---
title: "Algebraic Manipulations as a Unification and Matching Strategy for Linear Equations in Signed Binary Trees"
authors:
  - "Claude Kirchner"
  - "Hélène Kirchner"
  - "Jean-Pierre Jouannaud"
doi: ""
url: "https://ijcai.org/proceedings/1981/194"
pdf: "https://ijcai.org/proceedings/1981/0194.pdf"
venue: "Proceedings of the Seventh International Joint Conference on Artificial Intelligence"
year: 1981
pages: "1016-1022"
track: "Automatic Programming"
keywords:
---

# Algebraic Manipulations as a Unification and Matching Strategy for Linear Equations in Signed Binary Trees

Claude Kirchner, Hélène Kirchner, Jean-Pierre Jouannaud

*Proceedings of the Seventh International Joint Conference on Artificial Intelligence*, pages 1016-1022.

## Abstract

We study the unification and matching problems in the signed binary trees theory. We show that any equation tl•t2 can be transformed into an equivalent one x=t. If x does not occur in t then (x ---> t) is the unique most general unifier in the theory (up to an isomorphism). We apply this technique to find recurrence relations between sets of terms. These relations are used to synthesize LISP programs from a set of input traces.