|
public export
|
||||||
GenStrong Either (FreeTraversing p) where
|
GenStrong Either (FreeTraversing p) where
|
||||||
strongr (MkFT l m r) = MkFT @{Compose {t=Either c}} (map l) m (map r)
|
strongr (MkFT l m r) = MkFT @{Compose {t=Either c}} (map l) m (map r)
|
||||||
strongl = dimap swap' swap' . strongr {p=FreeTraversing p}
|
strongl = dimap swap' swap' . strongr {p=FreeTraversing p}
|
||||||
|
|
||||||
export
|
public export
|
||||||
Traversing (FreeTraversing p) where
|
Traversing (FreeTraversing p) where
|
||||||
traverse' (MkFT l m r) = MkFT @{Compose} (map l) m (map r)
|
traverse' (MkFT l m r) = MkFT @{Compose} (map l) m (map r)
|
||||||
|
|
||||||
export
|
public export
|
||||||
ProfunctorFunctor FreeTraversing where
|
ProfunctorFunctor FreeTraversing where
|
||||||
promap f (MkFT l m r) = MkFT l (f m) r
|
promap f (MkFT l m r) = MkFT l (f m) r
|
||||||
|
|
||||||
export
|
public export
|
||||||
ProfunctorMonad FreeTraversing where
|
ProfunctorMonad FreeTraversing where
|
||||||
propure p = MkFT @{TraversableIdentity} runIdentity p Id
|
propure p = MkFT @{TraversableIdentity} runIdentity p Id
|
||||||
projoin (MkFT l' (MkFT l m r) r') = MkFT @{Compose} (l' . map l) m (map r . r')
|
projoin (MkFT l' (MkFT l m r) r') = MkFT @{Compose} (l' . map l) m (map r . r')
|
||||||
|
|
||||||
|
|
||||||
export
|
public export
|
||||||
freeTraversing : Traversing q => p :-> q -> FreeTraversing p :-> q
|
freeTraversing : Traversing q => p :-> q -> FreeTraversing p :-> q
|
||||||
freeTraversing fn (MkFT {f} l m r) = dimap r l (traverse' {f} (fn m))
|
freeTraversing fn (MkFT {f} l m r) = dimap r l (traverse' {f} (fn m))
|
||||||
|
|
||||||
export
|
public export
|
||||||
unfreeTraversing : FreeTraversing p :-> q -> p :-> q
|
unfreeTraversing : FreeTraversing p :-> q -> p :-> q
|
||||||
unfreeTraversing f p = f (MkFT @{TraversableIdentity} runIdentity p Id)
|
unfreeTraversing f p = f (MkFT @{TraversableIdentity} runIdentity p Id)
|
||||||
|
|
|
@ -59,7 +59,7 @@ p :-> q = forall a, b. p a b -> q a b
|
||||||
------------------------------------------------------------------------------
|
------------------------------------------------------------------------------
|
||||||
|
|
||||||
|
|
||||||
export
|
public export
|
||||||
Profunctor Morphism where
|
Profunctor Morphism where
|
||||||
dimap f g (Mor h) = Mor (g . h . f)
|
dimap f g (Mor h) = Mor (g . h . f)
|
||||||
lmap f (Mor g) = Mor (g . f)
|
lmap f (Mor g) = Mor (g . f)
|
||||||
|
@ -68,13 +68,13 @@ Profunctor Morphism where
|
||||||
namespace Profunctor
|
namespace Profunctor
|
||||||
||| A named implementation of `Profunctor` for function types.
|
||| A named implementation of `Profunctor` for function types.
|
||||||
||| Use this to avoid having to use a type wrapper like `Morphism`.
|
||| Use this to avoid having to use a type wrapper like `Morphism`.
|
||||||
export
|
public export
|
||||||
[Function] Profunctor (\a,b => a -> b) where
|
[Function] Profunctor (\a,b => a -> b) where
|
||||||
dimap f g h = g . h . f
|
dimap f g h = g . h . f
|
||||||
lmap = flip (.)
|
lmap = flip (.)
|
||||||
rmap = (.)
|
rmap = (.)
