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´ilia, Bras´ilia DF, Brasil.
FAIROUZ KAMAREDDINE, School of Mathematical and Computer
Sciences, Heriot-Watt University, Edinburgh, Scotland.
MAURICIO AYALA-RINC ´ON, Departamento de Matem´atica,
Universidade de Bras´ilia, Bras´ilia DF, Brasil. E-mail: 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 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
in the language of the simply typed -calculus. In addition, we show how Dowek's third-order
matching decision procedure can be adapted to the whole language of the simply typed -calculus