Control.Category.Discrete

Documentation

data Discrete a b where

The discrete category is the category with the minimum possible amount of arrows: for any given type, there is id, and that's all. You can use this to provide a proof that some endomorphism (of not closer specified category) is the identity.

Constructors

Refl :: Discrete a a

Instances

Category k (Discrete k)

Methods

id :: cat a a

(.) :: cat b c -> cat a b -> cat a c

Functor [] (Discrete *) (Discrete *)

Methods

fmap :: (Object (Discrete *) a, Object (Discrete *) [a], Object (Discrete *) b, Object (Discrete *) [b]) => Discrete * a b -> Discrete * [a] [b]

Functor Maybe (Discrete *) (Discrete *)

Methods

fmap :: (Object (Discrete *) a, Object (Discrete *) (Maybe a), Object (Discrete *) b, Object (Discrete *) (Maybe b)) => Discrete * a b -> Discrete * (Maybe a) (Maybe b)

Functor IO (Discrete *) (Discrete *)

Methods

fmap :: (Object (Discrete *) a, Object (Discrete *) (IO a), Object (Discrete *) b, Object (Discrete *) (IO b)) => Discrete * a b -> Discrete * (IO a) (IO b)

Functor Complex (Discrete *) (Discrete *)

Methods

fmap :: (Object (Discrete *) a, Object (Discrete *) (Complex a), Object (Discrete *) b, Object (Discrete *) (Complex b)) => Discrete * a b -> Discrete * (Complex a) (Complex b)

HasAgent (Discrete *)

Associated Types

type AgentVal (Discrete * :: * -> * -> *) a v :: *

Methods

alg :: (Object (Discrete *) a, Object (Discrete *) b) => (forall q. Object (Discrete *) q => AgentVal (Discrete *) q a -> AgentVal (Discrete *) q b) -> Discrete * a b

($~) :: (Object (Discrete *) a, Object (Discrete *) b, Object (Discrete *) c) => Discrete * b c -> AgentVal (Discrete *) a b -> AgentVal (Discrete *) a c

Category (Discrete *)

Associated Types

type Object (Discrete * :: * -> * -> *) o :: Constraint

Methods

id :: Object (Discrete *) a => Discrete * a a

(.) :: (Object (Discrete *) a, Object (Discrete *) b, Object (Discrete *) c) => Discrete * b c -> Discrete * a b -> Discrete * a c

EnhancedCat (Coercion *) (Discrete *)

Methods

arr :: (Object (Discrete *) b, Object (Discrete *) c, Object (Coercion *) b, Object (Coercion *) c) => Discrete * b c -> Coercion * b c

Functor (Either a) (Discrete *) (Discrete *)

Methods

fmap :: (Object (Discrete *) a, Object (Discrete *) (Either a a), Object (Discrete *) b, Object (Discrete *) (Either a b)) => Discrete * a b -> Discrete * (Either a a) (Either a b)

Functor ((,) a) (Discrete *) (Discrete *)

Methods

fmap :: (Object (Discrete *) a, Object (Discrete *) (a, a), Object (Discrete *) b, Object (Discrete *) (a, b)) => Discrete * a b -> Discrete * (a, a) (a, b)

EnhancedCat (Discrete *) f => EnhancedCat (Discrete *) (ConstrainedCategory f o)

Methods

arr :: (Object (ConstrainedCategory f o) b, Object (ConstrainedCategory f o) c, Object (Discrete *) b, Object (Discrete *) c) => ConstrainedCategory f o b c -> Discrete * b c

EnhancedCat ((->) LiftedRep LiftedRep) (Discrete *)

Methods

arr :: (Object (Discrete *) b, Object (Discrete *) c, Object (LiftedRep -> LiftedRep) b, Object (LiftedRep -> LiftedRep) c) => Discrete * b c -> (LiftedRep -> LiftedRep) b c

Category f => EnhancedCat (ConstrainedCategory f o) (Discrete *)

Methods

arr :: (Object (Discrete *) b, Object (Discrete *) c, Object (ConstrainedCategory f o) b, Object (ConstrainedCategory f o) c) => Discrete * b c -> ConstrainedCategory f o b c

Functor ((->) LiftedRep LiftedRep a) (Discrete *) (Discrete *)

Methods

fmap :: (Object (Discrete *) a, Object (Discrete *) ((LiftedRep -> LiftedRep) a a), Object (Discrete *) b, Object (Discrete *) ((LiftedRep -> LiftedRep) a b)) => Discrete * a b -> Discrete * ((LiftedRep -> LiftedRep) a a) ((LiftedRep -> LiftedRep) a b)

type Object (Discrete *) o

type Object (Discrete *) o = ()

type AgentVal (Discrete *) a v

type AgentVal (Discrete *) a v = GenericAgent (Discrete *) a v