Data.Comp.Multi.Ops

This module provides operators on higher-order functors. All definitions are generalised versions of those in Data.Comp.Ops.

Documentation

data (f :+: g) h e

Data type defining coproducts.

Constructors

Inl (f h e)

Inr (g h e)

Instances

f :<: g => f :<: (:+: h g)

f :<: (:+: f g)

(HFunctor f, HFunctor g) => HFunctor (:+: f g)

(HFoldable f, HFoldable g) => HFoldable (:+: f g)

(HTraversable f, HTraversable g) => HTraversable (:+: f g)

(HEqF f, HEqF g) => HEqF (:+: f g)

EqF is propagated through sums.

(HShowF f, HShowF g) => HShowF (:+: f g)

(HasVars f v, HasVars g v) => HasVars (:+: f g) v

DistProd s p s' => DistProd (:+: f s) p (:+: (:&: f p) s')

RemoveP s s' => RemoveP (:+: (:&: f p) s) (:+: f s')

class sub :<: sup where

The subsumption relation.

Methods

inj :: sub a :-> sup a

proj :: NatM Maybe (sup a) (sub a)

Instances

f :<: f

f :<: g => f :<: (:+: h g)

f :<: (:+: f g)

data (f :*: g) a

Constructors

(f a) :*: (g a)

fst :: (f :*: g) a -> f a

snd :: (f :*: g) a -> g a

data (f :&: a) g e

This data type adds a constant product to a signature. Alternatively, this could have also been defined as

data (f :&: a) (g ::  * -> *) e = f g e :&: a e

This is too general, however, for example for productHTermHom.

Constructors

(f g e) :&: a

Instances

DistProd f p (:&: f p)

HFunctor f => HFunctor (:&: f a)

HFoldable f => HFoldable (:&: f a)

HTraversable f => HTraversable (:&: f a)

(HShowF f, Show p) => HShowF (:&: f p)

RemoveP (:&: f p) f

DistProd s p s' => DistProd (:+: f s) p (:+: (:&: f p) s')

RemoveP s s' => RemoveP (:+: (:&: f p) s) (:+: f s')

class DistProd s p s' | s' -> s, s' -> p where

This class defines how to distribute a product over a sum of signatures.

Methods

injectP :: p -> s a :-> s' a

This function injects a product a value over a signature.

projectP :: s' a :-> (s a :&: p)

Instances

DistProd f p (:&: f p)

DistProd s p s' => DistProd (:+: f s) p (:+: (:&: f p) s')

class RemoveP s s' | s -> s' where

Methods

removeP :: s a :-> s' a

Instances

RemoveP (:&: f p) f

RemoveP s s' => RemoveP (:+: (:&: f p) s) (:+: f s')