|
||||||
|
|
||||||
export
|
public export
|
||||||
Functor f => Profunctor (Kleislimorphism f) where
|
Functor f => Profunctor (Kleislimorphism f) where
|
||||||
dimap f g (Kleisli h) = Kleisli (map g . h . f)
|
dimap f g (Kleisli h) = Kleisli (map g . h . f)
|
||||||
lmap f (Kleisli g) = Kleisli (g . f)
|
lmap f (Kleisli g) = Kleisli (g . f)
|
||||||
|
@ -95,27 +95,27 @@ record Star {0 k : Type} (f : k -> Type) a (b : k) where
|
||||||
constructor MkStar
|
constructor MkStar
|
||||||
applyStar : a -> f b
|
applyStar : a -> f b
|
||||||
|
|
||||||
export
|
public export
|
||||||
Functor f => Functor (Star f a) where
|
Functor f => Functor (Star f a) where
|
||||||
map f (MkStar g) = MkStar (map f . g)
|
map f (MkStar g) = MkStar (map f . g)
|
||||||
|
|
||||||
export
|
public export
|
||||||
Applicative f => Applicative (Star f a) where
|
Applicative f => Applicative (Star f a) where
|
||||||
pure = MkStar . const . pure
|
pure = MkStar . const . pure
|
||||||
MkStar f <*> MkStar g = MkStar (\x => f x <*> g x)
|
MkStar f <*> MkStar g = MkStar (\x => f x <*> g x)
|
||||||
|
|
||||||
export
|
public export
|
||||||
Monad f => Monad (Star f a) where
|
Monad f => Monad (Star f a) where
|
||||||
MkStar f >>= g = MkStar $ \x => do
|
MkStar f >>= g = MkStar $ \x => do
|
||||||
a <- f x
|
a <- f x
|
||||||
applyStar (g a) x
|
applyStar (g a) x
|
||||||
|
|
||||||
export
|
public export
|
||||||
Contravariant f => Contravariant (Star f a) where
|
Contravariant f => Contravariant (Star f a) where
|
||||||
contramap f (MkStar g) = MkStar (contramap f . g)
|
contramap f (MkStar g) = MkStar (contramap f . g)
|
||||||
|
|
||||||
|
|
||||||
export
|
public export
|
||||||
Functor f => Profunctor (Star f) where
|
Functor f => Profunctor (Star f) where
|
||||||
dimap f g (MkStar h) = MkStar (map g . h . f)
|
dimap f g (MkStar h) = MkStar (map g . h . f)
|
||||||
lmap f (MkStar g) = MkStar (g . f)
|
lmap f (MkStar g) = MkStar (g . f)
|
||||||
|
@ -128,20 +128,20 @@ record Costar {0 k : Type} (f : k -> Type) (a : k) b where
|
||||||
constructor MkCostar
|
constructor MkCostar
|
||||||
applyCostar : f a -> b
|
applyCostar : f a -> b
|
||||||
|
|
||||||
export
|
public export
|
||||||
Functor (Costar f a) where
|
Functor (Costar f a) where
|
||||||
map f (MkCostar g) = MkCostar (f . g)
|
map f (MkCostar g) = MkCostar (f . g)
|
||||||
|
|
||||||
export
|
public export
|
||||||
Applicative (Costar f a) where
|
Applicative (Costar f a) where
|
||||||
pure = MkCostar . const
|
pure = MkCostar . const
|
||||||
MkCostar f <*> MkCostar g = MkCostar (\x => f x (g x))
|
MkCostar f <*> MkCostar g = MkCostar (\x => f x (g x))
|
||||||
|
|
||||||
export
|
public export
|
||||||
Monad (Costar f a) where
|
Monad (Costar f a) where
|
||||||
MkCostar f >>= g = MkCostar (\x => applyCostar (g (f x)) x)
|
MkCostar f >>= g = MkCostar (\x => applyCostar (g (f x)) x)
|
||||||
|
|
||||||
export
|
public export
|
||||||
Functor f => Profunctor (Costar f) where
|
Functor f => Profunctor (Costar f) where
|
||||||
dimap f g (MkCostar h) = MkCostar (g . h . map f)
|
dimap f g (MkCostar h) = MkCostar (g . h . map f)
|
||||||
lmap f (MkCostar g) = MkCostar (g . map f)
|
lmap f (MkCostar g) = MkCostar (g . map f)
|
||||||
|
@ -160,21 +160,21 @@ public export
|
||||||
