The bound package

[Tags:bsd3, library, test]

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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Versions 0.1, 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, 1.0.7
Change log CHANGELOG.markdown
Dependencies base (==4.*), bifunctors (==3.*), binary (>=0.5 && <0.8), bytes (>=0.4 && <1), cereal (>= && <0.5), comonad (>=3 && <5), ghc-prim, hashable (>=1.1 && <1.3), hashable-extras (>=0.1 && <1), prelude-extras (>=0.3 && <1), profunctors (>=3.3 && <5), transformers (>=0.2 && <0.4) [details]
License BSD3
Copyright Copyright (C) 2012-2013 Edward A. Kmett
Author Edward A. Kmett
Maintainer Edward A. Kmett <>
Stability experimental
Category Language, Compilers/Interpreters
Home page
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Source repository head: git clone git://
Uploaded Sun Oct 13 22:50:21 UTC 2013 by EdwardKmett
Distributions NixOS:1.0.7
Downloads 8293 total (19 in the last 30 days)
3 []
Status Docs available [build log]
Successful builds reported [all 1 reports]




Maintainer's Corner

For package maintainers and hackage trustees

Readme for bound

Readme for bound-0.9.1


Build Status


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:

{-# LANGUAGE DeriveFunctor #-}
{-# LANGUAGE DeriveFoldable #-}
{-# LANGUAGE DeriveTraversable #-}
import Bound
import Prelude.Extras
import Control.Applicative
import Control.Monad
import Data.Foldable
import Data.Traversable

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