Control.Monad.Trans.Category

Basic definitions in the category (* -> *).

Documentation

type :-> m n = forall a. m a -> n a

m :-> n is the set of morphisms (from m to n, naturally) in our category.

newtype (t :$ m) a

If t is an endofunctor in our category, then t :$ m is basically the same as t m.

Constructors

ApplyF

Fields

runApplyF :: t m a

Instances

MonadTrans t => MonadTrans (:$ t)

(Monad m, TransM t) => Monad (:$ t m)

(MonadFix m, TransF t) => MonadFix (:$ t m)

(MonadPlus m, TransP t) => MonadPlus (:$ t m)

newtype (t2 :. t1) m a

If t1 and t2 are endofunctorsm then t2 :. t1 is their composition (which is also an endofunctor)

Constructors

ComposeF

Fields

runComposeF :: (t2 :$ (t1 :$ m)) a

Instances

(TransM t1, MonadTrans t2) => MonadTrans (:. t2 t1)

(TransM t1, TransM t2) => TransM (:. t2 t1)

(TransF t1, TransF t2) => TransF (:. t2 t1)

(TransP t1, TransP t2) => TransP (:. t2 t1)

(Monad m, TransM t1, TransM t2) => Monad (:. t2 t1 m)

(MonadFix m, TransF t1, TransF t2) => MonadFix (:. t2 t1 m)

(MonadPlus m, TransP t1, TransP t2) => MonadPlus (:. t2 t1 m)

type Inst c m = c m :-> m

If m is an algebra over an endofunctor t, then it's structure morphism has the type Inst t m.