compdata-0.6.1.3: Compositional Data Types

Portability non-portable (GHC Extensions) experimental Tom Hvitved None

Data.Comp.Param.Sum

Description

This module provides the infrastructure to extend signatures.

Synopsis

Documentation

class sub :<: sup whereSource

Signature containment relation for automatic injections. The left-hand must be an atomic signature, where as the right-hand side must have a list-like structure. Examples include `f :<: f :+: g` and `g :<: f :+: (g :+: h)`, non-examples include `f :+: g :<: f :+: (g :+: h)` and `f :<: (f :+: g) :+: h`.

Methods

inj :: sub a b -> sup a bSource

proj :: sup a b -> Maybe (sub a b)Source

Instances

 f :<: f :<: f g => f :<: (:+: h g) f :<: (:+: f g)

data (f :+: g) a b Source

Formal sum of signatures (difunctors).

Instances

 :<: f g => f :<: (:+: h g) f :<: (:+: f g) (Difunctor f, Difunctor g) => Difunctor (:+: f g) (Ditraversable f, Ditraversable g) => Ditraversable (:+: f g) (EqD f, EqD g) => EqD (:+: f g) `EqD` is propagated through sums. (OrdD f, OrdD g) => OrdD (:+: f g) `OrdD` is propagated through sums. (ShowD f, ShowD g) => ShowD (:+: f g) (Desugar f h, Desugar g h) => Desugar (:+: f g) h DistAnn s p s' => DistAnn (:+: f s) p (:+: (:&: f p) s') RemA s s' => RemA (:+: (:&: f p) s) (:+: f s') (Eq (f a b), Eq (g a b)) => Eq (:+: f g a b) (Ord (f a b), Ord (g a b)) => Ord (:+: f g a b) (Show (f a b), Show (g a b)) => Show (:+: f g a b)

caseD :: (f a b -> c) -> (g a b -> c) -> (f :+: g) a b -> cSource

Utility function to case on a difunctor sum, without exposing the internal representation of sums.

Projections for Signatures and Terms

proj2 :: forall f a b g1 g2. (:<: g1 f, :<: g2 f) => f a b -> Maybe (:+: g2 g1 a b)Source

proj3 :: forall f a b g1 g2 g3. (:<: g1 f, :<: g2 f, :<: g3 f) => f a b -> Maybe (:+: g3 (:+: g2 g1) a b)Source

proj4 :: forall f a b g1 g2 g3 g4. (:<: g1 f, :<: g2 f, :<: g3 f, :<: g4 f) => f a b -> Maybe (:+: g4 (:+: g3 (:+: g2 g1)) a b)Source

proj5 :: forall f a b g1 g2 g3 g4 g5. (:<: g1 f, :<: g2 f, :<: g3 f, :<: g4 f, :<: g5 f) => f a b -> Maybe (:+: g5 (:+: g4 (:+: g3 (:+: g2 g1))) a b)Source

proj6 :: forall f a b g1 g2 g3 g4 g5 g6. (:<: g1 f, :<: g2 f, :<: g3 f, :<: g4 f, :<: g5 f, :<: g6 f) => f a b -> Maybe (:+: g6 (:+: g5 (:+: g4 (:+: g3 (:+: g2 g1)))) a b)Source

proj7 :: forall f a b g1 g2 g3 g4 g5 g6 g7. (:<: g1 f, :<: g2 f, :<: g3 f, :<: g4 f, :<: g5 f, :<: g6 f, :<: g7 f) => f a b -> Maybe (:+: g7 (:+: g6 (:+: g5 (:+: g4 (:+: g3 (:+: g2 g1))))) a b)Source

proj8 :: forall f a b g1 g2 g3 g4 g5 g6 g7 g8. (:<: g1 f, :<: g2 f, :<: g3 f, :<: g4 f, :<: g5 f, :<: g6 f, :<: g7 f, :<: g8 f) => f a b -> Maybe (:+: g8 (:+: g7 (:+: g6 (:+: g5 (:+: g4 (:+: g3 (:+: g2 g1)))))) a b)Source

