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SecondOrder Matching via Explicit Substitutions #
 

Summary: Second­Order Matching via Explicit
Substitutions #
Fl’avio L. C. de Moura ##1 and Fairouz Kamareddine 2 and Mauricio
Ayala­Rinc’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, Heriot­Watt University,
Edinburgh, Scotland. fairouz@macs.hw.ac.uk
Abstract. Matching is a basic operation extensively used in computa­
tion. Second­order 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 higher­order
unification. In this paper, we will make use of explicit substitutions to
facilitate matching: we develop a second­order 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 second­order matching problems which is essential to
prove termination of the algorithm. In addition, we illustrate how the

  

Source: Ayala-Rincón, Mauricio - Departamento de Matemática, Universidade de Brasília
Kamareddine, Fairouz - Computer Science Department, Heriot-Watt University

 

Collections: Computer Technologies and Information Sciences; Mathematics