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Third-Order Matching via Explicit Substitutions Flavio L. C. de Moura 1

Summary: Third-Order Matching via Explicit Substitutions
Fl´avio L. C. de Moura 1
and Mauricio Ayala-Rinc´on 1
and Fairouz
Departamento de Matem´atica, Universidade de Bras´ilia, Bras´ilia D.F., Brasil.
School of Mathematical and Computer Sciences, Heriot-Watt University,
Edinburgh, Scotland. fairouz@macs.hw.ac.uk
Abstract. We show how Dowek's third-order matching decision proce-
dure can be adapted to the simply typed -calculus of explicit substitu-
tions. The advantages of this approach include being closer to low-level
implementations based on the -calculus, where substitution has to be
made explicit. The work is done by, firstly, reducing matching problems
to interpolation problems in the language of the -calculus and, sec-
ondly, showing that if an interpolation problem has a solution then it
is possible to find a solution which depends only on a measure of the
structure of the initial matching problem, where this measure is based


Source: Ayala-Rincón, Mauricio - Departamento de Matemática, Universidade de Brasília
Lucero, Jorge Carlos - Departamento de Matemática, Universidade de Brasília


Collections: Mathematics