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

Defined in Data.Comp.Ops

Methods

injectA :: forall (a :: k0). p -> (f :+: s) a -> ((f :&: p) :+: s') a

projectA :: forall (a :: k0). ((f :&: p) :+: s') a -> ((f :+: s) a, p)

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

Defined in Data.Comp.Ops

Methods

remA :: forall (a :: k0). ((f :&: p) :+: s) a -> (f :+: s') a

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

Defined in Data.Comp.Ops

Methods

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

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

Defined in Data.Comp.Ops

Methods

traverse :: Applicative f0 => (a -> f0 b) -> (f :+: g) a -> f0 ((f :+: g) b)

sequenceA :: Applicative f0 => (f :+: g) (f0 a) -> f0 ((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)

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

Defined in Data.Comp.Ops

Methods

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

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

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

Instances of ArbitraryF are closed under forming sums.

Defined in Data.Comp.Arbitrary

Methods

arbitraryF' :: Arbitrary v => [(Int, Gen ((f :+: g) v))]

arbitraryF :: Arbitrary v => Gen ((f :+: g) v)

shrinkF :: Arbitrary v => (f :+: g) v -> [(f :+: g) v]

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

Defined in Data.Comp.DeepSeq

Methods

rnfF :: NFData a => (f :+: g) a -> ()

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

EqF is propagated through sums.

Defined in Data.Comp.Equality

Methods

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

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

OrdF is propagated through sums.

Defined in Data.Comp.Ordering

Methods

compareF :: Ord a => (f :+: g) a -> (f :+: g) a -> Ordering

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

Defined in Data.Comp.Show

Methods

showConstr :: (f :+: g) a -> String

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

Defined in Data.Comp.Show

Methods

showF :: (f :+: g) String -> String

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

Defined in Data.Comp.Render

Methods

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

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

Defined in Data.Comp.Desugar

Methods

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

desugHom' :: Alg (f :+: g) (Context h a)

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

Defined in Data.Comp.Variables

Methods

isVar :: (f :+: g) a -> Maybe v

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

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

Defined in Data.Comp.Sum

Methods

showsPrec :: Int -> (f :+: g) a -> ShowS

show :: (f :+: g) a -> String

showList :: [(f :+: g) a] -> ShowS

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

Defined in Data.Comp.Sum

Methods

(==) :: (f :+: g) a -> (f :+: g) a -> Bool

(/=) :: (f :+: g) a -> (f :+: g) a -> Bool

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

Defined in Data.Comp.Sum

Methods

compare :: (f :+: g) a -> (f :+: g) a -> Ordering

(<) :: (f :+: g) a -> (f :+: g) a -> Bool

(<=) :: (f :+: g) a -> (f :+: g) a -> Bool

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

(>=) :: (f :+: g) a -> (f :+: g) a -> Bool

max :: (f :+: g) a -> (f :+: g) a -> (f :+: g) a

min :: (f :+: g) a -> (f :+: g) a -> (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 :: Type -> Type) (g :: Type -> Type) :: 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 :: Emb) (f :: Type -> Type) (g :: Type -> Type) 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

Instances

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

Defined in Data.Comp.Ops

Methods

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

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

Defined in Data.Comp.Ops

Methods

traverse :: Applicative f0 => (a -> f0 b) -> (f :*: g) a -> f0 ((f :*: g) b)

sequenceA :: Applicative f0 => (f :*: g) (f0 a) -> f0 ((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)

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

Defined in Data.Comp.Ops

Methods

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

(<$) :: a -> (f :*: g) b -> (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 (f :: k -> TYPE LiftedRep) p (f :&: p :: k -> Type)

Defined in Data.Comp.Ops

Methods

injectA :: forall (a :: k0). p -> f a -> (f :&: p) a

projectA :: forall (a :: k0). (f :&: p) a -> (f a, p)

RemA (f :&: p :: k -> Type) (f :: k -> Type)

Defined in Data.Comp.Ops

Methods

remA :: forall (a :: k0). (f :&: p) a -> f a

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

Defined in Data.Comp.Ops

Methods

injectA :: forall (a :: k0). p -> (f :+: s) a -> ((f :&: p) :+: s') a

projectA :: forall (a :: k0). ((f :&: p) :+: s') a -> ((f :+: s) a, p)

