Safe Haskell	None
Language	Haskell2010

Proarrow.Promonad

Documentation

class Profunctor p => Promonad (p :: PRO k k) where Source Comments #

Methods

id :: forall (a :: k). Ob a => p a a Source Comments #

(.) :: forall (b :: k) (c :: k) (a :: k). p b c -> p a b -> p a c infixr 9 Source Comments #

Instances

Instances details

Promonad Booleans Source Comments #
Instance details Defined in Proarrow.Category.Instance.Bool Methods id :: forall (a :: BOOL). Ob a => Booleans a a Source Comments # (.) :: forall (b :: BOOL) (c :: BOOL) (a :: BOOL). Booleans b c -> Booleans a b -> Booleans a c Source Comments #
Promonad Cat Source Comments #
Instance details Defined in Proarrow.Category.Instance.Cat Methods id :: forall (a :: KIND). Ob a => Cat a a Source Comments # (.) :: forall (b :: KIND) (c :: KIND) (a :: KIND). Cat b c -> Cat a b -> Cat a c Source Comments #
Promonad (:-) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Constraint Methods id :: forall (a :: CONSTRAINT). Ob a => a :- a Source Comments # (.) :: forall (b :: CONSTRAINT) (c :: CONSTRAINT) (a :: CONSTRAINT). (b :- c) -> (a :- b) -> a :- c Source Comments #
Promonad Linear Source Comments #
Instance details Defined in Proarrow.Category.Instance.Linear Methods id :: forall (a :: LINEAR). Ob a => Linear a a Source Comments # (.) :: forall (b :: LINEAR) (c :: LINEAR) (a :: LINEAR). Linear b c -> Linear a b -> Linear a c Source Comments #
Promonad Pointed Source Comments #
Instance details Defined in Proarrow.Category.Instance.PointedHask Methods id :: forall (a :: POINTED). Ob a => Pointed a a Source Comments # (.) :: forall (b :: POINTED) (c :: POINTED) (a :: POINTED). Pointed b c -> Pointed a b -> Pointed a c Source Comments #
Promonad Simplex Source Comments #
Instance details Defined in Proarrow.Category.Instance.Simplex Methods id :: forall (a :: Nat). Ob a => Simplex a a Source Comments # (.) :: forall (b :: Nat) (c :: Nat) (a :: Nat). Simplex b c -> Simplex a b -> Simplex a c Source Comments #
Promonad Zero Source Comments #
Instance details Defined in Proarrow.Category.Instance.Zero Methods id :: forall (a :: VOID). Ob a => Zero a a Source Comments # (.) :: forall (b :: VOID) (c :: VOID) (a :: VOID). Zero b c -> Zero a b -> Zero a c Source Comments #
Promonad Unit Source Comments #
Instance details Defined in Proarrow.Category.Instance.Unit Methods id :: forall (a :: ()). Ob a => Unit a a Source Comments # (.) :: forall (b :: ()) (c :: ()) (a :: ()). Unit b c -> Unit a b -> Unit a c Source Comments #
Comonoid w => Promonad (ComonoidAsCat w :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Nat Methods id :: Ob a => ComonoidAsCat w a a Source Comments # (.) :: ComonoidAsCat w b c -> ComonoidAsCat w a b -> ComonoidAsCat w a c Source Comments #
Promonad (Reader r :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad.Reader Methods id :: Ob a => Reader r a a Source Comments # (.) :: Reader r b c -> Reader r a b -> Reader r a c Source Comments #
Monoid m => Promonad (Writer m :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad.Writer Methods id :: Ob a => Writer m a a Source Comments # (.) :: Writer m b c -> Writer m a b -> Writer m a c Source Comments #
CategoryOf k => Promonad (Id :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Identity Methods id :: forall (a :: k). Ob a => Id a a Source Comments # (.) :: forall (b :: k) (c :: k) (a :: k). Id b c -> Id a b -> Id a c Source Comments #
Promonad (->) Source Comments #
Instance details Defined in Proarrow.Core Methods id :: Ob a => a -> a Source Comments # (.) :: (b -> c) -> (a -> b) -> a -> c Source Comments #
Profunctor p => Promonad (FreePromonad p :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Free Methods id :: forall (a :: k). Ob a => FreePromonad p a a Source Comments # (.) :: forall (b :: k) (c :: k) (a :: k). FreePromonad p b c -> FreePromonad p a b -> FreePromonad p a c Source Comments #
(Monoidal k, Ob s) => Promonad (State s :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad.State Methods id :: forall (a :: k). Ob a => State s a a Source Comments # (.) :: forall (b :: k) (c :: k) (a :: k). State s b c -> State s a b -> State s a c Source Comments #
Monad m => Promonad (Star (Prelude m) :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods id :: Ob a => Star (Prelude m) a a Source Comments # (.) :: Star (Prelude m) b c -> Star (Prelude m) a b -> Star (Prelude m) a c Source Comments #
