Summary: Second and ThirdOrder Matching
via Explicit Substitutions
AVIO LEONARDO CAVALCANTI DE MOURA, Departamento de
Ciencia da Computacao, Universidade de Braslia, Braslia DF, Brasil.
FAIROUZ KAMAREDDINE, School of Mathematical and Computer
Sciences, HeriotWatt University, Edinburgh, Scotland.
ON, Departamento de Matematica,
Universidade de Braslia, Braslia DF, Brasil. Email: firstname.lastname@example.org
The past few years have established the benefits of using explicit substitutions in the treatment
of problems such as unification and matching related to higherorder automated deduction and
the implementation of programming languages. Matching is a basic operation extensively used in
computation and deduction. Second and thirdorder 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 secondorder matching problems in the
language of the ##calculus of explicit substitutions. This class includes all the problems originated