Lem is a tool for lightweight executable mathematics, for writing, managing, and publishing large-scale portable semantic definitions, with export to LaTeX, executable code (currently OCaml) and interactive theorem provers (currently Coq, HOL4, and Isabelle/HOL).

It is also intended as an intermediate language for generating definitions from domain-specific tools, and for porting definitions between interactive theorem proving systems.

Lem is under active development and has been used in several applications, some of which can be found in the examples directory. It is made available under the BSD 3-clause license, with the exception of a few files derived from OCaml, which are under the GNU Library GPL.

Lem depends on OCaml. Lem is tested against OCaml 3.12.1. and 4.02.0. Other versions might or might not work. Lem requires the OCaml ZArith library for arbitrary precision arithmetic. Lem has been tested against ZArith version 1.2. Other versions might or might not work.

To build Lem run 'make' in the top-level directory. This builds the executable 'lem', and places a symbolic link to it in that directory. Instructions on building the libraries for particular targets are in the manual.

Documentation can be found in doc/built-doc, including:

  • a high-level description of Lem in the draft paper lem-draft.pdf;
  • the manual, in lem-manual.html and lem-manual.pdf;
  • the Ott grammar and type system for Lem, in lem.pdf, built from the definition in language/lem.ott;
  • the Lem library documentation, in lem-libs.pdf;
  • the type signatures of the pervasives and pervasives-extra libaries, in lem-libs-pervasives.txt and lem-libs-pervasives-extra.txt; and
  • source documentation, in html-doc and lem-doc.pdf, with a dependency diagram of the source modules in dep.pdf.

Supported versions of software

Lem is tested against the following versions of the backend software:

  • OCaml: 3.12.1, 4.00.0, 4.01.0, and 4.02.0
  • Coq: 8.4pl3 and 8.4pl2
  • Isabelle: Isabelle-2013-2
  • HOL: HOL4 Kananaskis 9