retag : Tagged a c -> Tagged b c
|
retag : Tagged a c -> Tagged b c
|
||||||
retag (Tag x) = Tag x
|
retag (Tag x) = Tag x
|
||||||
|
|
||||||
export
|
public export
|
||||||
Functor (Tagged a) where
|
Functor (Tagged a) where
|
||||||
map f (Tag x) = Tag (f x)
|
map f (Tag x) = Tag (f x)
|
||||||
|
|
||||||
export
|
public export
|
||||||
Applicative (Tagged a) where
|
Applicative (Tagged a) where
|
||||||
pure = Tag
|
pure = Tag
|
||||||
Tag f <*> Tag x = Tag (f x)
|
Tag f <*> Tag x = Tag (f x)
|
||||||
|
|
||||||
export
|
public export
|
||||||
Monad (Tagged a) where
|
Monad (Tagged a) where
|
||||||
join = runTagged
|
join = runTagged
|
||||||
Tag x >>= f = f x
|
Tag x >>= f = f x
|
||||||
|
|
||||||
export
|
public export
|
||||||
Foldable (Tagged a) where
|
Foldable (Tagged a) where
|
||||||
foldr f x (Tag y) = f y x
|
foldr f x (Tag y) = f y x
|
||||||
foldl f x (Tag y) = f x y
|
foldl f x (Tag y) = f x y
|
||||||
|
@ -183,11 +183,11 @@ Foldable (Tagged a) where
|
||||||
toList (Tag x) = [x]
|
toList (Tag x) = [x]
|
||||||
foldMap f (Tag x) = f x
|
foldMap f (Tag x) = f x
|
||||||
|
|
||||||
export
|
public export
|
||||||
Traversable (Tagged a) where
|
Traversable (Tagged a) where
|
||||||
traverse f (Tag x) = map Tag (f x)
|
traverse f (Tag x) = map Tag (f x)
|
||||||
|
|
||||||
export
|
public export
|
||||||
Profunctor Tagged where
|
Profunctor Tagged where
|
||||||
dimap _ f (Tag x) = Tag (f x)
|
dimap _ f (Tag x) = Tag (f x)
|
||||||
lmap = const retag
|
lmap = const retag
|
||||||
|
@ -204,25 +204,25 @@ public export
|
||||||
reforget : Forget r a b -> Forget r a c
|
reforget : Forget r a b -> Forget r a c
|
||||||
reforget (MkForget k) = MkForget k
|
reforget (MkForget k) = MkForget k
|
||||||
|
|
||||||
export
|
public export
|
||||||
Functor (Forget r a) where
|
Functor (Forget r a) where
|
||||||
map _ = reforget
|
map _ = reforget
|
||||||
|
|
||||||
export
|
public export
|
||||||
Contravariant (Forget {k=Type} r a) where
|
Contravariant (Forget {k=Type} r a) where
|
||||||
contramap _ = reforget
|
contramap _ = reforget
|
||||||
|
|
||||||
export
|
public export
|
||||||
Monoid r => Applicative (Forget r a) where
|
Monoid r => Applicative (Forget r a) where
|
||||||
pure _ = MkForget (const neutral)
|
pure _ = MkForget (const neutral)
|
||||||
MkForget f <*> MkForget g = MkForget (f <+> g)
|
MkForget f <*> MkForget g = MkForget (f <+> g)
|
||||||
|
|
||||||
export
|
public export
|
||||||
Monoid r => Monad (Forget {k=Type} r a) where
|
Monoid r => Monad (Forget {k=Type} r a) where
|
||||||
join = reforget
|
join = reforget
|
||||||
(>>=) = reforget .: const
|
(>>=) = reforget .: const
|
||||||
|
|
||||||
export
|
public export
|
||||||
Foldable (Forget r a) where
|
Foldable (Forget r a) where
|
||||||
foldr _ x _ = x
|
foldr _ x _ = x
|
||||||
foldl _ x _ = x
|
foldl _ x _ = x
|
||||||
|
@ -231,11 +231,11 @@ Foldable (Forget r a) where
|
||||||
toList _ = []
|
toList _ = []
|
||||||
foldMap _ _ = neutral
|
foldMap _ _ = neutral
|
||||||
|
|
||||||
export
|
public export
|
||||||
Traversable (Forget r a) where
|
Traversable (Forget r a) where
|
||||||
traverse _ = pure . reforget
|
traverse _ = pure . reforget
|
||||||
|
|
||||||
export
|
public export
|
||||||
Profunctor (Forget r) where
|
Profunctor (Forget r) where
|
