name: bound category: Language, Compilers/Interpreters version: 0.1.4 license: BSD3 cabal-version: >= 1.6 license-file: LICENSE author: Edward A. Kmett maintainer: Edward A. Kmett stability: experimental homepage: http://github.com/ekmett/bound/ bug-reports: http://github.com/ekmett/bound/issues copyright: Copyright (C) 2012 Edward A. Kmett synopsis: Haskell 98 Locally-Nameless Generalized de Bruijn Terms description: We represent the target language itself as an ideal monad supplied by the user, and provide a 'Scope' monad transformer for introducing bound variables in user supplied terms. Users supply a 'Monad' and 'Traversable' instance, and we traverse to find free variables, and use the Monad to perform substitution that avoids bound variables. . An untyped lambda calculus: . > import Bound > import Prelude.Extras . > infixl 9 :@ > data Exp a = V a | Exp a :@ Exp a | Lam (Scope () Exp a) > deriving (Eq,Ord,Show,Read,Functor,Foldable,Traversable) . > instance Eq1 Exp where (==#) = (==) > instance Ord1 Exp where compare1 = compare > instance Show1 Exp where showsPrec1 = showsPrec > instance Read1 Exp where readsPrec1 = readsPrec > instance Applicative Exp where pure = V; (<*>) = ap . > instance Monad Exp where > return = V > V a >>= f = f a > (x :@ y) >>= f = (x >>= f) :@ (y >>= f) > Lam e >>= f = Lam (e >>>= f) > > lam :: Eq a => a -> Exp a -> Exp a > lam v b = Lam (abstract1 v b) . > whnf :: Exp a -> Exp a > whnf (f :@ a) = case whnf f of > Lam b -> whnf (instantiate1 a b) > f' -> f' :@ a > whnf e = e . The classes from Prelude.Extras are used to facilitate the automatic deriving of 'Eq', 'Ord', 'Show, and 'Read' in the presence of polymorphic recursion used inside 'Scope'. . The goal of this package is to make it as easy as possible to deal with name binding without forcing an awkward monadic style on the user. . With generalized de Bruijn term you can 'lift' whole trees instead of just applying 'succ' to individual variables, weakening the all variables bound by a scope. and by giving binders more structure we can permit easy simultaneous substitution. . The approach was first elaborated upon by Richard Bird and Ross Patterson in \"de Bruijn notation as a nested data type\", available from . However, the combinators they used required higher rank types. Here we demonstrate that the higher rank @gfold@ combinator they used isn't necessary to build the monad and use a monad transformer to encapsulate the novel recursion pattern in their generalized de Bruijn representation. It is named 'Scope' to match up with the terminology and usage pattern from Conor McBride and James McKinna's \"I am not a number: I am a free variable\", available from , but since the set of variables is visible in the type, we can provide stronger type safety guarantees. . There are longer worked examples in the @examples/@ folder: . . (1) /Simple.hs/ provides an untyped lambda calculus with recursive let bindings. and includes an evaluator for the untyped lambda calculus and a longer example taken from Lennart Augustsson's "λ-calculus cooked four ways" available from . 2. /Derived.hs/ shows how much of the API can be automated with DeriveTraversable and adds combinators for building binders that support pattern matching. . 3. /Overkill.hs/ provides very strongly typed pattern matching many modern type extensions, including polymorphic kinds to ensure type safety. In general, the approach taken by Derived seems to deliver a better power to weight ratio. build-type: Simple extra-source-files: .travis.yml examples/Simple.hs examples/Deriving.hs examples/Overkill.hs source-repository head type: git location: git://github.com/ekmett/bound.git library build-depends: base >= 4 && < 5, bifunctors >= 0.1.3 && < 0.2, prelude-extras >= 0.2 && < 0.3, transformers >= 0.2 && < 0.4 exposed-modules: Bound Bound.Class Bound.Scope Bound.Term Bound.Var ghc-options: -Wall