proj9 :: forall f a b g1 g2 g3 g4 g5 g6 g7 g8 g9. (:<: g1 f, :<: g2 f, :<: g3 f, :<: g4 f, :<: g5 f, :<: g6 f, :<: g7 f, :<: g8 f, :<: g9 f) => f a b -> Maybe (:+: g9 (:+: g8 (:+: g7 (:+: g6 (:+: g5 (:+: g4 (:+: g3 (:+: g2 g1))))))) a b)Source

proj10 :: forall f a b g1 g2 g3 g4 g5 g6 g7 g8 g9 g10. (:<: g1 f, :<: g2 f, :<: g3 f, :<: g4 f, :<: g5 f, :<: g6 f, :<: g7 f, :<: g8 f, :<: g9 f, :<: g10 f) => f a b -> Maybe (:+: g10 (:+: g9 (:+: g8 (:+: g7 (:+: g6 (:+: g5 (:+: g4 (:+: g3 (:+: g2 g1)))))))) a b)Source

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

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

project2 :: forall h f a b g1 g2. (:<: g1 f, :<: g2 f) => Cxt h f a b -> Maybe (:+: g2 g1 a (Cxt h f a b))Source

project3 :: forall h f a b g1 g2 g3. (:<: g1 f, :<: g2 f, :<: g3 f) => Cxt h f a b -> Maybe (:+: g3 (:+: g2 g1) a (Cxt h f a b))Source

project4 :: forall h f a b g1 g2 g3 g4. (:<: g1 f, :<: g2 f, :<: g3 f, :<: g4 f) => Cxt h f a b -> Maybe (:+: g4 (:+: g3 (:+: g2 g1)) a (Cxt h f a b))Source

project5 :: forall h f a b g1 g2 g3 g4 g5. (:<: g1 f, :<: g2 f, :<: g3 f, :<: g4 f, :<: g5 f) => Cxt h f a b -> Maybe (:+: g5 (:+: g4 (:+: g3 (:+: g2 g1))) a (Cxt h f a b))Source

project6 :: forall h f a b g1 g2 g3 g4 g5 g6. (:<: g1 f, :<: g2 f, :<: g3 f, :<: g4 f, :<: g5 f, :<: g6 f) => Cxt h f a b -> Maybe (:+: g6 (:+: g5 (:+: g4 (:+: g3 (:+: g2 g1)))) a (Cxt h f a b))Source

project7 :: forall h f a b g1 g2 g3 g4 g5 g6 g7. (:<: g1 f, :<: g2 f, :<: g3 f, :<: g4 f, :<: g5 f, :<: g6 f, :<: g7 f) => Cxt h f a b -> Maybe (:+: g7 (:+: g6 (:+: g5 (:+: g4 (:+: g3 (:+: g2 g1))))) a (Cxt h f a b))Source

project8 :: forall h f a b g1 g2 g3 g4 g5 g6 g7 g8. (:<: g1 f, :<: g2 f, :<: g3 f, :<: g4 f, :<: g5 f, :<: g6 f, :<: g7 f, :<: g8 f) => Cxt h f a b -> Maybe (:+: g8 (:+: g7 (:+: g6 (:+: g5 (:+: g4 (:+: g3 (:+: g2 g1)))))) a (Cxt h f a b))Source

project9 :: forall h f a b g1 g2 g3 g4 g5 g6 g7 g8 g9. (:<: g1 f, :<: g2 f, :<: g3 f, :<: g4 f, :<: g5 f, :<: g6 f, :<: g7 f, :<: g8 f, :<: g9 f) => Cxt h f a b -> Maybe (:+: g9 (:+: g8 (:+: g7 (:+: g6 (:+: g5 (:+: g4 (:+: g3 (:+: g2 g1))))))) a (Cxt h f a b))Source

