Data.Comp.Term

This module defines the central notion of terms and its generalisation to contexts.

Documentation

data Cxt :: * -> (* -> *) -> * -> * 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 Hole and NoHole. The second parameter is the signature of the context. The third parameter is the type of the holes.

Constructors

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

Hole :: a -> Cxt Hole f a

Instances

Functor f => Monad (Context f)

Defined in Data.Comp.Term

Methods

(>>=) :: Context f a -> (a -> Context f b) -> Context f b

(>>) :: Context f a -> Context f b -> Context f b

return :: a -> Context f a

Functor f => Applicative (Context f)

Defined in Data.Comp.Term

Methods

pure :: a -> Context f a

(<*>) :: Context f (a -> b) -> Context f a -> Context f b

liftA2 :: (a -> b -> c) -> Context f a -> Context f b -> Context f c

(*>) :: Context f a -> Context f b -> Context f b

(<*) :: Context f a -> Context f b -> Context f a

ArbitraryF f => Arbitrary (Term f)

This lifts instances of ArbitraryF to instances of Arbitrary for the corresponding term type.

Defined in Data.Comp.Arbitrary

Methods

arbitrary :: Gen (Term f)

shrink :: Term f -> [Term f]

ArbitraryF f => ArbitraryF (Context f)

This lifts instances of ArbitraryF to instances of ArbitraryF for the corresponding context functor.

Defined in Data.Comp.Arbitrary

Methods

arbitraryF' :: Arbitrary v => [(Int, Gen (Context f v))]

arbitraryF :: Arbitrary v => Gen (Context f v)

shrinkF :: Arbitrary v => Context f v -> [Context f v]

Functor f => Functor (Cxt h f)

Defined in Data.Comp.Term

Methods

fmap :: (a -> b) -> Cxt h f a -> Cxt h f b

(<$) :: a -> Cxt h f b -> Cxt h f a

Foldable f => Foldable (Cxt h f)

Defined in Data.Comp.Term

Methods

fold :: Monoid m => Cxt h f m -> m

foldMap :: Monoid m => (a -> m) -> Cxt h f a -> m

foldMap' :: Monoid m => (a -> m) -> Cxt h f a -> m

foldr :: (a -> b -> b) -> b -> Cxt h f a -> b

foldr' :: (a -> b -> b) -> b -> Cxt h f a -> b

foldl :: (b -> a -> b) -> b -> Cxt h f a -> b

foldl' :: (b -> a -> b) -> b -> Cxt h f a -> b

foldr1 :: (a -> a -> a) -> Cxt h f a -> a

foldl1 :: (a -> a -> a) -> Cxt h f a -> a

toList :: Cxt h f a -> [a]

null :: Cxt h f a -> Bool

length :: Cxt h f a -> Int

elem :: Eq a => a -> Cxt h f a -> Bool

maximum :: Ord a => Cxt h f a -> a

minimum :: Ord a => Cxt h f a -> a

sum :: Num a => Cxt h f a -> a

product :: Num a => Cxt h f a -> a

Traversable f => Traversable (Cxt h f)

Defined in Data.Comp.Term

Methods

traverse :: Applicative f0 => (a -> f0 b) -> Cxt h f a -> f0 (Cxt h f b)

sequenceA :: Applicative f0 => Cxt h f (f0 a) -> f0 (Cxt h f a)

mapM :: Monad m => (a -> m b) -> Cxt h f a -> m (Cxt h f b)

sequence :: Monad m => Cxt h f (m a) -> m (Cxt h f a)

(ArbitraryF f, Arbitrary a) => Arbitrary (Context f a)

This lifts instances of ArbitraryF to instances of Arbitrary for the corresponding context type.

Defined in Data.Comp.Arbitrary

Methods

arbitrary :: Gen (Context f a)

shrink :: Context f a -> [Context f a]

(Functor f, ShowF f) => ShowF (Cxt h f)

Defined in Data.Comp.Show

Methods

showF :: Cxt h f String -> String

EqF f => EqF (Cxt h f)

Defined in Data.Comp.Equality

Methods

eqF :: Eq a => Cxt h f a -> Cxt h f a -> Bool

OrdF f => OrdF (Cxt h f)

Defined in Data.Comp.Ordering

Methods

compareF :: Ord a => Cxt h f a -> Cxt h f a -> Ordering

(EqF f, Eq a) => Eq (Cxt h f a)

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

Defined in Data.Comp.Equality

Methods

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

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

(OrdF f, Ord a) => Ord (Cxt h f a)

From an OrdF functor an Ord instance of the corresponding term type can be derived.

Defined in Data.Comp.Ordering

Methods

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

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

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

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

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

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

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

(Functor f, ShowF f, Show a) => Show (Cxt h f a)

Defined in Data.Comp.Show

Methods

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

show :: Cxt h f a -> String

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

(NFDataF f, NFData a) => NFData (Cxt h f a)

Defined in Data.Comp.DeepSeq

Methods

rnf :: Cxt h f a -> ()

data Hole

Phantom type that signals that a Cxt might contain holes.

Instances

Functor f => Monad (Context f)

Defined in Data.Comp.Term

Methods

(>>=) :: Context f a -> (a -> Context f b) -> Context f b

(>>) :: Context f a -> Context f b -> Context f b

return :: a -> Context f a

Functor f => Applicative (Context f)

Defined in Data.Comp.Term

Methods

pure :: a -> Context f a

(<*>) :: Context f (a -> b) -> Context f a -> Context f b

liftA2 :: (a -> b -> c) -> Context f a -> Context f b -> Context f c

(*>) :: Context f a -> Context f b -> Context f b

(<*) :: Context f a -> Context f b -> Context f a

ArbitraryF f => ArbitraryF (Context f)

This lifts instances of ArbitraryF to instances of ArbitraryF for the corresponding context functor.

Defined in Data.Comp.Arbitrary

Methods

arbitraryF' :: Arbitrary v => [(Int, Gen (Context f v))]

arbitraryF :: Arbitrary v => Gen (Context f v)

shrinkF :: Arbitrary v => Context f v -> [Context f v]

(ArbitraryF f, Arbitrary a) => Arbitrary (Context f a)

This lifts instances of ArbitraryF to instances of Arbitrary for the corresponding context type.

Defined in Data.Comp.Arbitrary

Methods

arbitrary :: Gen (Context f a)

shrink :: Context f a -> [Context f a]

data NoHole

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

Instances

ArbitraryF f => Arbitrary (Term f)

This lifts instances of ArbitraryF to instances of Arbitrary for the corresponding term type.

Defined in Data.Comp.Arbitrary

Methods

arbitrary :: Gen (Term f)

shrink :: Term f -> [Term f]

type Context = Cxt Hole

type Term f = Cxt NoHole f ()

A term is a context with no holes.

type PTerm f = forall h a. Cxt h f a

Polymorphic definition of a term. This formulation is more natural than Term, it leads to impredicative types in some cases, though.

type Const f = f ()

unTerm :: Cxt NoHole f a -> f (Cxt NoHole f a)

This function unravels the given term at the topmost layer.

simpCxt :: Functor f => f a -> Context f a

Convert a functorial value into a context.

toCxt :: Functor f => Term f -> Cxt h f a

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

constTerm :: Functor 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.