Promonad p => Promonad (Wrapped p :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Wrapped Methods id :: forall (a :: k). Ob a => Wrapped p a a Source Comments # (.) :: forall (b :: k) (c :: k) (a :: k). Wrapped p b c -> Wrapped p a b -> Wrapped p a c Source Comments #
Adjunction p q => Promonad (q :.: p :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Adjunction Methods id :: forall (a :: k). Ob a => (q :.: p) a a Source Comments # (.) :: forall (b :: k) (c :: k) (a :: k). (q :.: p) b c -> (q :.: p) a b -> (q :.: p) a c Source Comments #
(p ~ j, Profunctor p) => Promonad (Ran ('OP p) p :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Ran Methods id :: forall (a :: k). Ob a => Ran ('OP p) p a a Source Comments # (.) :: forall (b :: k) (c :: k) (a :: k). Ran ('OP p) p b c -> Ran ('OP p) p a b -> Ran ('OP p) p a c Source Comments #
(p ~ j, Profunctor p) => Promonad (Rift ('OP p) p :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Rift Methods id :: forall (a :: k). Ob a => Rift ('OP p) p a a Source Comments # (.) :: forall (b :: k) (c :: k) (a :: k). Rift ('OP p) p b c -> Rift ('OP p) p a b -> Rift ('OP p) p a c Source Comments #
Promonad (LTE :: FIN n -> FIN n -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Fin Methods id :: forall (a :: FIN n). Ob a => LTE a a Source Comments # (.) :: forall (b :: FIN n) (c :: FIN n) (a :: FIN n). LTE b c -> LTE a b -> LTE a c Source Comments #
CategoryOf k => Promonad (List :: LIST k -> LIST k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.List Methods id :: forall (a :: LIST k). Ob a => List a a Source Comments # (.) :: forall (b :: LIST k) (c :: LIST k) (a :: LIST k). List b c -> List a b -> List a c Source Comments #
Num a => Promonad (Mat :: MatK a -> MatK a -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Mat Methods id :: forall (a0 :: MatK a). Ob a0 => Mat a0 a0 Source Comments # (.) :: forall (b :: MatK a) (c :: MatK a) (a0 :: MatK a). Mat b c -> Mat a0 b -> Mat a0 c Source Comments #
PreorderOf k => Promonad (PoAsCat :: POCATK k -> POCATK k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.PreorderAsCategory Methods id :: forall (a :: POCATK k). Ob a => PoAsCat a a Source Comments # (.) :: forall (b :: POCATK k) (c :: POCATK k) (a :: POCATK k). PoAsCat b c -> PoAsCat a b -> PoAsCat a c Source Comments #
BiCCC k => Promonad (FreeCCC :: FK k -> FK k -> Type) Source Comments #
Instance details Defined in Proarrow.Helper.CCC Methods id :: forall (a :: FK k). Ob a => FreeCCC a a Source Comments # (.) :: forall (b :: FK k) (c :: FK k) (a :: FK k). FreeCCC b c -> FreeCCC a b -> FreeCCC a c Source Comments #
Monoidal k => Promonad (Strictified :: [k] -> [k] -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Strictified Methods id :: forall (a :: [k]). Ob a => Strictified a a Source Comments # (.) :: forall (b :: [k]) (c :: [k]) (a :: [k]). Strictified b c -> Strictified a b -> Strictified a c Source Comments #
Promonad p => Promonad (Rev p :: REV j -> REV j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Rev Methods id :: forall (a :: REV j). Ob a => Rev p a a Source Comments # (.) :: forall (b :: REV j) (c :: REV j) (a :: REV j). Rev p b c -> Rev p a b -> Rev p a c Source Comments #
Promonad c => Promonad (Op c :: OPPOSITE j -> OPPOSITE j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Opposite Methods id :: forall (a :: OPPOSITE j). Ob a => Op c a a Source Comments # (.) :: forall (b :: OPPOSITE j) (c0 :: OPPOSITE j) (a :: OPPOSITE j). Op c b c0 -> Op c a b -> Op c a c0 Source Comments #
Promonad p => Promonad (Coprod p :: COPROD j -> COPROD j -> Type) Source Comments #
Instance details Defined in Proarrow.Object.BinaryCoproduct Methods id :: forall (a :: COPROD j). Ob a => Coprod p a a Source Comments # (.) :: forall (b :: COPROD j) (c :: COPROD j) (a :: COPROD j). Coprod p b c -> Coprod p a b -> Coprod p a c Source Comments #
Promonad p => Promonad (Prod p :: PROD j -> PROD j -> Type) Source Comments #
Instance details Defined in Proarrow.Object.BinaryProduct Methods id :: forall (a :: PROD j). Ob a => Prod p a a Source Comments # (.) :: forall (b :: PROD j) (c :: PROD j) (a :: PROD j). Prod p b c -> Prod p a b -> Prod p a c Source Comments #
