lol-calculus: Calculus for LOL (λω language).

[ gpl, language ] [ Propose Tags ]

WARNING: this is a research program written as I learn and explore lambda calculii: please understand well by yourself whatever you may take from it; any question or contribution being welcome :-)

This package implements an explicitely typed (aka. à la Church) lambda calculus with: simples types, parametric polymorphism, higher-rank polymorphism and constructors of types (I have no need for dependent types so far, but it should be straightforward to add them to allow the full Calculus of constructions (CoC)).

This is mainly done by means of: a common Algebraic Data Type (ADT) for terms and types to build a Pure Type System (PTS), generalized DeBruijn indices to implement capture-avoiding substitution of variables, and Typeable axioms to embed Haskell types and terms (the most experimental and tricky part).

The inspiring programs I studied which explore similar problems: Simon Peyton Jones and Erik Meijer's Henk, Dan Doel's pts, Gabriel Gonzalez's morte, Richard Eisenberg's glambda, Edward Kmett's bound.

See also: the lol-typing package studying the type inferencing.

NOTE: if you are just interested in building an Embedded Domain Specific Language (EDSL) you may as well study Oleg Kiselyov, Jacques Carette and Chung-chieh Shan's Typed Tagless Final Interpreters, which you may find being a much more simple, efficient and robust approach.

Versions [faq] 1.20160822
Dependencies base (>=4.6 && <5), containers (==0.5.*), directory, filepath, haskeline (==0.7.*), lol-calculus, mtl (>=2.0), parsec (>=3.1.2 && <4), text, text-format, transformers (==0.4.*) [details]
License GPL-3.0-only
Author Julien Moutinho <>
Maintainer Julien Moutinho <>
Category Language
Source repo head: git clone git://
Uploaded by julm at 2016-08-23T05:14:54Z
Distributions NixOS:1.20160822
Executables lol-calculus
Downloads 641 total (1 in the last 30 days)
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Status Hackage Matrix CI
Docs not available [build log]
All reported builds failed as of 2016-11-20 [all 1 reports]


  • Language
    • LOL
      • Language.LOL.Calculus
        • Language.LOL.Calculus.Abstraction
        • Language.LOL.Calculus.Axiom
        • Language.LOL.Calculus.Form
        • Language.LOL.Calculus.Read
        • Language.LOL.Calculus.Term
        • Language.LOL.Calculus.Type



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