bound-0.2.1: Haskell 98 Locally-Nameless Generalized de Bruijn Terms

Portabilityportable
Stabilityexperimental
MaintainerEdward Kmett <ekmett@gmail.com>
Safe HaskellSafe-Infered

Bound.Scope

Contents

Description

 

Synopsis

Documentation

newtype Scope b f a Source

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

We store bound variables as their generalized de Bruijn representation in that we're allowed to lift (using F) an entire tree rather than only succ individual variables, but we're still only allowed to do so once per Scope. Weakening trees permits O(1) weakening and permits 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 generalized de Bruijn representation and return the same result as a traditional de Bruijn representation would.

Logically you can think of this as if the shape were the traditional f (Var b a), but the extra f a inside permits us a cheaper lift.

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 aSource

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

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

Abstract over a single variable

Instantiation

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 that binds one variable, instantiating it

Traditional de Bruijn

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

fromScope quotients out the possible placements of F in Scope by distributing them all to the leaves. This yields a more traditional de Bruijn 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

Convert from traditional de Bruijn to generalized de Bruijn indices.

This requires a full tree traversal

Bound variable manipulation

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

bindings :: Foldable f => Scope b f a -> [b]Source

mapBound :: Functor f => (b -> b') -> Scope b f a -> Scope b' f aSource

Perform a change of variables on bound variables

mapScope :: Functor f => (b -> d) -> (a -> c) -> Scope b f a -> Scope d f cSource

Perform a change of variables, reassigning both bound and free variables.

liftMBound :: Monad m => (b -> b') -> Scope b m a -> Scope b' m aSource

Perform a change of variables on bound variables given only a Monad instance

liftMScope :: Monad m => (b -> d) -> (a -> c) -> Scope b m a -> Scope d m cSource

A version of mapScope that can be used when you only have the Monad instance

foldMapBound :: (Foldable f, Monoid r) => (b -> r) -> Scope b f a -> rSource

Obtain a result by collecting information from both bound and free variables

foldMapScope :: (Foldable f, Monoid r) => (b -> r) -> (a -> r) -> Scope b f a -> rSource

Obtain a result by collecting information from both bound and free variables

traverseBound_ :: (Applicative g, Foldable f) => (b -> g d) -> Scope b f a -> g ()Source

traverseScope_ :: (Applicative g, Foldable f) => (b -> g d) -> (a -> g c) -> Scope b f a -> g ()Source

mapMBound_ :: (Monad g, Foldable f) => (b -> g d) -> Scope b f a -> g ()Source

mapM_ over the variables bound by this scope

mapMScope_ :: (Monad m, Foldable f) => (b -> m d) -> (a -> m c) -> Scope b f a -> m ()Source

A traverseScope_ that can be used when you only have a Monad instance

traverseBound :: (Applicative g, Traversable f) => (b -> g c) -> Scope b f a -> g (Scope c f a)Source

traverseScope :: (Applicative g, Traversable f) => (b -> g d) -> (a -> g c) -> Scope b f a -> g (Scope d f c)Source

mapMBound :: (Monad m, Traversable f) => (b -> m c) -> Scope b f a -> m (Scope c f a)Source

mapMScope :: (Monad m, Traversable f) => (b -> m d) -> (a -> m c) -> Scope b f a -> m (Scope d f c)Source