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Comparing and Implementing Calculi of Explicit Substitutions with Eta-Reduction ?

Summary: Comparing and Implementing Calculi of
Explicit Substitutions with Eta-Reduction ?
Mauricio Ayala-Rincon 1 , Flavio L. C. de Moura 2
Departamento de Matematica, Universidade de Braslia, Braslia D.F., Brasil.
Fairouz Kamareddine
Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh,
The past decade has seen an explosion of work on calculi of explicit substitutions.
Numerous work has illustrated the usefulness of these calculi for practical notions
like the implementation of typed functional programming languages and higher or-
der proof assistants. It has also been shown that eta-reduction is useful for adapting
substitution calculi for practical problems like higher order uni cation. This paper
concentrates on rewrite rules for eta-reduction in three di erent styles of explicit
substitution calculi: , s e and the suspension calculus. Both  and s e when
extended with eta-reduction rules, have proved useful for solving higher order uni-
cation. We enlarge the suspension calculus with an adequate eta-reduction rule
which we show to preserve termination and con uence of the associated substitu-
tion calculus and to correspond to the eta rules of the other two calculi. We prove
that  and s e as well as  and the suspension calculus are non comparable


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


Collections: Mathematics