Summary: Second�Order Matching via Explicit
Substitutions #
Fl�avio L. C. de Moura ##1 and Fairouz Kamareddine 2 and Mauricio
Ayala�Rinc�on # # #1
1 Departamento de Matem�atica, Universidade de Bras��lia, Bras��lia D.F., Brasil.
flavio@mat.unb.br,ayala@mat.unb.br
2 School of Mathematical and Computer Sciences, Heriot�Watt University,
Edinburgh, Scotland. fairouz@macs.hw.ac.uk
Abstract. Matching is a basic operation extensively used in computa�
tion. Second�order matching, in particular, provides an adequate envi�
ronment for expressing program transformations and pattern recognition
for automated deduction. The past few years have established the ben�
efit of using explicit substitutions for theorem proving and higher�order
unification. In this paper, we will make use of explicit substitutions to
facilitate matching: we develop a second�order matching algorithm via
the ##�style of explicit substitutions. We introduce a convenient nota�
tion for matching in the ##�calculus. This notation keeps the matching
equations separated from the incremental graftings. We characterise an
important class of second�order matching problems which is essential to
prove termination of the algorithm. In addition, we illustrate how the

Source: Ayala-Rinc�n, Mauricio - Departamento de Matem�tica, Universidade de Bras�lia
Kamareddine, Fairouz - Computer Science Department, Heriot-Watt University

Collections: Computer Technologies and Information Sciences; Mathematics