Data.Comp.Multi.Term

This module defines the central notion of mutual recursive (or, higher-order) terms and its generalisation to (higher-order) contexts. All definitions are generalised versions of those in Data.Comp.Term.

Documentation

data Cxt h f a i where

This data type represents contexts over a signature. Contexts are terms containing zero or more holes. The first type parameter is supposed to be one of the phantom types Cxt and NoHole. The second parameter is the signature of the context. The third parameter is the type family of the holes. The last parameter is the index/label.

Constructors

Term :: f (Cxt h f a) i -> Cxt h f a i

Hole :: a i -> Cxt Hole f a i

Instances

(ShowHF f, HFunctor f) => ShowHF (Cxt h f)

Defined in Data.Comp.Multi.Show

Methods

showHF :: Alg (Cxt h f) (K String)

showHF' :: Cxt h f (K String) :=> String

EqHF f => EqHF (Cxt h f)

Defined in Data.Comp.Multi.Equality

Methods

eqHF :: forall (g :: Type -> Type) i j. KEq g => Cxt h f g i -> Cxt h f g j -> Bool

HFoldable f => HFoldable (Cxt h f)

Defined in Data.Comp.Multi.Term

Methods

hfold :: Monoid m => Cxt h f (K m) :=> m

hfoldMap :: forall m (a :: Type -> Type). Monoid m => (a :=> m) -> Cxt h f a :=> m

hfoldr :: forall (a :: Type -> Type) b. (a :=> (b -> b)) -> b -> Cxt h f a :=> b

hfoldl :: forall b (a :: Type -> Type). (b -> a :=> b) -> b -> Cxt h f a :=> b

hfoldr1 :: (a -> a -> a) -> Cxt h f (K a) :=> a

hfoldl1 :: (a -> a -> a) -> Cxt h f (K a) :=> a

HFunctor f => HFunctor (Cxt h f)

Defined in Data.Comp.Multi.Term

Methods

hfmap :: forall (f0 :: Type -> Type) (g :: Type -> Type). (f0 :-> g) -> Cxt h f f0 :-> Cxt h f g

HTraversable f => HTraversable (Cxt h f)

Defined in Data.Comp.Multi.Term

Methods

hmapM :: forall (m :: Type -> Type) (a :: Type -> Type) (b :: Type -> Type). Monad m => NatM m a b -> NatM m (Cxt h f a) (Cxt h f b)

htraverse :: forall (f0 :: Type -> Type) (a :: Type -> Type) (b :: Type -> Type). Applicative f0 => NatM f0 a b -> NatM f0 (Cxt h f a) (Cxt h f b)

(HFunctor f, OrdHF f) => OrdHF (Cxt h f)

From an OrdHF difunctor an Ord instance of the corresponding term type can be derived.

Defined in Data.Comp.Multi.Ordering

Methods

compareHF :: forall (a :: Type -> Type) i j. KOrd a => Cxt h f a i -> Cxt h f a j -> Ordering

(ShowHF f, HFunctor f, KShow a) => KShow (Cxt h f a)

Defined in Data.Comp.Multi.Show

Methods

kshow :: Cxt h f a i -> K String i

(EqHF f, KEq a) => KEq (Cxt h f a)

Defined in Data.Comp.Multi.Equality

Methods

keq :: Cxt h f a i -> Cxt h f a j -> Bool

(HFunctor f, OrdHF f, KOrd a) => KOrd (Cxt h f a)

Defined in Data.Comp.Multi.Ordering

Methods

kcompare :: Cxt h f a i -> Cxt h f a j -> Ordering

KShow (Cxt h f a) => Show (Cxt h f a i)

Defined in Data.Comp.Multi.Show

Methods

showsPrec :: Int -> Cxt h f a i -> ShowS

show :: Cxt h f a i -> String

showList :: [Cxt h f a i] -> ShowS

(EqHF f, KEq a) => Eq (Cxt h f a i)

From an EqF functor an Eq instance of the corresponding term type can be derived.

Defined in Data.Comp.Multi.Equality

Methods

(==) :: Cxt h f a i -> Cxt h f a i -> Bool

(/=) :: Cxt h f a i -> Cxt h f a i -> Bool

(HFunctor f, OrdHF f, KOrd a) => Ord (Cxt h f a i)

Ordering of terms.

Defined in Data.Comp.Multi.Ordering

Methods

compare :: Cxt h f a i -> Cxt h f a i -> Ordering

(<) :: Cxt h f a i -> Cxt h f a i -> Bool

(<=) :: Cxt h f a i -> Cxt h f a i -> Bool

(>) :: Cxt h f a i -> Cxt h f a i -> Bool

(>=) :: Cxt h f a i -> Cxt h f a i -> Bool

max :: Cxt h f a i -> Cxt h f a i -> Cxt h f a i

min :: Cxt h f a i -> Cxt h f a i -> Cxt h f a i

data Hole

Phantom type that signals that a Cxt might contain holes.

data NoHole

Phantom type that signals that a Cxt does not contain holes.

type Context = Cxt Hole

A context might contain holes.

type Term f = Cxt NoHole f (K ())

A (higher-order) term is a context with no holes.

type Const (f :: (Type -> Type) -> Type -> Type) = f (K ())

constTerm :: HFunctor f => Const f :-> Term f

This function converts a constant to a term. This assumes that the argument is indeed a constant, i.e. does not have a value for the argument type of the functor f.

unTerm :: Term f t -> f (Term f) t

This function unravels the given term at the topmost layer.

toCxt :: HFunctor f => Term f :-> Context f a

Cast a term over a signature to a context over the same signature.

simpCxt :: HFunctor f => f a i -> Context f a i