||||||
dimap f _ (MkForget k) = MkForget (k . f)
|
dimap f _ (MkForget k) = MkForget (k . f)
|
||||||
lmap f (MkForget k) = MkForget (k . f)
|
lmap f (MkForget k) = MkForget (k . f)
|
||||||
|
@ -252,21 +252,27 @@ public export
|
||||||
recoforget : Coforget r a c -> Coforget r b c
|
recoforget : Coforget r a c -> Coforget r b c
|
||||||
recoforget (MkCoforget k) = MkCoforget k
|
recoforget (MkCoforget k) = MkCoforget k
|
||||||
|
|
||||||
export
|
public export
|
||||||
Functor (Coforget r a) where
|
Functor (Coforget r a) where
|
||||||
map f (MkCoforget k) = MkCoforget (f . k)
|
map f (MkCoforget k) = MkCoforget (f . k)
|
||||||
|
|
||||||
export
|
public export
|
||||||
|
Bifunctor (Coforget r) where
|
||||||
|
bimap _ f (MkCoforget k) = MkCoforget (f . k)
|
||||||
|
mapFst _ = recoforget
|
||||||
|
mapSnd = map
|
||||||
|
|
||||||
|
public export
|
||||||
Applicative (Coforget r a) where
|
Applicative (Coforget r a) where
|
||||||
pure = MkCoforget . const
|
pure = MkCoforget . const
|
||||||
MkCoforget f <*> MkCoforget g = MkCoforget (\r => f r (g r))
|
MkCoforget f <*> MkCoforget g = MkCoforget (\r => f r (g r))
|
||||||
|
|
||||||
export
|
public export
|
||||||
Monad (Coforget r a) where
|
Monad (Coforget r a) where
|
||||||
MkCoforget k >>= f = MkCoforget (\r => runCoforget (f $ k r) r)
|
MkCoforget k >>= f = MkCoforget (\r => runCoforget (f $ k r) r)
|
||||||
|
|
||||||
export
|
public export
|
||||||
Profunctor (Coforget f) where
|
Profunctor (Coforget r) where
|
||||||
dimap _ f (MkCoforget k) = MkCoforget (f . k)
|
dimap _ f (MkCoforget k) = MkCoforget (f . k)
|
||||||
lmap _ = recoforget
|
lmap _ = recoforget
|
||||||
rmap = map
|
rmap = map
|
||||||
|
|
|
@ -20,69 +20,69 @@ record Yoneda p a b where
|
||||||
constructor MkYoneda
|
constructor MkYoneda
|
||||||
runYoneda : forall x, y. (x -> a) -> (b -> y) -> p x y
|
runYoneda : forall x, y. (x -> a) -> (b -> y) -> p x y
|
||||||
|
|
||||||
export
|
public export
|
||||||
Profunctor (Yoneda p) where
|
Profunctor (Yoneda p) where
|
||||||
lmap f (MkYoneda p) = MkYoneda $ \l,r => p (f . l) r
|
lmap f (MkYoneda p) = MkYoneda $ \l,r => p (f . l) r
|
||||||
rmap f (MkYoneda p) = MkYoneda $ \l,r => p l (r . f)
|
rmap f (MkYoneda p) = MkYoneda $ \l,r => p l (r . f)
|
||||||
dimap f g (MkYoneda p) = MkYoneda $ \l,r => p (f . l) (r . g)
|
dimap f g (MkYoneda p) = MkYoneda $ \l,r => p (f . l) (r . g)
|
||||||
|
|
||||||
export
|
public export
|
||||||
ProfunctorFunctor Yoneda where
|
ProfunctorFunctor Yoneda where
|
||||||
promap f (MkYoneda p) = MkYoneda $ f .: p
|
promap f (MkYoneda p) = MkYoneda $ f .: p
|
||||||
|
|
||||||
export
|
public export
|
||||||
ProfunctorMonad Yoneda where
|
ProfunctorMonad Yoneda where
|
||||||
propure p = MkYoneda $ \l,r => dimap l r p
|
propure p = MkYoneda $ \l,r => dimap l r p
|
||||||
projoin (MkYoneda p) = p id id
|
projoin (MkYoneda p) = p id id
|
||||||
|
|
||||||
export
|
public export
|
||||||
ProfunctorComonad Yoneda where
|
ProfunctorComonad Yoneda where
|
||||||
proextract (MkYoneda p) = p id id
|
proextract (MkYoneda p) = p id id
|
||||||
produplicate p = MkYoneda $ \l,r => dimap l r p
|
produplicate p = MkYoneda $ \l,r => dimap l r p
|
||||||
|
|
||||||
||| A witness that `Yoneda p` and `p` are equivalent when `p` is a profunctor.
