Data.Comp.Param.Multi.Ops

This module provides operators on higher-order difunctors.

Documentation

data (f :+: g) (a :: * -> *) (b :: * -> *) i infixr 6

Formal sum of signatures (difunctors).

Constructors

Inl (f a b i)

Inr (g a b i)

Instances

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

Defined in Data.Comp.Param.Multi.Ops

Methods

inj :: f a b i -> (h :+: g) a b i

proj :: (h :+: g) a b i -> Maybe (f a b i)

f :<: (f :+: g)

Defined in Data.Comp.Param.Multi.Ops

Methods

inj :: f a b i -> (f :+: g) a b i

proj :: (f :+: g) a b i -> Maybe (f a b i)

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

Defined in Data.Comp.Param.Multi.Ops

Methods

hdimap :: (a :-> b) -> (c :-> d) -> (f :+: g) b c :-> (f :+: g) a d

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

Defined in Data.Comp.Param.Multi.Show

Methods

showHD :: (f :+: g) Name (K (FreshM String)) i -> FreshM String

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

Defined in Data.Comp.Param.Multi.Ops

Methods

hdimapM :: Monad m => NatM m b c -> NatM m ((f :+: g) a b) ((f :+: g) a c)

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

EqHD is propagated through sums.

Defined in Data.Comp.Param.Multi.Equality

Methods

eqHD :: PEq a => (f :+: g) Name a i -> (f :+: g) Name a j -> FreshM Bool

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

OrdHD is propagated through sums.

Defined in Data.Comp.Param.Multi.Ordering

Methods

compareHD :: POrd a => (f :+: g) Name a i -> (f :+: g) Name a j -> FreshM Ordering

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

Defined in Data.Comp.Param.Multi.Desugar

Methods

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

desugHom' :: (f :+: g) a (Cxt h0 h a b) i -> Cxt h0 h a b i

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

Defined in Data.Comp.Param.Multi.Ops

Methods

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

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

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

Defined in Data.Comp.Param.Multi.Ops

Methods

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

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

Defined in Data.Comp.Param.Multi.Sum

Methods

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

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

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

Defined in Data.Comp.Param.Multi.Sum

Methods

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

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

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

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

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

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

min :: (f :+: g) a b i -> (f :+: g) a b i -> (f :+: g) a b i

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

Defined in Data.Comp.Param.Multi.Sum

Methods

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

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

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

caseHD :: (f a b i -> c) -> (g a b i -> c) -> (f :+: g) a b i -> c

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

class (sub :: (* -> *) -> (* -> *) -> * -> *) :<: sup where

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.

Minimal complete definition

inj, proj

Methods

inj :: sub a b :-> sup a b

proj :: NatM Maybe (sup a b) (sub a b)

Instances

f :<: f

Defined in Data.Comp.Param.Multi.Ops

Methods

inj :: f a b i -> f a b i

proj :: f a b i -> Maybe (f a b i)

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

Defined in Data.Comp.Param.Multi.Ops

Methods

inj :: f a b i -> (h :+: g) a b i

proj :: (h :+: g) a b i -> Maybe (f a b i)

f :<: (f :+: g)

Defined in Data.Comp.Param.Multi.Ops

Methods

inj :: f a b i -> (f :+: g) a b i

proj :: (f :+: g) a b i -> Maybe (f a b i)

data (f :*: g) a b i infixr 8

Formal product of signatures (higher-order difunctors).

Constructors

(f a b i) :*: (g a b i) infixr 8

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

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

data (f :&: p) (a :: * -> *) (b :: * -> *) i infixr 7

This data type adds a constant product to a signature.

Constructors

(f a b i) :&: p infixr 7

Instances

DistAnn f p (f :&: p)

Defined in Data.Comp.Param.Multi.Ops

Methods

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

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

HDifunctor f => HDifunctor (f :&: p)

Defined in Data.Comp.Param.Multi.Ops

Methods

hdimap :: (a :-> b) -> (c :-> d) -> (f :&: p) b c :-> (f :&: p) a d

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

Defined in Data.Comp.Param.Multi.Show

Methods

showHD :: (f :&: p) Name (K (FreshM String)) i -> FreshM String

HDitraversable f => HDitraversable (f :&: p)

Defined in Data.Comp.Param.Multi.Ops

Methods

hdimapM :: Monad m => NatM m b c -> NatM m ((f :&: p) a b) ((f :&: p) a c)

RemA (f :&: p) f

Defined in Data.Comp.Param.Multi.Ops

Methods

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

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

Defined in Data.Comp.Param.Multi.Ops

Methods

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

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

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

Defined in Data.Comp.Param.Multi.Ops

Methods

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

Inject an annotation over a signature.

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

Project an annotation from a signature.

Instances

DistAnn f p (f :&: p)

Defined in Data.Comp.Param.Multi.Ops

Methods

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

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

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

Defined in Data.Comp.Param.Multi.Ops

Methods

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

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

class RemA (s :: (* -> *) -> (* -> *) -> * -> *) s' | s -> s' where

Minimal complete definition

remA

Methods

remA :: s a b :-> s' a b

Remove annotations from a signature.

Instances

RemA (f :&: p) f

Defined in Data.Comp.Param.Multi.Ops

Methods

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

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

Defined in Data.Comp.Param.Multi.Ops

Methods

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