Control.Category.Free

Documentation

data IsCategory

Constructors

HasCategory

NoCategory

data IsSymmetricProduct

Constructors

HasSymmetricProduct

NoSymmetricProduct

data IsSymmetricSum

Constructors

HasSymmetricSum

NoSymmetricSum

data IsMonoidalProduct

Constructors

HasMonoidalProduct

NoMonoidalProduct

data IsMonoidalSum

Constructors

HasMonoidalSum

NoMonoidalSum

data IsCartesian

Constructors

HasCartesian

NoCartesian

data IsCocartesian

Constructors

HasCocartesian

NoCocartesian

data IsRecursive

Constructors

HasRecursive

NoRecursive

data IsFixed

Constructors

HasFixed

NoFixed

data Requirements

Constructors

Req IsCategory IsSymmetricProduct IsSymmetricSum IsMonoidalProduct IsMonoidalSum IsCartesian IsCocartesian IsRecursive IsFixed

type family ConstraintsOf (x :: anykind) (k :: * -> * -> *) = (c :: Constraint) where ...

Equations

ConstraintsOf ('Req cat symP symS monP monS cart cocart rec fix) k = (ConstraintsOf cat k, ConstraintsOf symP k, ConstraintsOf symS k, ConstraintsOf monP k, ConstraintsOf monS k, ConstraintsOf cart k, ConstraintsOf cocart k, ConstraintsOf rec k, ConstraintsOf fix k)

ConstraintsOf 'HasCategory cat = Category cat

ConstraintsOf 'HasSymmetricProduct cat = SymmetricProduct cat

ConstraintsOf 'HasSymmetricSum cat = SymmetricSum cat

ConstraintsOf 'HasMonoidalProduct cat = MonoidalProduct cat

ConstraintsOf 'HasMonoidalSum cat = MonoidalSum cat

ConstraintsOf 'HasCartesian cat = Cartesian cat

ConstraintsOf 'HasCocartesian cat = Cocartesian cat

ConstraintsOf 'HasRecursive cat = Recursive cat

ConstraintsOf 'HasFixed cat = Fixed cat

ConstraintsOf 'NoCategory cat = ()

ConstraintsOf 'NoSymmetricProduct cat = ()

ConstraintsOf 'NoSymmetricSum cat = ()

ConstraintsOf 'NoMonoidalProduct cat = ()

ConstraintsOf 'NoMonoidalSum cat = ()

ConstraintsOf 'NoCartesian cat = ()

ConstraintsOf 'NoCocartesian cat = ()

ConstraintsOf 'NoRecursive cat = ()

ConstraintsOf 'NoFixed cat = ()

type FreeFunction c a b = Catalyst ('Req 'HasCategory 'HasSymmetricProduct 'HasSymmetricSum 'HasMonoidalProduct 'HasMonoidalSum 'HasCartesian 'HasCocartesian 'HasRecursive 'HasFixed) c

data Catalyst (r :: Requirements) (p :: * -> * -> *) a b where

Constructors

ID :: r ~ 'Req 'HasCategory symP symS monP monS cart cocart rec fix => Catalyst r p x x

Comp :: Catalyst ('Req 'HasCategory symP symS monP monS cart cocart rec fix) p x y -> Catalyst ('Req 'HasCategory symP symS monP monS cart cocart rec fix) p y z -> Catalyst ('Req 'HasCategory symP symS monP monS cart cocart rec fix) p x z

Swap :: r ~ 'Req 'HasCategory 'HasSymmetricProduct symS monP monS cart cocart rec fix => Catalyst r p (a, b) (b, a)

Reassoc :: r ~ 'Req 'HasCategory 'HasSymmetricProduct symS monP monS cart cocart rec fix => Catalyst r p (a, (b, c)) ((a, b), c)

SwapE :: r ~ 'Req cat symP 'HasSymmetricSum monP monS cart cocart rec fix => Catalyst r p (Either a b) (Either b a)