|
||| A witness that `Yoneda p` and `p` are equivalent when `p` is a profunctor.
|
||||||
export
|
public export
|
||||||
yonedaEqv : Profunctor p => p a b <=> Yoneda p a b
|
yonedaEqv : Profunctor p => p a b <=> Yoneda p a b
|
||||||
yonedaEqv = MkEquivalence propure proextract
|
yonedaEqv = MkEquivalence propure proextract
|
||||||
|
|
||||||
export
|
public export
|
||||||
yonedaIso : (Profunctor q, Profunctor r) => forall p. Profunctor p =>
|
yonedaIso : (Profunctor q, Profunctor r) => forall p. Profunctor p =>
|
||||||
p (q a b) (r a' b') -> p (Yoneda q a b) (Yoneda r a' b')
|
p (q a b) (r a' b') -> p (Yoneda q a b) (Yoneda r a' b')
|
||||||
yonedaIso = dimap proextract propure
|
yonedaIso = dimap proextract propure
|
||||||
|
|
||||||
export
|
public export
|
||||||
Functor (Yoneda p a) where
|
Functor (Yoneda p a) where
|
||||||
map = rmap
|
map = rmap
|
||||||
|
|
||||||
export
|
public export
|
||||||
GenStrong ten p => GenStrong ten (Yoneda p) where
|
GenStrong ten p => GenStrong ten (Yoneda p) where
|
||||||
strongl = propure . strongl {ten,p} . proextract
|
strongl = propure . strongl {ten,p} . proextract
|
||||||
strongr = propure . strongr {ten,p} . proextract
|
strongr = propure . strongr {ten,p} . proextract
|
||||||
|
|
||||||
export
|
public export
|
||||||
GenCostrong ten p => GenCostrong ten (Yoneda p) where
|
GenCostrong ten p => GenCostrong ten (Yoneda p) where
|
||||||
costrongl = propure . costrongl {ten,p} . proextract
|
costrongl = propure . costrongl {ten,p} . proextract
|
||||||
costrongr = propure . costrongr {ten,p} . proextract
|
costrongr = propure . costrongr {ten,p} . proextract
|
||||||
|
|
||||||
export
|
public export
|
||||||
Closed p => Closed (Yoneda p) where
|
Closed p => Closed (Yoneda p) where
|
||||||
closed = propure . closed . proextract
|
closed = propure . closed . proextract
|
||||||
|
|
||||||
export
|
public export
|
||||||
Traversing p => Traversing (Yoneda p) where
|
Traversing p => Traversing (Yoneda p) where
|
||||||
traverse' = propure . traverse' . proextract
|
traverse' = propure . traverse' . proextract
|
||||||
wander f = propure . wander f . proextract
|
wander f = propure . wander f . proextract
|
||||||
|
|
||||||
export
|
public export
|
||||||
Mapping p => Mapping (Yoneda p) where
|
Mapping p => Mapping (Yoneda p) where
|
||||||
map' = propure . map' . proextract
|
map' = propure . map' . proextract
|
||||||
roam f = propure . roam f . proextract
|
roam f = propure . roam f . proextract
|
||||||
|
|
||||||
export
|
public export
|
||||||
Sieve p f => Sieve (Yoneda p) f where
|
Sieve p f => Sieve (Yoneda p) f where
|
||||||
sieve = sieve . proextract
|
sieve = sieve . proextract
|
||||||
|
|
||||||
export
|
public export
|
||||||
Cosieve p f => Cosieve (Yoneda p) f where
|
Cosieve p f => Cosieve (Yoneda p) f where
|
||||||
cosieve = cosieve . proextract
|
cosieve = cosieve . proextract
|
||||||
|
|
||||||
|
@ -98,68 +98,68 @@ data Coyoneda : (p : Type -> Type -> Type) -> Type -> Type -> Type where
|
||||||
MkCoyoneda : (a -> x) -> (y -> b) -> p x y -> Coyoneda p a b
|
MkCoyoneda : (a -> x) -> (y -> b) -> p x y -> Coyoneda p a b
|
||||||
|
|
||||||
|
|
||||||
export
|
public export
|
||||||
