Data.Comp.Multi.Ops

This module provides operators on higher-order functors. All definitions are generalised versions of those in Data.Comp.Ops.

Documentation

data (f :+: g) h e infixr 6

Data type defining coproducts.

Constructors

Inl (f h e)

Inr (g h e)

Instances

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

Methods

hfmap :: (f :-> g) -> (* :+: f) g f :-> (* :+: f) g g

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

Methods

hfold :: Monoid m => (* :+: f) g (K m) :=> m

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

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

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

hfoldr1 :: (a -> a -> a) -> (* :+: f) g (K a) :=> a

hfoldl1 :: (a -> a -> a) -> (* :+: f) g (K a) :=> a

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

Methods

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

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

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

EqF is propagated through sums.

Methods

eqHF :: KEq g => (* :+: f) g g i -> (* :+: f) g g j -> Bool

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

OrdHF is propagated through sums.

Methods

compareHF :: KOrd a => (* :+: f) g a i -> (* :+: f) g a j -> Ordering

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

Methods

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

desugHom' :: (* :+: f) g (Context h a) i -> Context h a i

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

Methods

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

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

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

Methods

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

projectA :: (* :+: (* :&: f) p) s' a i -> (* :&: (* :+: f) s a) p i

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

Methods

remA :: (* :+: (* :&: f) p) s a i -> (* :+: f) s' a i

caseH :: (f a b -> c) -> (g a b -> c) -> (f :+: g) a b -> c

Utility function to case on a higher-order 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 -> NatM Maybe (g a) (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 => NatM Maybe (g a) (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 :&: a) g e infixr 7

This data type adds a constant product to a signature. Alternatively, this could have also been defined as

data (f :&: a) (g ::  * -> *) e = f g e :&: a e

This is too general, however, for example for productHHom.

Constructors

(f g e) :&: a infixr 7

Instances

DistAnn f p ((:&:) * f p)

Methods

injectA :: p -> f a :-> (* :&: f) p a

projectA :: (* :&: f) p a i -> (* :&: f a) p i

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

Methods

hfmap :: (f :-> g) -> (* :&: f) a f :-> (* :&: f) a g

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

Methods

hfold :: Monoid m => (* :&: f) a (K m) :=> m

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

hfoldr :: (a :=> (b -> b)) -> b -> (* :&: f) a a :=> b

hfoldl :: (b -> a :=> b) -> b -> (* :&: f) a a :=> b

hfoldr1 :: (a -> a -> a) -> (* :&: f) a (K a) :=> a

hfoldl1 :: (a -> a -> a) -> (* :&: f) a (K a) :=> a

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

Methods

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

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

RemA ((:&:) * f p) f

Methods

remA :: (* :&: f) p a i -> f a i

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

Methods

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

projectA :: (* :+: (* :&: f) p) s' a i -> (* :&: (* :+: f) s a) p i

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

Methods

remA :: (* :+: (* :&: f) p) s a i -> (* :+: f) s' a i

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

This function injects an annotation over a signature.

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

Instances

DistAnn f p ((:&:) * f p)

Methods

injectA :: p -> f a :-> (* :&: f) p a

projectA :: (* :&: f) p a i -> (* :&: f a) p i

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

Methods

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

projectA :: (* :+: (* :&: f) p) s' a i -> (* :&: (* :+: f) s a) p i

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

Minimal complete definition

remA

Methods

remA :: s a :-> s' a

Instances

RemA ((:&:) * f p) f

Methods

remA :: (* :&: f) p a i -> f a i

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

Methods

remA :: (* :+: (* :&: f) p) s a i -> (* :+: f) s' a i

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