# Computation of Permuting Matcher for Lambda Terms

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

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:
• The symbols A-Z, a-z, 1-9 are allowed for variable names and function names. Names can be of any length.
• If the first letter of the name is within [u,z] or [U,Z], then it is a variable.
• The backslash "\" is used for the lambda symbol.
• The colon ":" is used to declare the type.
• The dash "-" is used as type constructor.
• Mixed mode of typed and untyped calculus is allowed.
 Equivariance problem set:(Use the semicolon to separate the equations of the system.) f(x,y) = f(y,x) Domain: Range: Maximum reduction recursion: Output format: SimpleVerboseProgressProgress (origin) 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 Project: SToUT - Symbolic Computation Techniques for Unranked Terms