ReassocE :: r ~ 'Req cat symP 'HasSymmetricSum monP monS cart cocart rec fix => Catalyst r p (Either a (Either b c)) (Either (Either a b) c)

First :: r ~ 'Req cat symP symS 'HasMonoidalProduct monS cart cocart rec fix => Catalyst r p a b -> Catalyst r p (a, m) (b, m)

Second :: r ~ 'Req cat symP symS 'HasMonoidalProduct monS cart cocart rec fix => Catalyst r p a b -> Catalyst r p (m, a) (m, b)

Alongside :: r ~ 'Req cat symP symS 'HasMonoidalProduct monS cart cocart rec fix => Catalyst r p a b -> Catalyst r p a' b' -> Catalyst r p (a, a') (b, b')

Fanout :: r ~ 'Req cat symP symS monP monS 'HasCartesian cocart rec fix => Catalyst r p a b -> Catalyst r p a b' -> Catalyst r p a (b, b')

Left' :: r ~ 'Req cat symP symS monP 'HasMonoidalSum cart cocart rec fix => Catalyst r p a b -> Catalyst r p (Either a x) (Either b x)

Right' :: r ~ 'Req cat symP symS monP 'HasMonoidalSum cart cocart rec fix => Catalyst r p a b -> Catalyst r p (Either x a) (Either x b)

EitherOf :: r ~ 'Req cat symP symS monP 'HasMonoidalSum cart cocart rec fix => Catalyst r p a b -> Catalyst r p a' b' -> Catalyst r p (Either a a') (Either b b')

Fanin :: r ~ 'Req cat symP symS monP monS cart 'HasCocartesian rec fix => Catalyst r p a b -> Catalyst r p a' b -> Catalyst r p (Either a a') b

Copy :: r ~ 'Req cat symP symS monP monS 'HasCartesian cocart rec fix => Catalyst r p x (x, x)

Consume :: r ~ 'Req cat symP symS monP monS 'HasCartesian cocart rec fix => Catalyst r p x ()

Fst :: r ~ 'Req cat symP symS monP monS 'HasCartesian cocart rec fix => Catalyst r p (a, b) a

Snd :: r ~ 'Req cat symP symS monP monS 'HasCartesian cocart rec fix => Catalyst r p (a, b) b

InjectL :: r ~ 'Req cat symP symS monP monS cart 'HasCocartesian rec fix => Catalyst r p a (Either a b)

InjectR :: r ~ 'Req cat symP symS monP monS cart 'HasCocartesian rec fix => Catalyst r p b (Either a b)

Unify :: r ~ 'Req cat symP symS monP monS cart 'HasCocartesian rec fix => Catalyst r p (Either a a) a

Tag :: r ~ 'Req cat symP symS monP monS cart 'HasCocartesian rec fix => Catalyst r p (Bool, a) (Either a a)

RecurseL :: r ~ 'Req cat symP symS monP monS cart cocart 'HasRecursive fix => Catalyst r p (Either a d) (Either b d) -> Catalyst r p a b

RecurseR :: r ~ 'Req cat symP symS monP monS cart cocart 'HasRecursive fix => Catalyst r p (Either d a) (Either d b) -> Catalyst r p a b

FixL :: r ~ 'Req cat symP symS monP monS cart cocart rec 'HasFixed => Catalyst r p (a, d) (b, d) -> Catalyst r p a b

FixR :: r ~ 'Req cat symP symS monP monS cart cocart rec 'HasFixed => Catalyst r p (d, a) (d, b) -> Catalyst r p a b

LiftC :: p a b -> Catalyst r p a b

Instances

r ~ 'Req 'HasCategory symP symS monP monS cart cocart rec fix => Category (Catalyst r c :: Type -> Type -> Type)

Defined in Control.Category.Free

Methods

id :: forall (a :: k). Catalyst r c a a

(.) :: forall (b :: k) (c0 :: k) (a :: k). Catalyst r c b c0 -> Catalyst r c a b -> Catalyst r c a c0

r ~ 'Req 'HasCategory symP 'HasSymmetricSum monP monS cart cocart rec fix => SymmetricSum (Catalyst r c)