project10 :: forall h f a b g1 g2 g3 g4 g5 g6 g7 g8 g9 g10. (:<: g1 f, :<: g2 f, :<: g3 f, :<: g4 f, :<: g5 f, :<: g6 f, :<: g7 f, :<: g8 f, :<: g9 f, :<: g10 f) => Cxt h f a b -> Maybe (:+: g10 (:+: g9 (:+: g8 (:+: g7 (:+: g6 (:+: g5 (:+: g4 (:+: g3 (:+: g2 g1)))))))) a (Cxt h f a b))Source

deepProject :: (Ditraversable g, g :<: f) => Term f -> Maybe (Term g)Source

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

deepProject2 :: forall f g1 g2. (Ditraversable (:+: g2 g1), :<: g1 f, :<: g2 f) => Term f -> Maybe (Term (:+: g2 g1))Source

deepProject3 :: forall f g1 g2 g3. (Ditraversable (:+: g3 (:+: g2 g1)), :<: g1 f, :<: g2 f, :<: g3 f) => Term f -> Maybe (Term (:+: g3 (:+: g2 g1)))Source

deepProject4 :: forall f g1 g2 g3 g4. (Ditraversable (:+: g4 (:+: g3 (:+: g2 g1))), :<: g1 f, :<: g2 f, :<: g3 f, :<: g4 f) => Term f -> Maybe (Term (:+: g4 (:+: g3 (:+: g2 g1))))Source

deepProject5 :: forall f g1 g2 g3 g4 g5. (Ditraversable (:+: g5 (:+: g4 (:+: g3 (:+: g2 g1)))), :<: g1 f, :<: g2 f, :<: g3 f, :<: g4 f, :<: g5 f) => Term f -> Maybe (Term (:+: g5 (:+: g4 (:+: g3 (:+: g2 g1)))))Source

deepProject6 :: forall f g1 g2 g3 g4 g5 g6. (Ditraversable (:+: g6 (:+: g5 (:+: g4 (:+: g3 (:+: g2 g1))))), :<: g1 f, :<: g2 f, :<: g3 f, :<: g4 f, :<: g5 f, :<: g6 f) => Term f -> Maybe (Term (:+: g6 (:+: g5 (:+: g4 (:+: g3 (:+: g2 g1))))))Source

deepProject7 :: forall f g1 g2 g3 g4 g5 g6 g7. (Ditraversable (:+: g7 (:+: g6 (:+: g5 (:+: g4 (:+: g3 (:+: g2 g1)))))), :<: g1 f, :<: g2 f, :<: g3 f, :<: g4 f, :<: g5 f, :<: g6 f, :<: g7 f) => Term f -> Maybe (Term (:+: g7 (:+: g6 (:+: g5 (:+: g4 (:+: g3 (:+: g2 g1)))))))Source

deepProject8 :: forall f g1 g2 g3 g4 g5 g6 g7 g8. (Ditraversable (:+: g8 (:+: g7 (:+: g6 (:+: g5 (:+: g4 (:+: g3 (:+: g2 g1))))))), :<: g1 f, :<: g2 f, :<: g3 f, :<: g4 f, :<: g5 f, :<: g6 f, :<: g7 f, :<: g8 f) => Term f -> Maybe (Term (:+: g8 (:+: g7 (:+: g6 (:+: g5 (:+: g4 (:+: g3 (:+: g2 g1))))))))Source

deepProject9 :: forall f g1 g2 g3 g4 g5 g6 g7 g8 g9. (Ditraversable (:+: g9 (:+: g8 (:+: g7 (:+: g6 (:+: g5 (:+: g4 (:+: g3 (:+: g2 g1)))))))), :<: g1 f, :<: g2 f, :<: g3 f, :<: g4 f, :<: g5 f, :<: g6 f, :<: g7 f, :<: g8 f, :<: g9 f) => Term f -> Maybe (Term (:+: g9 (:+: g8 (:+: g7 (:+: g6 (:+: g5 (:+: g4 (:+: g3 (:+: g2 g1)))))))))Source

