Summary: Second� and Third�Order Matching
via Explicit Substitutions
FL �
AVIO LEONARDO CAVALCANTI DE MOURA, Departamento de
Ci�encia da Computa�c�ao, Universidade de Bras��lia, Bras��lia DF, Brasil.
E�mail: flavio@cic.unb.br
FAIROUZ KAMAREDDINE, School of Mathematical and Computer
Sciences, Heriot�Watt University, Edinburgh, Scotland.
E�mail: fairouz@macs.hw.ac.uk
MAURICIO AYALA�RINC �
ON, Departamento de Matem�atica,
Universidade de Bras��lia, Bras��lia DF, Brasil. E�mail: ayala@unb.br
Abstract
The past few years have established the benefits of using explicit substitutions in the treatment
of problems such as unification and matching related to higher�order automated deduction and
the implementation of programming languages. Matching is a basic operation extensively used in
computation and deduction. Second and third�order matching, in particular, provide an adequate
environment for expressing pattern recognition and program transformation or simplification.
We present a practical algorithm which solves a class of second�order matching problems in the
language of the ##�calculus of explicit substitutions. This class includes all the problems originated

Source: Ayala-Rinc�n, Mauricio - Departamento de Matem�tica, Universidade de Bras�lia

Collections: Mathematics