Promonad (Prof :: PROFK j k -> PROFK j k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Prof Methods id :: forall (a :: PROFK j k). Ob a => Prof a a Source Comments # (.) :: forall (b :: PROFK j k) (c :: PROFK j k) (a :: PROFK j k). Prof b c -> Prof a b -> Prof a c Source Comments #
Rewrite g => Promonad (Free :: FREE g -> FREE g -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Free Methods id :: forall (a :: FREE g). Ob a => Free a a Source Comments # (.) :: forall (b :: FREE g) (c :: FREE g) (a :: FREE g). Free b c -> Free a b -> Free a c Source Comments #
Promonad p => Promonad (Kleisli :: KLEISLI p -> KLEISLI p -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Kleisli Methods id :: forall (a :: KLEISLI p). Ob a => Kleisli a a Source Comments # (.) :: forall (b :: KLEISLI p) (c :: KLEISLI p) (a :: KLEISLI p). Kleisli b c -> Kleisli a b -> Kleisli a c Source Comments #
Promonad (Nat' :: NatK j k -> NatK j k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Nat Methods id :: forall (a :: NatK j k). Ob a => Nat' a a Source Comments # (.) :: forall (b :: NatK j k) (c :: NatK j k) (a :: NatK j k). Nat' b c -> Nat' a b -> Nat' a c Source Comments #
Promonad (BiSimplex :: Simplex j k -> Simplex j k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Simplex Methods id :: forall (a :: Simplex j k). Ob a => BiSimplex a a Source Comments # (.) :: forall (b :: Simplex j k) (c :: Simplex j k) (a :: Simplex j k). BiSimplex b c -> BiSimplex a b -> BiSimplex a c Source Comments #
Promonad (Terminal :: Unit '() '() -> Unit '() '() -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Terminal Methods id :: forall (a :: Unit '() '()). Ob a => Terminal a a Source Comments # (.) :: forall (b :: Unit '() '()) (c :: Unit '() '()) (a :: Unit '() '()). Terminal b c -> Terminal a b -> Terminal a c Source Comments #
Promonad (Prof :: (j +-> k) -> (j +-> k) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Prof Methods id :: forall (a :: j +-> k). Ob a => Prof a a Source Comments # (.) :: forall (b :: j +-> k) (c :: j +-> k) (a :: j +-> k). Prof b c -> Prof a b -> Prof a c Source Comments #
Promonad (Nat :: (j -> Type) -> (j -> Type) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Nat Methods id :: forall (a :: j -> Type). Ob a => Nat a a Source Comments # (.) :: forall (b :: j -> Type) (c :: j -> Type) (a :: j -> Type). Nat b c -> Nat a b -> Nat a c Source Comments #
Promonad (Nat :: (k1 -> k2 -> k3 -> k4 -> Type) -> (k1 -> k2 -> k3 -> k4 -> Type) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Nat Methods id :: forall (a :: k1 -> k2 -> k3 -> k4 -> Type). Ob a => Nat a a Source Comments # (.) :: forall (b :: k1 -> k2 -> k3 -> k4 -> Type) (c :: k1 -> k2 -> k3 -> k4 -> Type) (a :: k1 -> k2 -> k3 -> k4 -> Type). Nat b c -> Nat a b -> Nat a c Source Comments #
Promonad (Nat :: (k1 -> k2 -> k3 -> Type) -> (k1 -> k2 -> k3 -> Type) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Nat Methods id :: forall (a :: k1 -> k2 -> k3 -> Type). Ob a => Nat a a Source Comments # (.) :: forall (b :: k1 -> k2 -> k3 -> Type) (c :: k1 -> k2 -> k3 -> Type) (a :: k1 -> k2 -> k3 -> Type). Nat b c -> Nat a b -> Nat a c Source Comments #
Promonad p => Promonad (Sub p :: SUBCAT ob -> SUBCAT ob -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Sub Methods id :: forall (a :: SUBCAT ob). Ob a => Sub p a a Source Comments # (.) :: forall (b :: SUBCAT ob) (c :: SUBCAT ob) (a :: SUBCAT ob). Sub p b c -> Sub p a b -> Sub p a c Source Comments #
(Promonad p, Promonad q) => Promonad (p :**: q :: (j1, j2) -> (j1, j2) -> Type) Source Comments #	The product promonad of promonads `p` and `q`.
Instance details Defined in Proarrow.Category.Instance.Product Methods id :: forall (a :: (j1, j2)). Ob a => (p :: q) a a Source Comments # (.) :: forall (b :: (j1, j2)) (c :: (j1, j2)) (a :: (j1, j2)). (p :: q) b c -> (p :: q) a b -> (p :: q) a c Source Comments #
(CategoryOf k, Ob i, Ob j) => Promonad (Category :: PLAINK k i j -> PLAINK k i j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.CategoryAsBi Methods id :: forall (a :: PLAINK k i j). Ob a => Category a a Source Comments # (.) :: forall (b :: PLAINK k i j) (c :: PLAINK k i j) (a :: PLAINK k i j). Category b c -> Category a b -> Category a c Source Comments #