deepProject10 :: forall f g1 g2 g3 g4 g5 g6 g7 g8 g9 g10. (Ditraversable (:+: g10 (:+: g9 (:+: g8 (:+: g7 (:+: g6 (:+: g5 (:+: g4 (:+: g3 (:+: g2 g1))))))))), :<: g1 f, :<: g2 f, :<: g3 f, :<: g4 f, :<: g5 f, :<: g6 f, :<: g7 f, :<: g8 f, :<: g9 f, :<: g10 f) => Term f -> Maybe (Term (:+: g10 (:+: g9 (:+: g8 (:+: g7 (:+: g6 (:+: g5 (:+: g4 (:+: g3 (:+: g2 g1))))))))))Source

Injections for Signatures and Terms

inj2 :: forall g a b f1 f2. (:<: f1 g, :<: f2 g) => :+: f2 f1 a b -> g a bSource

inj3 :: forall g a b f1 f2 f3. (:<: f1 g, :<: f2 g, :<: f3 g) => :+: f3 (:+: f2 f1) a b -> g a bSource

inj4 :: forall g a b f1 f2 f3 f4. (:<: f1 g, :<: f2 g, :<: f3 g, :<: f4 g) => :+: f4 (:+: f3 (:+: f2 f1)) a b -> g a bSource

inj5 :: forall g a b f1 f2 f3 f4 f5. (:<: f1 g, :<: f2 g, :<: f3 g, :<: f4 g, :<: f5 g) => :+: f5 (:+: f4 (:+: f3 (:+: f2 f1))) a b -> g a bSource

inj6 :: forall g a b f1 f2 f3 f4 f5 f6. (:<: f1 g, :<: f2 g, :<: f3 g, :<: f4 g, :<: f5 g, :<: f6 g) => :+: f6 (:+: f5 (:+: f4 (:+: f3 (:+: f2 f1)))) a b -> g a bSource

inj7 :: forall g a b f1 f2 f3 f4 f5 f6 f7. (:<: f1 g, :<: f2 g, :<: f3 g, :<: f4 g, :<: f5 g, :<: f6 g, :<: f7 g) => :+: f7 (:+: f6 (:+: f5 (:+: f4 (:+: f3 (:+: f2 f1))))) a b -> g a bSource

inj8 :: forall g a b f1 f2 f3 f4 f5 f6 f7 f8. (:<: f1 g, :<: f2 g, :<: f3 g, :<: f4 g, :<: f5 g, :<: f6 g, :<: f7 g, :<: f8 g) => :+: f8 (:+: f7 (:+: f6 (:+: f5 (:+: f4 (:+: f3 (:+: f2 f1)))))) a b -> g a bSource

inj9 :: forall g a b f1 f2 f3 f4 f5 f6 f7 f8 f9. (:<: f1 g, :<: f2 g, :<: f3 g, :<: f4 g, :<: f5 g, :<: f6 g, :<: f7 g, :<: f8 g, :<: f9 g) => :+: f9 (:+: f8 (:+: f7 (:+: f6 (:+: f5 (:+: f4 (:+: f3 (:+: f2 f1))))))) a b -> g a bSource

inj10 :: forall g a b f1 f2 f3 f4 f5 f6 f7 f8 f9 f10. (:<: f1 g, :<: f2 g, :<: f3 g, :<: f4 g, :<: f5 g, :<: f6 g, :<: f7 g, :<: f8 g, :<: f9 g, :<: f10 g) => :+: f10 (:+: f9 (:+: f8 (:+: f7 (:+: f6 (:+: f5 (:+: f4 (:+: f3 (:+: f2 f1)))))))) a b -> g a bSource

