Data.Comp.Product

This module defines products on signatures.

Documentation

data (f :&: a) e

This data type adds a constant product to a signature.

Constructors

(f e) :&: a

Instances

DistProd f p (:&: f p)

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

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

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

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

(ArbitraryF f, Arbitrary p) => ArbitraryF (:&: 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')

data (f :*: g) a

Formal product of signatures (functors).

Constructors

(f a) :*: (g a)

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

Inject a product value over a signature.

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

Project a product value from a signature.

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

Remove products from a signature.

Instances

RemoveP (:&: f p) f

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

liftP :: RemoveP s s' => (s' a -> t) -> s a -> t

Transform a function with a domain constructed from a functor to a function with a domain constructed with the same functor, but with an additional product.

liftP' :: (DistProd s' p s, Functor s, Functor s') => (s' a -> Cxt h s' a) -> s a -> Cxt h s a

Transform a function with a domain constructed from a functor to a function with a domain constructed with the same functor, but with an additional product.

stripP :: (Functor f, RemoveP g f, Functor g) => Cxt h g a -> Cxt h f a

Strip the products from a term over a functor with products.

productTermHom :: (DistProd f p f', DistProd g p g', Functor g, Functor g') => TermHom f g -> TermHom f' g'

Lift a term homomorphism over signatures f and g to a term homomorphism over the same signatures, but extended with products.

constP :: (DistProd f p g, Functor f, Functor g) => p -> Cxt h f a -> Cxt h g a

Annotate each node of a term with a constant value.

project' :: (s :<: f, RemoveP s s') => Cxt h f a -> Maybe (s' (Cxt h f a))