CategoryOf k => Promonad (Mon2 :: MonK k i j -> MonK k i j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.MonoidalAsBi Methods id :: forall (a :: MonK k i j). Ob a => Mon2 a a Source Comments # (.) :: forall (b :: MonK k i j) (c :: MonK k i j) (a :: MonK k i j). Mon2 b c -> Mon2 a b -> Mon2 a c Source Comments #
Profunctor p => Promonad (Collage :: COLLAGE p -> COLLAGE p -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Collage Methods id :: forall (a :: COLLAGE p). Ob a => Collage a a Source Comments # (.) :: forall (b :: COLLAGE p) (c :: COLLAGE p) (a :: COLLAGE p). Collage b c -> Collage a b -> Collage a c Source Comments #
(Bicategory kk, Ob0 kk k) => Promonad (Endo :: ENDO kk k -> ENDO kk k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Endo Methods id :: forall (a :: ENDO kk k). Ob a => Endo a a Source Comments # (.) :: forall (b :: ENDO kk k) (c :: ENDO kk k) (a :: ENDO kk k). Endo b c -> Endo a b -> Endo a c Source Comments #
Promonad (Bidiscrete :: DiscreteK ob j k -> DiscreteK ob j k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Bidiscrete Methods id :: forall (a :: DiscreteK ob j k). Ob a => Bidiscrete a a Source Comments # (.) :: forall (b :: DiscreteK ob j k) (c0 :: DiscreteK ob j k) (a :: DiscreteK ob j k). Bidiscrete b c0 -> Bidiscrete a b -> Bidiscrete a c0 Source Comments #
CategoryOf (kk j k2) => Promonad (Co :: COK kk j k2 -> COK kk j k2 -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Co Methods id :: forall (a :: COK kk j k2). Ob a => Co a a Source Comments # (.) :: forall (b :: COK kk j k2) (c :: COK kk j k2) (a :: COK kk j k2). Co b c -> Co a b -> Co a c Source Comments #
CategoryOf (kk k2 j) => Promonad (Op :: OPK kk j k2 -> OPK kk j k2 -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Op Methods id :: forall (a :: OPK kk j k2). Ob a => Op a a Source Comments # (.) :: forall (b :: OPK kk j k2) (c :: OPK kk j k2) (a :: OPK kk j k2). Op b c -> Op a b -> Op a c Source Comments #
(CategoryOf (kk j k2), Bicategory kk) => Promonad (Strictified :: Path kk j k2 -> Path kk j k2 -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Strictified Methods id :: forall (a :: Path kk j k2). Ob a => Strictified a a Source Comments # (.) :: forall (b :: Path kk j k2) (c :: Path kk j k2) (a :: Path kk j k2). Strictified b c -> Strictified a b -> Strictified a c Source Comments #
Promonad ((~>) :: CAT (kk i j)) => Promonad (HomW :: HK kk i j -> HK kk i j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Hom Methods id :: forall (a :: HK kk i j). Ob a => HomW a a Source Comments # (.) :: forall (b :: HK kk i j) (c :: HK kk i j) (a :: HK kk i j). HomW b c -> HomW a b -> HomW a c Source Comments #
Promonad ((~>) :: CAT (kk i j)) => Promonad (Sub :: SUBCAT tag kk i j -> SUBCAT tag kk i j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Sub Methods id :: forall (a :: SUBCAT tag kk i j). Ob a => Sub a a Source Comments # (.) :: forall (b :: SUBCAT tag kk i j) (c :: SUBCAT tag kk i j) (a :: SUBCAT tag kk i j). Sub b c -> Sub a b -> Sub a c Source Comments #
CategoryOf (kk i j) => Promonad (W :: WKK kk i j -> WKK kk i j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Equipment.BiAsEquipment Methods id :: forall (a :: WKK kk i j). Ob a => W a a Source Comments # (.) :: forall (b :: WKK kk i j) (c :: WKK kk i j) (a :: WKK kk i j). W b c -> W a b -> W a c Source Comments #
CategoryOf (kk i j) => Promonad (Q2 :: QKK kk i j -> QKK kk i j -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Equipment.Quintet Methods id :: forall (a :: QKK kk i j). Ob a => Q2 a a Source Comments # (.) :: forall (b :: QKK kk i j) (c :: QKK kk i j) (a :: QKK kk i j). Q2 b c -> Q2 a b -> Q2 a c Source Comments #
IsOptic w c d => Promonad (OpticCat :: OPTIC w c d -> OPTIC w c d -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods id :: forall (a :: OPTIC w c d). Ob a => OpticCat a a Source Comments # (.) :: forall (b :: OPTIC w c d) (c0 :: OPTIC w c d) (a :: OPTIC w c d). OpticCat b c0 -> OpticCat a b -> OpticCat a c0 Source Comments #
(CategoryOf (jj (Fst ik) (Fst jl)), CategoryOf (kk (Snd ik) (Snd jl))) => Promonad (Prod :: PRODK jj kk ik jl -> PRODK jj kk ik jl -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Product Methods id :: forall (a :: PRODK jj kk ik jl). Ob a => Prod a a Source Comments # (.) :: forall (b :: PRODK jj kk ik jl) (c :: PRODK jj kk ik jl) (a :: PRODK jj kk ik jl). Prod b c -> Prod a b -> Prod a c Source Comments #

