TLC: a non-constructive library for Coq

TLC is a general purpose Coq library that provides an alternative to Coq's standard library.
  • TLC takes as axiom extensionality, classical logic and indefinite description (Hilbert's epsilon). These axioms allow for significantly simpler formal definitions in many cases.
  • TLC takes advantage of the type class mechanism. In particular, this allows for common operators and lemma names for all container data structures and all order relations.
  • TLC includes the optimal fixed point combinator, which can be used for building arbitrarily-complex recursive and co-recursive definitions.
  • TLC provides a collection of tactics that enhance the default tactics provided by Coq. These tactics help constructing more concise and more robust proof scripts.


  • The source files can be obtained by running:
    git clone
  • TLC compiles with Coq v8.6 and v8.7 (tags are available for prior versions).
  • TLC 2.0 (beta) was released in November 2017, with a complete polishing phase.
  • Disclaimer: to allow improving the design of TLC, backward compatibility is not guaranteed.
  • TLC should not be incompatible with use of the standard library.
  • All the files are distributed under the GNU-LGPL license.

Related publications

The Optimal Fixed Point Combinator
Arthur Charguéraud
ITP: International Conference on Interactive Theorem Proving, July 2010