RISC RISC Research Institute for Symbolic Computation  

Computation of Permuting Matcher for Lambda Terms

This is a Java implementation of the permuting matcher computation for lambda terms described in:

Part of the Library of Unification and Anti-Unification Algorithms.

The algorithm solves the following problem:

GIVEN: A set of equations of the form t ≈ s where t and s are lambda terms, and two sets of variables, the Domain and the Range.
FIND: A variable renaming ρ:Domain --> Range, such that ρ(t) is alpha equivalent to s for all equations t ≈ s.

The equivariance algorithm is a part of an algorithm which solves the higher-order anti-unification problem. This anti-unification algorithm has also been implemented and is available online.

Input Syntax:
Equivariance problem set:
(Use the semicolon to separate
the equations of the system.)
Domain: Range:
Maximum reduction recursion:
Output format: User friendly:


This software is released under the GNU Lesser General Public License ("LGPL"). For presentation purpose, the Java source code has been translated into JavaScript by the GWT compiler.
Some examples (click on them to prepared the input form):

  • \y.f(x,y) = \x.f(y,x)
  • x(y,z) = y(z,x)
  • x:i-o(y:i-o,z:i) = y:i-o(z:i,x:i-o)
  • \u.u(f(x,z),u(y,z),f(y,v)) = \v.v(f(y,x),v(z,x),f(z,u))

Author: Alexander Baumgartner FWF Der Wissenschaftsfond
Project: SToUT - Symbolic Computation Techniques for Unranked Terms