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')

Methods

injectA :: (k :+: (k :&: f) p) s' -> p a -> s' a

projectA :: s' a -> (p a, (k :+: (k :&: f) p) s')

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

Methods

remA :: (k :+: f) s' a -> s' a

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

Methods

fmap :: (a -> b) -> (* :+: f) g a -> (* :+: f) g b

(<$) :: a -> (* :+: f) g b -> (* :+: f) g a

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

Methods

fold :: Monoid m => (* :+: f) g m -> m

foldMap :: Monoid m => (a -> m) -> (* :+: f) g a -> m

foldr :: (a -> b -> b) -> b -> (* :+: f) g a -> b

foldr' :: (a -> b -> b) -> b -> (* :+: f) g a -> b

foldl :: (b -> a -> b) -> b -> (* :+: f) g a -> b

foldl' :: (b -> a -> b) -> b -> (* :+: f) g a -> b

foldr1 :: (a -> a -> a) -> (* :+: f) g a -> a

foldl1 :: (a -> a -> a) -> (* :+: f) g a -> a

toList :: (* :+: f) g a -> [a]

null :: (* :+: f) g a -> Bool

length :: (* :+: f) g a -> Int

elem :: Eq a => a -> (* :+: f) g a -> Bool

maximum :: Ord a => (* :+: f) g a -> a

minimum :: Ord a => (* :+: f) g a -> a

sum :: Num a => (* :+: f) g a -> a

product :: Num a => (* :+: f) g a -> a

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

Methods

traverse :: Applicative f => (a -> f b) -> (* :+: f) g a -> f ((* :+: f) g b)

sequenceA :: Applicative f => (* :+: f) g (f a) -> f ((* :+: f) g a)

mapM :: Monad m => (a -> m b) -> (* :+: f) g a -> m ((* :+: f) g b)

sequence :: Monad m => (* :+: f) g (m a) -> m ((* :+: f) g a)

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

Methods

stringTreeAlg :: Alg ((* :+: f) g) (Tree String)

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

Methods

isVar :: (* :+: f) g a -> Maybe v0

bindsVars :: Mapping m a => (* :+: f) g a -> m (Set v0)

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

Methods

desugHom :: Hom ((* :+: f) g) h

desugHom' :: Alg ((* :+: f) g) (Context h 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 where ...

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

class Subsume e f g where

Minimal complete definition

inj', prj'

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

Instances

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

Methods

fmap :: (a -> b) -> (* :*: f) g a -> (* :*: f) g b

(<$) :: a -> (* :*: f) g b -> (* :*: f) g a

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

Methods

fold :: Monoid m => (* :*: f) g m -> m

foldMap :: Monoid m => (a -> m) -> (* :*: f) g a -> m

foldr :: (a -> b -> b) -> b -> (* :*: f) g a -> b

foldr' :: (a -> b -> b) -> b -> (* :*: f) g a -> b

foldl :: (b -> a -> b) -> b -> (* :*: f) g a -> b

foldl' :: (b -> a -> b) -> b -> (* :*: f) g a -> b

foldr1 :: (a -> a -> a) -> (* :*: f) g a -> a

foldl1 :: (a -> a -> a) -> (* :*: f) g a -> a

toList :: (* :*: f) g a -> [a]

null :: (* :*: f) g a -> Bool

length :: (* :*: f) g a -> Int

elem :: Eq a => a -> (* :*: f) g a -> Bool

maximum :: Ord a => (* :*: f) g a -> a

minimum :: Ord a => (* :*: f) g a -> a

sum :: Num a => (* :*: f) g a -> a

product :: Num a => (* :*: f) g a -> a

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

Methods

traverse :: Applicative f => (a -> f b) -> (* :*: f) g a -> f ((* :*: f) g b)

sequenceA :: Applicative f => (* :*: f) g (f a) -> f ((* :*: f) g a)

mapM :: Monad m => (a -> m b) -> (* :*: f) g a -> m ((* :*: f) g b)

sequence :: Monad m => (* :*: f) g (m a) -> m ((* :*: f) g a)

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)

Methods

injectA :: (k :&: f) p -> p a -> s' a

projectA :: s' a -> (p a, (k :&: f) p)

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

Methods

remA :: f a -> s' a

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

Methods

injectA :: (k :+: (k :&: f) p) s' -> p a -> s' a

projectA :: s' a -> (p a, (k :+: (k :&: f) p) s')

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

Methods

remA :: (k :+: f) s' a -> s' a

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

Methods

fmap :: (a -> b) -> (* :&: f) a a -> (* :&: f) a b

(<$) :: a -> (* :&: f) a b -> (* :&: f) a a

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

Methods

fold :: Monoid m => (* :&: f) a m -> m

foldMap :: Monoid m => (a -> m) -> (* :&: f) a a -> m

foldr :: (a -> b -> b) -> b -> (* :&: f) a a -> b

foldr' :: (a -> b -> b) -> b -> (* :&: f) a a -> b

foldl :: (b -> a -> b) -> b -> (* :&: f) a a -> b

foldl' :: (b -> a -> b) -> b -> (* :&: f) a a -> b

foldr1 :: (a -> a -> a) -> (* :&: f) a a -> a

foldl1 :: (a -> a -> a) -> (* :&: f) a a -> a

toList :: (* :&: f) a a -> [a]

null :: (* :&: f) a a -> Bool

length :: (* :&: f) a a -> Int

elem :: Eq a => a -> (* :&: f) a a -> Bool

maximum :: Ord a => (* :&: f) a a -> a

minimum :: Ord a => (* :&: f) a a -> a

sum :: Num a => (* :&: f) a a -> a

product :: Num a => (* :&: f) a a -> a

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

Methods

traverse :: Applicative f => (a -> f b) -> (* :&: f) a a -> f ((* :&: f) a b)

sequenceA :: Applicative f => (* :&: f) a (f a) -> f ((* :&: f) a a)

mapM :: Monad m => (a -> m b) -> (* :&: f) a a -> m ((* :&: f) a b)

sequence :: Monad m => (* :&: f) a (m a) -> m ((* :&: f) a a)

HasVars f v => HasVars ((:&:) * f a) v

Methods

isVar :: (* :&: f) a a -> Maybe v

bindsVars :: Mapping m a => (* :&: f) a a -> m (Set v)

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

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

Minimal complete definition

injectA, projectA

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)

Methods

injectA :: (k :&: f) p -> p a -> s' a

projectA :: s' a -> (p a, (k :&: f) p)

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

Methods

injectA :: (k :+: (k :&: f) p) s' -> p a -> s' a

projectA :: s' a -> (p a, (k :+: (k :&: f) p) s')

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

Minimal complete definition

remA

Methods

remA :: s a -> s' a

Remove annotations from a signature.

Instances

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

Methods

remA :: f a -> s' a

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

Methods

remA :: (k :+: f) s' a -> s' a