Data.Comp.Sum

This module provides the infrastructure to extend signatures.

Documentation

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.

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

data (f :+: g) e infixr 6

Formal sum of signatures (functors).

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)

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.

Projections for Signatures and Terms

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

project :: g :<: f => Cxt h f a -> Maybe (g (Cxt h f a))

Project the outermost layer of a term to a sub signature. If the signature g is compound of n atomic signatures, use projectn instead.

deepProject :: (Traversable g, g :<: f) => CxtFunM Maybe f g

Tries to coerce a termcontext to a termcontext over a sub-signature. If the signature g is compound of n atomic signatures, use deepProjectn instead.

project_ :: SigFunM Maybe f g -> Cxt h f a -> Maybe (g (Cxt h f a))

Project the outermost layer of a term to a sub signature. If the signature g is compound of n atomic signatures, use projectn instead.

deepProject_ :: Traversable g => SigFunM Maybe f g -> CxtFunM Maybe f g

Tries to coerce a termcontext to a termcontext over a sub-signature. If the signature g is compound of n atomic signatures, use deepProjectn instead.

Injections for Signatures and Terms

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

inject :: g :<: f => g (Cxt h f a) -> Cxt h f a

Inject a term where the outermost layer is a sub signature. If the signature g is compound of n atomic signatures, use injectn instead.

deepInject :: (Functor g, g :<: f) => CxtFun g f

Inject a term over a sub signature to a term over larger signature. If the signature g is compound of n atomic signatures, use deepInjectn instead.

inject_ :: SigFun g f -> g (Cxt h f a) -> Cxt h f a

Inject a term where the outermost layer is a sub signature. If the signature g is compound of n atomic signatures, use injectn instead.

deepInject_ :: Functor g => SigFun g f -> CxtFun g f

Inject a term over a sub signature to a term over larger signature. If the signature g is compound of n atomic signatures, use deepInjectn instead.

split :: f :=: (f1 :+: f2) => (f1 (Term f) -> a) -> (f2 (Term f) -> a) -> Term f -> a

Injections and Projections for Constants

injectConst :: (Functor g, g :<: f) => Const g -> Cxt h f a

projectConst :: (Functor g, g :<: f) => Cxt h f a -> Maybe (Const g)

injectCxt :: (Functor g, g :<: f) => Cxt h' g (Cxt h f a) -> Cxt h f a

This function injects a whole context into another context.

liftCxt :: (Functor f, g :<: f) => g a -> Context f a

This function lifts the given functor to a context.

substHoles :: (Functor f, Functor g, f :<: g) => Cxt h' f v -> (v -> Cxt h g a) -> Cxt h g a

This function applies the given context with hole type a to a family f of contexts (possibly terms) indexed by a. That is, each hole h is replaced by the context f h.

substHoles' :: (Functor f, Functor g, f :<: g, Ord v) => Cxt h' f v -> Map v (Cxt h g a) -> Cxt h g a

Orphan instances

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

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)

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

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

Methods

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

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

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