Copyright	(c) 2011 Patrick Bahr
License	BSD3
Maintainer	Patrick Bahr <paba@diku.dk>
Stability	experimental
Portability	non-portable (GHC Extensions)
Safe Haskell	None
Language	Haskell98

Data.Comp.Multi.Term

Description

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.

Synopsis

data Cxt h f a i where
- Term :: f (Cxt h f a) i -> Cxt h f a i
- Hole :: a i -> Cxt Hole f a i
data Hole
data NoHole
type Context = Cxt Hole
type ContextS fs a = CxtS Hole fs a
type HFix f = Cxt NoHole f (K ())
type Term fs = HFix (Sum fs)
type CxtS h fs a = Cxt h (Sum fs) a
type Const (f :: (* -> *) -> * -> *) = f (K ())
constTerm :: HFunctor f => Const f :-> HFix f
unTerm :: HFix f t -> f (HFix f) t
toCxt :: HFunctor f => HFix f :-> Context f a
simpCxt :: HFunctor f => f a i -> Context f a i

Documentation

data Cxt h f a i where Source #

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 Hole 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

Instances details

Generic (f (HFix f) l) => Generic (HFix f l) Source #
Instance details Defined in Data.Comp.Multi.Derive.Generic Associated Types type Rep (HFix f l) :: Type -> Type # Methods from :: HFix f l -> Rep (HFix f l) x # to :: Rep (HFix f l) x -> HFix f l #
HFunctor f => HFunctor (Cxt h f) Source #
Instance details 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 Source #
HFoldable f => HFoldable (Cxt h f) Source #
Instance details Defined in Data.Comp.Multi.Term Methods hfold :: Monoid m => Cxt h f (K m) :=> m Source # hfoldMap :: forall m (a :: Type -> Type). Monoid m => (a :=> m) -> Cxt h f a :=> m Source # hfoldr :: forall (a :: Type -> Type) b. (a :=> (b -> b)) -> b -> Cxt h f a :=> b Source # hfoldl :: forall b (a :: Type -> Type). (b -> a :=> b) -> b -> Cxt h f a :=> b Source # hfoldr1 :: (a -> a -> a) -> Cxt h f (K a) :=> a Source # hfoldl1 :: (a -> a -> a) -> Cxt h f (K a) :=> a Source #
HTraversable f => HTraversable (Cxt h f) Source #
Instance details 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) Source # 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) Source #
EqHF f => EqHF (Cxt h f) Source #
Instance details 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 Source #
(HFunctor f, OrdHF f) => OrdHF (Cxt h f) Source #	From an `OrdHF` difunctor an `Ord` instance of the corresponding term type can be derived.
Instance details 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 Source #
(ShowHF f, HFunctor f) => ShowHF (Cxt h f) Source #
Instance details Defined in Data.Comp.Multi.Show Methods showHF :: Alg (Cxt h f) (K String) Source # showHF' :: Cxt h f (K String) :=> String Source #
(EqHF f, KEq a) => KEq (Cxt h f a) Source #
Instance details Defined in Data.Comp.Multi.Equality Methods keq :: Cxt h f a i -> Cxt h f a j -> Bool Source #
(HFunctor f, OrdHF f, KOrd a) => KOrd (Cxt h f a) Source #
Instance details Defined in Data.Comp.Multi.Ordering Methods kcompare :: Cxt h f a i -> Cxt h f a j -> Ordering Source #
(ShowHF f, HFunctor f, KShow a) => KShow (Cxt h f a) Source #
Instance details Defined in Data.Comp.Multi.Show Methods kshow :: Cxt h f a i -> K String i Source #
(EqHF f, KEq a) => Eq (Cxt h f a i) Source #	From an `EqF` functor an `Eq` instance of the corresponding term type can be derived.
Instance details 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) Source #	Ordering of terms.
Instance details 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 #
KShow (Cxt h f a) => Show (Cxt h f a i) Source #
Instance details 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 #
type Rep (HFix f l) Source #
Instance details Defined in Data.Comp.Multi.Derive.Generic type Rep (HFix f l) = Rep (f (HFix f) l)

data Hole Source #

Phantom type that signals that a Cxt might contain holes.

data NoHole Source #

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

Instances

Instances details

Generic (f (HFix f) l) => Generic (HFix f l) Source #
Instance details Defined in Data.Comp.Multi.Derive.Generic Associated Types type Rep (HFix f l) :: Type -> Type # Methods from :: HFix f l -> Rep (HFix f l) x # to :: Rep (HFix f l) x -> HFix f l #
type Rep (HFix f l) Source #
Instance details Defined in Data.Comp.Multi.Derive.Generic type Rep (HFix f l) = Rep (f (HFix f) l)

type Context = Cxt Hole Source #

A context might contain holes.

type ContextS fs a = CxtS Hole fs a Source #

type HFix f = Cxt NoHole f (K ()) Source #

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

type Term fs = HFix (Sum fs) Source #

type CxtS h fs a = Cxt h (Sum fs) a Source #

type Const (f :: (* -> *) -> * -> *) = f (K ()) Source #

constTerm :: HFunctor f => Const f :-> HFix f Source #

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 :: HFix f t -> f (HFix f) t Source #

This function unravels the given term at the topmost layer.

toCxt :: HFunctor f => HFix f :-> Context f a Source #

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

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