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

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

inject' :: (Difunctor g, g :<: f) => g (Cxt h f a b) (Cxt h f a b) -> Cxt h f a bSource

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

inject2 :: forall h g a b f1 f2. (:<: f1 g, :<: f2 g) => :+: f2 f1 a (Cxt h g a b) -> Cxt h g a bSource

inject3 :: forall h g a b f1 f2 f3. (:<: f1 g, :<: f2 g, :<: f3 g) => :+: f3 (:+: f2 f1) a (Cxt h g a b) -> Cxt h g a bSource

inject4 :: forall h g a b f1 f2 f3 f4. (:<: f1 g, :<: f2 g, :<: f3 g, :<: f4 g) => :+: f4 (:+: f3 (:+: f2 f1)) a (Cxt h g a b) -> Cxt h g a bSource

inject5 :: forall h g a b f1 f2 f3 f4 f5. (:<: f1 g, :<: f2 g, :<: f3 g, :<: f4 g, :<: f5 g) => :+: f5 (:+: f4 (:+: f3 (:+: f2 f1))) a (Cxt h g a b) -> Cxt h g a bSource

inject6 :: forall h g a b f1 f2 f3 f4 f5 f6. (:<: f1 g, :<: f2 g, :<: f3 g, :<: f4 g, :<: f5 g, :<: f6 g) => :+: f6 (:+: f5 (:+: f4 (:+: f3 (:+: f2 f1)))) a (Cxt h g a b) -> Cxt h g a bSource

inject7 :: forall h g a b f1 f2 f3 f4 f5 f6 f7. (:<: f1 g, :<: f2 g, :<: f3 g, :<: f4 g, :<: f5 g, :<: f6 g, :<: f7 g) => :+: f7 (:+: f6 (:+: f5 (:+: f4 (:+: f3 (:+: f2 f1))))) a (Cxt h g a b) -> Cxt h g a bSource

inject8 :: forall h g a b f1 f2 f3 f4 f5 f6 f7 f8. (:<: f1 g, :<: f2 g, :<: f3 g, :<: f4 g, :<: f5 g, :<: f6 g, :<: f7 g, :<: f8 g) => :+: f8 (:+: f7 (:+: f6 (:+: f5 (:+: f4 (:+: f3 (:+: f2 f1)))))) a (Cxt h g a b) -> Cxt h g a bSource

inject9 :: forall h g a b f1 f2 f3 f4 f5 f6 f7 f8 f9. (:<: f1 g, :<: f2 g, :<: f3 g, :<: f4 g, :<: f5 g, :<: f6 g, :<: f7 g, :<: f8 g, :<: f9 g) => :+: f9 (:+: f8 (:+: f7 (:+: f6 (:+: f5 (:+: f4 (:+: f3 (:+: f2 f1))))))) a (Cxt h g a b) -> Cxt h g a bSource

inject10 :: forall h g a b f1 f2 f3 f4 f5 f6 f7 f8 f9 f10. (:<: f1 g, :<: f2 g, :<: f3 g, :<: f4 g, :<: f5 g, :<: f6 g, :<: f7 g, :<: f8 g, :<: f9 g, :<: f10 g) => :+: f10 (:+: f9 (:+: f8 (:+: f7 (:+: f6 (:+: f5 (:+: f4 (:+: f3 (:+: f2 f1)))))))) a (Cxt h g a b) -> Cxt h g a bSource

deepInject :: (Difunctor g, g :<: f) => Term g -> Term fSource

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

deepInject2 :: forall g f1 f2. (Difunctor (:+: f2 f1), :<: f1 g, :<: f2 g) => CxtFun (:+: f2 f1) gSource

deepInject3 :: forall g f1 f2 f3. (Difunctor (:+: f3 (:+: f2 f1)), :<: f1 g, :<: f2 g, :<: f3 g) => CxtFun (:+: f3 (:+: f2 f1)) gSource

