Bound.Scope

Documentation

newtype Scope b f a

Scope b f a is a an f expression with bound variables in b, and free variables in a

This stores bound variables as their generalized de Bruijn representation, in that the succ's for variable ids are allowed to occur anywhere within the tree permitting O(1) weakening and allowing more sharing opportunities. Here the deBruijn 0 is represented by the B constructor of Var, while the de Bruijn succ (which may be applied to an entire tree!) is handled by F.

NB: equality and comparison quotient out the distinct F placements allowed by the choice of a generalized de Bruijn representation and return the same result as a traditional de Bruijn representation would.

Constructors

Scope

Fields

unscope :: f (Var b (f a))

Instances

MonadTrans (Scope b)

Bound (Scope b)

Monad f => Monad (Scope b f)

The monad permits substitution on free variables, while preserving bound variables

Functor f => Functor (Scope b f)

Foldable f => Foldable (Scope b f)

toList is provides a list (with duplicates) of the free variables

Traversable f => Traversable (Scope b f)

(Monad f, Eq b, Eq1 f) => Eq1 (Scope b f)

(Monad f, Ord b, Ord1 f) => Ord1 (Scope b f)

(Functor f, Show b, Show1 f) => Show1 (Scope b f)

(Functor f, Read b, Read1 f) => Read1 (Scope b f)

(Monad f, Eq b, Eq1 f, Eq a) => Eq (Scope b f a)

(Monad f, Ord b, Ord1 f, Ord a) => Ord (Scope b f a)

(Functor f, Read b, Read1 f, Read a) => Read (Scope b f a)

(Functor f, Show b, Show1 f, Show a) => Show (Scope b f a)

Abstraction

abstract :: Monad f => (a -> Maybe b) -> f a -> Scope b f a

Capture some free variables in an expression to yield a Scope with bound variables

abstract1 :: (Monad f, Eq a) => a -> f a -> Scope () f a

Abstract over a single variable

Instantiation

instantiate :: Monad f => (b -> f a) -> Scope b f a -> f a

Enter a scope, instantiating all bound variables

instantiate1 :: Monad f => f a -> Scope () f a -> f a

Enter a scope with one bound variable, instantiating it

Substitution

splat :: Monad f => (a -> f c) -> (b -> f c) -> Scope b f a -> f c

Perform substitution on both bound and free variables in a scope

Quotienting

fromScope :: Monad f => Scope b f a -> f (Var b a)

fromScope quotients out the possible placements of F in Scope distributing them all to the leaves. This yields a traditional deBruijn indexing scheme for bound variables.

 fromScope . toScope = id
 fromScope . toScope . fromScope = fromScope

(toScope . fromScope) is idempotent

toScope :: Monad f => f (Var b a) -> Scope b f a