The bound package

[Tags: bsd3, library]

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.

Slides describing and motivating this approach to name binding are available online at:

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 greatly speeding up instantiation. By giving binders more structure we permit easy simultaneous substitution and further speed up instantiation.

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Versions0.1, 0.1.1, 0.1.2, 0.1.3, 0.1.4, 0.2, 0.2.1, 0.3.1, 0.3.2, 0.4, 0.5,,, 0.5.1, 0.6, 0.6.1, 0.7, 0.8, 0.8.1, 0.9,, 0.9.1,, 1.0, 1.0.1, 1.0.2, 1.0.3, 1.0.4, 1.0.5, 1.0.6
Change logCHANGELOG.markdown
Dependenciesbase (==4.*), bifunctors (==3.*), comonad (==3.*), ghc-prim, hashable (>=1.1 && <1.3), hashable-extras (>=0.1 && <1), prelude-extras (>=0.3 && <1), profunctors (>=3.3 && <4), transformers (>=0.2 && <0.4) [details]
CopyrightCopyright (C) 2012 Edward A. Kmett
AuthorEdward A. Kmett
MaintainerEdward A. Kmett <>
CategoryLanguage, Compilers/Interpreters
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Source repositoryhead: git clone git://
UploadedFri Mar 22 21:09:03 UTC 2013 by EdwardKmett
DistributionsLTSHaskell:1.0.6, NixOS:1.0.6, Stackage:1.0.6
Downloads6808 total (179 in last 30 days)
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For package maintainers and hackage trustees

Readme for bound-0.7


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This library provides convenient combinators for working with "locally-nameless" terms. These can be useful when writing a type checker, evalator, parser, or pretty printer for terms that contain binders like forall or lambda, as they ease the task of avoiding variable capture and testing for alpha-equivalence.

See the documentation on hackage for more information, but here is an example:

 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
 instance Ord1 Exp
 instance Show1 Exp
 instance Read1 Exp
 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

There are longer examples in the examples/ folder.

Contact Information

Contributions and bug reports are welcome!

Please feel free to contact me through github or on the #haskell IRC channel on

-Edward Kmett