Copyright	(c) 2011 Patrick Bahr, Tom Hvitved
License	BSD3
Maintainer	Tom Hvitved <hvitved@diku.dk>
Stability	experimental
Portability	non-portable (GHC Extensions)
Safe Haskell	None
Language	Haskell98

Data.Comp.Param.Multi.Ops

Description

This module provides operators on higher-order difunctors.

Synopsis

Documentation

data (f :+: g) a b i infixr 6 Source

Formal sum of signatures (difunctors).

Constructors

Inl (f a b i)
Inr (g a b i)

Instances

(:<:) f g => f :<: ((:+:) h g)
f :<: ((:+:) f g)
(HDifunctor f, HDifunctor g) => HDifunctor ((:+:) f g)
(HDitraversable f, HDitraversable g) => HDitraversable ((:+:) f g)
(ShowHD f, ShowHD g) => ShowHD ((:+:) f g)
(EqHD f, EqHD g) => EqHD ((:+:) f g)	`EqHD` is propagated through sums.
(OrdHD f, OrdHD g) => OrdHD ((:+:) f g)	`OrdHD` is propagated through sums.
(Desugar f h, Desugar g h) => Desugar ((:+:) f g) h
DistAnn s p s' => DistAnn ((:+:) f s) p ((:+:) ((:&:) f p) s')
RemA s s' => RemA ((:+:) ((:&:) f p) s) ((:+:) f s')
(Eq (f a b i), Eq (g a b i)) => Eq ((:+:) f g a b i)
(Ord (f a b i), Ord (g a b i)) => Ord ((:+:) f g a b i)
(Show (f a b i), Show (g a b i)) => Show ((:+:) f g a b i)

caseHD :: (f a b i -> c) -> (g a b i -> c) -> (f :+: g) a b i -> c Source

Utility function to case on a higher-order difunctor sum, without exposing the internal representation of sums.

class sub :<: sup where Source

Signature containment relation for automatic injections. The left-hand must be an atomic signature, where as the right-hand side must have a list-like structure. Examples include f :<: f :+: g and g :<: f :+: (g :+: h), non-examples include f :+: g :<: f :+: (g :+: h) and f :<: (f :+: g) :+: h.

Methods

inj :: sub a b :-> sup a b Source

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

Instances

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

data (f :*: g) a b infixr 8 Source

Formal product of signatures (higher-order difunctors).

Constructors

(f a b) :*: (g a b) infixr 8

ffst :: (f :*: g) a b -> f a b Source

fsnd :: (f :*: g) a b -> g a b Source

data (f :&: p) a b i infixr 7 Source

This data type adds a constant product to a signature.

Constructors

(f a b i) :&: p infixr 7

Instances

DistAnn f p ((:&:) f p)
HDifunctor f => HDifunctor ((:&:) f p)
HDitraversable f => HDitraversable ((:&:) f p)
(ShowHD f, Show p) => ShowHD ((:&:) f p)
RemA ((:&:) f p) f
DistAnn s p s' => DistAnn ((:+:) f s) p ((:+:) ((:&:) f p) s')
RemA s s' => RemA ((:+:) ((:&:) f p) s) ((:+:) f s')

class DistAnn s p s' | s' -> s, s' -> p where Source

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

Methods

injectA :: p -> s a b :-> s' a b Source

Inject an annotation over a signature.

projectA :: s' a b :-> (s a b :&: p) Source

Project an annotation from a signature.

Instances

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

class RemA s s' | s -> s' where Source

Methods

remA :: s a b :-> s' a b Source

Remove annotations from a signature.

Instances

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