compdata-0.11: Compositional Data Types

Copyright(c) 2011 Patrick Bahr
LicenseBSD3
MaintainerPatrick Bahr <paba@diku.dk>
Stabilityexperimental
Portabilitynon-portable (GHC Extensions)
Safe HaskellSafe
LanguageHaskell98

Data.Comp.Multi.Ops

Description

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

Synopsis

Documentation

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

Data type defining coproducts.

Constructors

Inl (f h e) 
Inr (g h e) 

Instances

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

Methods

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

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

Methods

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

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

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

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

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

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

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

Methods

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

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

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

EqF is propagated through sums.

Methods

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

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

OrdHF is propagated through sums.

Methods

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

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

Methods

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

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

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

Methods

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

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

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

Methods

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

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

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

Methods

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

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

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

type family Elem (f :: (* -> *) -> * -> *) (g :: (* -> *) -> * -> *) :: Emb where ... Source #

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 Source #

Minimal complete definition

inj', prj'

Methods

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

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

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

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 Source #

proj :: forall f g a. f :<: g => NatM Maybe (g a) (f a) Source #

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

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

data (f :&: a) g e infixr 7 Source #

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) Source # 

Methods

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

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

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

Methods

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

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

Methods

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

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

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

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

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

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

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

Methods

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

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

RemA ((:&:) * f p) f Source # 

Methods

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

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

Methods

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

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

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

Methods

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

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

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 Source #

This function injects an annotation over a signature.

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

Instances

DistAnn f p ((:&:) * f p) Source # 

Methods

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

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

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

Methods

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

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

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

Minimal complete definition

remA

Methods

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

Instances

RemA ((:&:) * f p) f Source # 

Methods

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

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

Methods

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

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

Formal product of signatures (functors).

Constructors

(f a) :*: (g a) infixr 8 

Instances

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

Methods

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

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

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

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) Source # 

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 Source #

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