Profunctor (Coyoneda p) where
|
Profunctor (Coyoneda p) where
|
||||||
lmap f (MkCoyoneda l r p) = MkCoyoneda (l . f) r p
|
lmap f (MkCoyoneda l r p) = MkCoyoneda (l . f) r p
|
||||||
rmap f (MkCoyoneda l r p) = MkCoyoneda l (f . r) p
|
rmap f (MkCoyoneda l r p) = MkCoyoneda l (f . r) p
|
||||||
dimap f g (MkCoyoneda l r p) = MkCoyoneda (l . f) (g . r) p
|
dimap f g (MkCoyoneda l r p) = MkCoyoneda (l . f) (g . r) p
|
||||||
|
|
||||||
export
|
public export
|
||||||
ProfunctorFunctor Coyoneda where
|
ProfunctorFunctor Coyoneda where
|
||||||
promap f (MkCoyoneda l r p) = MkCoyoneda l r (f p)
|
promap f (MkCoyoneda l r p) = MkCoyoneda l r (f p)
|
||||||
|
|
||||||
export
|
public export
|
||||||
ProfunctorMonad Coyoneda where
|
ProfunctorMonad Coyoneda where
|
||||||
propure = MkCoyoneda id id
|
propure = MkCoyoneda id id
|
||||||
projoin (MkCoyoneda l r p) = dimap l r p
|
projoin (MkCoyoneda l r p) = dimap l r p
|
||||||
|
|
||||||
export
|
public export
|
||||||
ProfunctorComonad Coyoneda where
|
ProfunctorComonad Coyoneda where
|
||||||
proextract (MkCoyoneda l r p) = dimap l r p
|
proextract (MkCoyoneda l r p) = dimap l r p
|
||||||
produplicate = MkCoyoneda id id
|
produplicate = MkCoyoneda id id
|
||||||
|
|
||||||
||| A witness that `Coyoneda p` and `p` are equivalent when `p` is a profunctor.
|
||| A witness that `Coyoneda p` and `p` are equivalent when `p` is a profunctor.
|
||||||
export
|
public export
|
||||||
coyonedaEqv : Profunctor p => p a b <=> Coyoneda p a b
|
coyonedaEqv : Profunctor p => p a b <=> Coyoneda p a b
|
||||||
coyonedaEqv = MkEquivalence propure proextract
|
coyonedaEqv = MkEquivalence propure proextract
|
||||||
|
|
||||||
export
|
public export
|
||||||
coyonedaIso : (Profunctor q, Profunctor r) => forall p. Profunctor p =>
|
coyonedaIso : (Profunctor q, Profunctor r) => forall p. Profunctor p =>
|
||||||
p (q a b) (r a' b') -> p (Coyoneda q a b) (Coyoneda r a' b')
|
p (q a b) (r a' b') -> p (Coyoneda q a b) (Coyoneda r a' b')
|
||||||
coyonedaIso = dimap proextract propure
|
coyonedaIso = dimap proextract propure
|
||||||
|
|
||||||
export
|
public export
|
||||||
Functor (Coyoneda p a) where
|
Functor (Coyoneda p a) where
|
||||||
map = rmap
|
map = rmap
|
||||||
|
|
||||||
export
|
public export
|
||||||
GenStrong ten p => GenStrong ten (Coyoneda p) where
|
GenStrong ten p => GenStrong ten (Coyoneda p) where
|
||||||
strongl = propure . strongl {ten,p} . proextract
|
strongl = propure . strongl {ten,p} . proextract
|
||||||
strongr = propure . strongr {ten,p} . proextract
|
strongr = propure . strongr {ten,p} . proextract
|
||||||
|
|
||||||
export
|
public export
|
||||||
GenCostrong ten p => GenCostrong ten (Coyoneda p) where
|
GenCostrong ten p => GenCostrong ten (Coyoneda p) where
|
||||||
costrongl = propure . costrongl {ten,p} . proextract
|
costrongl = propure . costrongl {ten,p} . proextract
|
||||||
costrongr = propure . costrongr {ten,p} . proextract
|
costrongr = propure . costrongr {ten,p} . proextract
|
||||||
|
|
||||||
export
|
public export
|
||||||
Closed p => Closed (Coyoneda p) where
|
Closed p => Closed (Coyoneda p) where
|
||||||
closed = propure . closed . proextract
|
closed = propure . closed . proextract