Defined in Control.Category.Free

Methods

swapE :: Catalyst r c (Either l r0) (Either r0 l)

reassocE :: Catalyst r c (Either a (Either b c0)) (Either (Either a b) c0)

r ~ 'Req 'HasCategory 'HasSymmetricProduct symS monP monS cart cocart rec fix => SymmetricProduct (Catalyst r c)

Defined in Control.Category.Free

Methods

swap :: Catalyst r c (l, r0) (r0, l)

reassoc :: Catalyst r c (a, (b, c0)) ((a, b), c0)

r ~ 'Req 'HasCategory symP 'HasSymmetricSum monP 'HasMonoidalSum cart cocart rec fix => MonoidalSum (Catalyst r c)

Defined in Control.Category.Free

Methods

(+++) :: Catalyst r c al bl -> Catalyst r c ar br -> Catalyst r c (Either al ar) (Either bl br)

left :: Catalyst r c a b -> Catalyst r c (Either a c0) (Either b c0)

right :: Catalyst r c a b -> Catalyst r c (Either c0 a) (Either c0 b)

r ~ 'Req 'HasCategory 'HasSymmetricProduct symS 'HasMonoidalProduct monS cart cocart rec fix => MonoidalProduct (Catalyst r c)

Defined in Control.Category.Free

Methods

(***) :: Catalyst r c al bl -> Catalyst r c ar br -> Catalyst r c (al, ar) (bl, br)

first' :: Catalyst r c a b -> Catalyst r c (a, c0) (b, c0)

second' :: Catalyst r c a b -> Catalyst r c (c0, a) (c0, b)

r ~ 'Req 'HasCategory symP 'HasSymmetricSum monP 'HasMonoidalSum cart 'HasCocartesian rec fix => Cocartesian (Catalyst r c)

Defined in Control.Category.Free

Methods

(|||) :: Catalyst r c al b -> Catalyst r c ar b -> Catalyst r c (Either al ar) b

injectL :: Catalyst r c a (Either a b)

injectR :: Catalyst r c a (Either b a)

unify :: Catalyst r c (Either a a) a

tag :: Catalyst r c (Bool, a) (Either a a)

r ~ 'Req 'HasCategory 'HasSymmetricProduct symS 'HasMonoidalProduct monS 'HasCartesian cocart rec fix => Cartesian (Catalyst r c)

Defined in Control.Category.Free

Methods

(&&&) :: Catalyst r c a l -> Catalyst r c a r0 -> Catalyst r c a (l, r0)

consume :: Catalyst r c a ()

copy :: Catalyst r c a (a, a)

fst' :: Catalyst r c (l, r0) l

snd' :: Catalyst r c (l, r0) r0

r ~ 'Req 'HasCategory symP symS monP monS cart cocart rec 'HasFixed => Fixed (Catalyst r c)

Defined in Control.Category.Free

Methods

fixL :: Catalyst r c (a, s) (b, s) -> Catalyst r c a b

fixR :: Catalyst r c (s, a) (s, b) -> Catalyst r c a b

r ~ 'Req 'HasCategory symP symS monP monS cart cocart 'HasRecursive fix => Recursive (Catalyst r c)

Defined in Control.Category.Free

Methods

recurseL :: Catalyst r c (Either a s) (Either b s) -> Catalyst r c a b

recurseR :: Catalyst r c (Either s a) (Either s b) -> Catalyst r c a b

(forall x y. Show (c x y)) => Show (Catalyst r c a b)

Defined in Control.Category.Free

Methods

showsPrec :: Int -> Catalyst r c a b -> ShowS

show :: Catalyst r c a b -> String

showList :: [Catalyst r c a b] -> ShowS

runFree :: forall r p c a b. ConstraintsOf r p => (forall x y. c x y -> p x y) -> Catalyst r c a b -> p a b

liftC :: c a b -> Catalyst r c a b