deepInject4 :: forall g f1 f2 f3 f4. (Difunctor (:+: f4 (:+: f3 (:+: f2 f1))), :<: f1 g, :<: f2 g, :<: f3 g, :<: f4 g) => CxtFun (:+: f4 (:+: f3 (:+: f2 f1))) gSource

deepInject5 :: forall g f1 f2 f3 f4 f5. (Difunctor (:+: f5 (:+: f4 (:+: f3 (:+: f2 f1)))), :<: f1 g, :<: f2 g, :<: f3 g, :<: f4 g, :<: f5 g) => CxtFun (:+: f5 (:+: f4 (:+: f3 (:+: f2 f1)))) gSource

deepInject6 :: forall g f1 f2 f3 f4 f5 f6. (Difunctor (:+: f6 (:+: f5 (:+: f4 (:+: f3 (:+: f2 f1))))), :<: f1 g, :<: f2 g, :<: f3 g, :<: f4 g, :<: f5 g, :<: f6 g) => CxtFun (:+: f6 (:+: f5 (:+: f4 (:+: f3 (:+: f2 f1))))) gSource

deepInject7 :: forall g f1 f2 f3 f4 f5 f6 f7. (Difunctor (:+: f7 (:+: f6 (:+: f5 (:+: f4 (:+: f3 (:+: f2 f1)))))), :<: f1 g, :<: f2 g, :<: f3 g, :<: f4 g, :<: f5 g, :<: f6 g, :<: f7 g) => CxtFun (:+: f7 (:+: f6 (:+: f5 (:+: f4 (:+: f3 (:+: f2 f1)))))) gSource

deepInject8 :: forall g f1 f2 f3 f4 f5 f6 f7 f8. (Difunctor (:+: f8 (:+: f7 (:+: f6 (:+: f5 (:+: f4 (:+: f3 (:+: f2 f1))))))), :<: f1 g, :<: f2 g, :<: f3 g, :<: f4 g, :<: f5 g, :<: f6 g, :<: f7 g, :<: f8 g) => CxtFun (:+: f8 (:+: f7 (:+: f6 (:+: f5 (:+: f4 (:+: f3 (:+: f2 f1))))))) gSource

deepInject9 :: forall g f1 f2 f3 f4 f5 f6 f7 f8 f9. (Difunctor (:+: f9 (:+: f8 (:+: f7 (:+: f6 (:+: f5 (:+: f4 (:+: f3 (:+: f2 f1)))))))), :<: f1 g, :<: f2 g, :<: f3 g, :<: f4 g, :<: f5 g, :<: f6 g, :<: f7 g, :<: f8 g, :<: f9 g) => CxtFun (:+: f9 (:+: f8 (:+: f7 (:+: f6 (:+: f5 (:+: f4 (:+: f3 (:+: f2 f1)))))))) gSource

deepInject10 :: forall g f1 f2 f3 f4 f5 f6 f7 f8 f9 f10. (Difunctor (:+: f10 (:+: f9 (:+: f8 (:+: f7 (:+: f6 (:+: f5 (:+: f4 (:+: f3 (:+: f2 f1))))))))), :<: f1 g, :<: f2 g, :<: f3 g, :<: f4 g, :<: f5 g, :<: f6 g, :<: f7 g, :<: f8 g, :<: f9 g, :<: f10 g) => CxtFun (:+: f10 (:+: f9 (:+: f8 (:+: f7 (:+: f6 (:+: f5 (:+: f4 (:+: f3 (:+: f2 f1))))))))) gSource

injectCxt :: (Difunctor g, g :<: f) => Cxt h g a (Cxt h f a b) -> Cxt h f a bSource

This function injects a whole context into another context.

liftCxt :: (Difunctor f, g :<: f) => g a b -> Cxt Hole f a bSource

This function lifts the given functor to a context.