|
||||||
|
|
||||||
export
|
public export
|
||||||
Traversing p => Traversing (Coyoneda p) where
|
Traversing p => Traversing (Coyoneda p) where
|
||||||
traverse' = propure . traverse' . proextract
|
traverse' = propure . traverse' . proextract
|
||||||
wander f = propure . wander f . proextract
|
wander f = propure . wander f . proextract
|
||||||
|
|
||||||
export
|
public export
|
||||||
Mapping p => Mapping (Coyoneda p) where
|
Mapping p => Mapping (Coyoneda p) where
|
||||||
map' = propure . map' . proextract
|
map' = propure . map' . proextract
|
||||||
roam f = propure . roam f . proextract
|
roam f = propure . roam f . proextract
|
||||||
|
|
||||||
export
|
public export
|
||||||
Sieve p f => Sieve (Coyoneda p) f where
|
Sieve p f => Sieve (Coyoneda p) f where
|
||||||
sieve = sieve . proextract
|
sieve = sieve . proextract
|
||||||
|
|
||||||
export
|
public export
|
||||||
Cosieve p f => Cosieve (Coyoneda p) f where
|
Cosieve p f => Cosieve (Coyoneda p) f where
|
||||||
cosieve = cosieve . proextract
|
cosieve = cosieve . proextract
|
||||||
|
|
|
@ -58,16 +58,16 @@ interface Associative ten => Tensor ten i | ten where
|
||||||
------------------------------------------------------------------------------
|
------------------------------------------------------------------------------
|
||||||
|
|
||||||
|
|
||||||
export
|
public export
|
||||||
Associative Pair where
|
Associative Pair where
|
||||||
assocl (x,(y,z)) = ((x,y),z)
|
assocl (x,(y,z)) = ((x,y),z)
|
||||||
assocr ((x,y),z) = (x,(y,z))
|
assocr ((x,y),z) = (x,(y,z))
|
||||||
|
|
||||||
export
|
public export
|
||||||
Symmetric Pair where
|
Symmetric Pair where
|
||||||
swap' = swap
|
swap' = swap
|
||||||
|
|
||||||
export
|
public export
|
||||||
Tensor Pair () where
|
Tensor Pair () where
|
||||||
unitl = MkEquivalence snd ((),)
|
unitl = MkEquivalence snd ((),)
|
||||||
unitr = MkEquivalence fst (,())
|
unitr = MkEquivalence fst (,())
|
||||||
|
@ -78,7 +78,7 @@ Tensor Pair () where
|
||||||
------------------------------------------------------------------------------
|
------------------------------------------------------------------------------
|
||||||
|
|
||||||
|
|
||||||
export
|
public export
|
||||||
Associative Either where
|
Associative Either where
|
||||||
assocl (Left x) = Left (Left x)
|
assocl (Left x) = Left (Left x)
|
||||||
assocl (Right (Left x)) = Left (Right x)
|
assocl (Right (Left x)) = Left (Right x)
|
||||||
|
@ -88,11 +88,11 @@ Associative Either where
|
||||||
assocr (Left (Right x)) = Right (Left x)
|
assocr (Left (Right x)) = Right (Left x)
|
||||||
assocr (Right x) = Right (Right x)
|
assocr (Right x) = Right (Right x)
|
||||||
|
|
||||||
export
|
public export
|
||||||
Symmetric Either where
|
Symmetric Either where
|
||||||
swap' = either Right Left
|
swap' = either Right Left
|
||||||
|
|
||||||
export
|
public export
|
||||||
Tensor Either Void where
|
Tensor Either Void where
|
||||||
unitl = MkEquivalence (either absurd id) Right
|
unitl = MkEquivalence (either absurd id) Right
|
||||||
unitr = MkEquivalence (either id absurd) Left
|
unitr = MkEquivalence (either id absurd) Left
|
||||||
|
|
Loading…
Reference in a new issue