RISC-Linz RISC-Linz Research Institute for Symbolic Computation  

Nominal Anti-Unification

This is a Java implementation of the anti-unification algorithm for nominal terms described in:

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

The algorithm solves the following problem:

GIVEN: Nominal terms t and s of the same sort, a freshness context ∇ and a finite set of atoms A such that t, s, and ∇ are based on A.
FIND: A term r and a freshness context Γ, such that the term-in-context <Γ, r> is an A-based least general generalization of the terms-in-context <∇, t> and <∇, s>.

The anti-unification algorithm relies on a subalgorithm that constructively decides equivariance between two terms-in-context. This subalgorithm can also be accessed separately.

Input Syntax:
Anti-unification problem:
(Use the semicolon to separate
the equations of the system.)
Freshness context: e.g. a#X, b#Y
Extra atoms: (Atoms from the problem set / freshness context are automatically carried over.)
Justify computed generalization: (An error will occure if the justification fails.)
Output format:


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):

  • f(a,b) =^= f(a,b)
  • f(a,a) =^= f(b,b)
  • f(a,a) =^= f(b,c)
  • f(a,b) =^= f(b,c)
  • f(a:i,a:i):o =^= f:i-i-o(b,b)
  • a.a =^= b.c
  • a.b =^= b.a
  • a.b =^= b.a with extra atom c
  • f(a,b) =^= f(Y,(a b)Y) with nabla {b#Y}
  • f(b,a) =^= f(Y,(a b)Y) with nabla {b#Y}
  • h(a.a, b.b) =^= h(c.Y, c.Y) with nabla {a#Y}
  • h(f(X1), c.f(X1)) =^= h(g(X2), c.g(X2)) with nabla {c#X1, c#X2}
  • h(f(X1), a.f((a c)X1)) =^= h(g(X2), b.g((b c)X2)) with nabla {a#X1,b#X1,c#X1,a#X2,b#X2,c#X2}
  • h(f(X1), a.f(X2)) =^= h(g(X1), a.g(X2)) with nabla {a#X1}
  • a.b.c =^= c.a.b
  • a.b.b =^= b.b.a
  • f(a.b, X) =^= f(b.a, Y) with nabla {c#X}

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