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

Defined in Data.Comp.Ops

Methods

remA :: forall (a :: k0). ((f :&: p) :+: s) a -> (f :+: s') a

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

Defined in Data.Comp.Ops

Methods

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

foldMap :: Monoid m => (a0 -> m) -> (f :&: a) a0 -> m

foldMap' :: Monoid m => (a0 -> m) -> (f :&: a) a0 -> m

foldr :: (a0 -> b -> b) -> b -> (f :&: a) a0 -> b

foldr' :: (a0 -> b -> b) -> b -> (f :&: a) a0 -> b

foldl :: (b -> a0 -> b) -> b -> (f :&: a) a0 -> b

foldl' :: (b -> a0 -> b) -> b -> (f :&: a) a0 -> b

foldr1 :: (a0 -> a0 -> a0) -> (f :&: a) a0 -> a0

foldl1 :: (a0 -> a0 -> a0) -> (f :&: a) a0 -> a0

toList :: (f :&: a) a0 -> [a0]

null :: (f :&: a) a0 -> Bool

length :: (f :&: a) a0 -> Int

elem :: Eq a0 => a0 -> (f :&: a) a0 -> Bool

maximum :: Ord a0 => (f :&: a) a0 -> a0

minimum :: Ord a0 => (f :&: a) a0 -> a0

sum :: Num a0 => (f :&: a) a0 -> a0

product :: Num a0 => (f :&: a) a0 -> a0

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

Defined in Data.Comp.Ops

Methods

traverse :: Applicative f0 => (a0 -> f0 b) -> (f :&: a) a0 -> f0 ((f :&: a) b)

sequenceA :: Applicative f0 => (f :&: a) (f0 a0) -> f0 ((f :&: a) a0)

mapM :: Monad m => (a0 -> m b) -> (f :&: a) a0 -> m ((f :&: a) b)

sequence :: Monad m => (f :&: a) (m a0) -> m ((f :&: a) a0)

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

Defined in Data.Comp.Ops

Methods

fmap :: (a0 -> b) -> (f :&: a) a0 -> (f :&: a) b

(<$) :: a0 -> (f :&: a) b -> (f :&: a) a0

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

Defined in Data.Comp.Arbitrary

Methods

arbitraryF' :: Arbitrary v => [(Int, Gen ((f :&: p) v))]

arbitraryF :: Arbitrary v => Gen ((f :&: p) v)

shrinkF :: Arbitrary v => (f :&: p) v -> [(f :&: p) v]

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

Defined in Data.Comp.DeepSeq

Methods

rnfF :: NFData a0 => (f :&: a) a0 -> ()

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

Defined in Data.Comp.Show

Methods

showConstr :: (f :&: p) a -> String

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

Defined in Data.Comp.Show

Methods

showF :: (f :&: p) String -> String

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

Defined in Data.Comp.Variables

Methods

isVar :: (f :&: a) a0 -> Maybe v

bindsVars :: Mapping m a0 => (f :&: a) a0 -> 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.

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 (f :: k -> TYPE LiftedRep) p (f :&: p :: k -> Type)

Defined in Data.Comp.Ops

Methods

injectA :: forall (a :: k0). p -> f a -> (f :&: p) a

projectA :: forall (a :: k0). (f :&: p) a -> (f a, p)

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

Defined in Data.Comp.Ops

Methods

injectA :: forall (a :: k0). p -> (f :+: s) a -> ((f :&: p) :+: s') a

projectA :: forall (a :: k0). ((f :&: p) :+: s') a -> ((f :+: s) a, p)

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

Methods

remA :: s a -> s' a

Remove annotations from a signature.

Instances

RemA (f :&: p :: k -> Type) (f :: k -> Type)

Defined in Data.Comp.Ops

Methods

remA :: forall (a :: k0). (f :&: p) a -> f a

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

Defined in Data.Comp.Ops

Methods

remA :: forall (a :: k0). ((f :&: p) :+: s) a -> (f :+: s') a