Data.Comp.Ops

This module provides operators on functors.

Documentation

data (f :+: g) e infixr 6

Formal sum of signatures (functors).

Constructors

Inl (f e)

Inr (g e)

Instances

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

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

(Functor f, Functor g) => Functor ((:+:) * f g)

(Foldable f, Foldable g) => Foldable ((:+:) * f g)

(Traversable f, Traversable g) => Traversable ((:+:) * f g)

(ShowConstr f, ShowConstr g) => ShowConstr ((:+:) * f g)

(ShowF f, ShowF g) => ShowF ((:+:) * f g)

(ArbitraryF f, ArbitraryF g) => ArbitraryF ((:+:) * f g)

Instances of ArbitraryF are closed under forming sums.

(NFDataF f, NFDataF g) => NFDataF ((:+:) * f g)

(EqF f, EqF g) => EqF ((:+:) * f g)

EqF is propagated through sums.

(OrdF f, OrdF g) => OrdF ((:+:) * f g)

OrdF is propagated through sums.

(Render f, Render g) => Render ((:+:) * f g)

(HasVars f v0, HasVars g v0) => HasVars ((:+:) * f g) v

(Desugar f h, Desugar g h) => Desugar ((:+:) * f g) h

(Eq (f a), Eq (g a)) => Eq ((:+:) * f g a)

(Ord (f a), Ord (g a)) => Ord ((:+:) * f g a)

(Show (f a), Show (g a)) => Show ((:+:) * f g a)

fromInl :: (f :+: g) e -> Maybe (f e)

fromInr :: (f :+: g) e -> Maybe (g e)

caseF :: (f a -> b) -> (g a -> b) -> (f :+: g) a -> b

Utility function to case on a functor sum, without exposing the internal representation of sums.

type family Elem f g :: Emb

Equations

Elem f f = Found Here

Elem (f1 :+: f2) g = Sum' (Elem f1 g) (Elem f2 g)

Elem f (g1 :+: g2) = Choose (Elem f g1) (Elem f g2)

Elem f g = NotFound

type family Choose e1 r :: Emb

Equations

Choose (Found x) (Found y) = Ambiguous

Choose Ambiguous y = Ambiguous

Choose x Ambiguous = Ambiguous

Choose (Found x) y = Found (Le x)

Choose x (Found y) = Found (Ri y)

Choose x y = NotFound

type family Sum' e1 r :: Emb

Equations

Sum' (Found x) (Found y) = Found (Sum x y)

Sum' Ambiguous y = Ambiguous

Sum' x Ambiguous = Ambiguous

Sum' NotFound y = NotFound

Sum' x NotFound = NotFound

data Proxy a

Constructors

P

class Subsume e f g where

Methods

inj' :: Proxy e -> f a -> g a

prj' :: Proxy e -> g a -> Maybe (f a)

type (:<:) f g = Subsume (ComprEmb (Elem f g)) f g infixl 5

A constraint f :<: g expresses that the signature f is subsumed by g, i.e. f can be used to construct elements in g.

inj :: forall f g a. f :<: g => f a -> g a

proj :: forall f g a. f :<: g => g a -> Maybe (f a)

type (:=:) f g = (f :<: g, g :<: f) infixl 5

spl :: f :=: (f1 :+: f2) => (f1 a -> b) -> (f2 a -> b) -> f a -> b

data (f :*: g) a infixr 8

Formal product of signatures (functors).

Constructors

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

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

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

data (f :&: a) e infixr 7

This data type adds a constant product (annotation) to a signature.

Constructors

(f e) :&: a infixr 7

Instances

DistAnn k f p ((:&:) k f p)

RemA k ((:&:) k f p) f

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

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

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

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

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

(ShowConstr f, Show p) => ShowConstr ((:&:) * f p)

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

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

(NFDataF f, NFData a) => NFDataF ((:&:) * f a)

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

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

Methods

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

Inject an annotation over a signature.

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

Project an annotation from a signature.

Instances

DistAnn k f p ((:&:) k f p)

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

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

Methods

remA :: s a -> s' a

Remove annotations from a signature.

Instances

RemA k ((:&:) k f p) f

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