class Profunctor p => Procomonad (p :: PRO i i) where Source Comments #

Methods

extract :: p :~> ((~>) :: CAT i) Source Comments #

duplicate :: p :~> (p :.: p) Source Comments #

Instances

Instances details

Monoid m => Procomonad (Reader m :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad.Reader Methods extract :: Reader m :~> ((~>) :: CAT Type) Source Comments # duplicate :: Reader m :~> (Reader m :.: Reader m) Source Comments #
Procomonad (Writer m :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad.Writer Methods extract :: Writer m :~> ((~>) :: CAT Type) Source Comments # duplicate :: Writer m :~> (Writer m :.: Writer m) Source Comments #
CategoryOf k => Procomonad (Id :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad Methods extract :: (Id :: k -> k -> Type) :~> ((~>) :: CAT k) Source Comments # duplicate :: (Id :: k -> k -> Type) :~> ((Id :: k -> k -> Type) :.: (Id :: k -> k -> Type)) Source Comments #
Monad m => Procomonad (Costar (Prelude m) :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Costar Methods extract :: Costar (Prelude m) :~> ((~>) :: CAT Type) Source Comments # duplicate :: Costar (Prelude m) :~> (Costar (Prelude m) :.: Costar (Prelude m)) Source Comments #
Adjunction p q => Procomonad (p :.: q :: i -> i -> Type) Source Comments #
Instance details Defined in Proarrow.Adjunction Methods extract :: (p :.: q) :~> ((~>) :: CAT i) Source Comments # duplicate :: (p :.: q) :~> ((p :.: q) :.: (p :.: q)) Source Comments #