bound-0.1: Combinators for manipulating locally-nameless generalized de Bruijn terms

MaintainerEdward Kmett <>
Safe HaskellSafe-Infered







newtype Scope b f a Source

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.




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


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) 


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

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

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

Abstract over a single variable


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

Enter a scope, instantiating all bound variables

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

Enter a scope with one bound variable, instantiating it


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

Perform substitution on both bound and free variables in a scope


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

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 aSource