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SUBSEXPL: A Framework for Simulating and Comparing Explicit Substitutions Calculi

Summary: SUBSEXPL: A Framework for Simulating and Comparing Explicit
Substitutions Calculi
A Tutorial
Fl´avio L. C. de Moura
Mauricio Ayala-Rinc´on Fairouz Kamareddine
January 27, 2005
In this paper we present a framework, called SUBSEXPL, for simulating and comparing explicit
substitutions calculi. This framework was developed in Ocaml, a language of the ML family, and it allows
the manipulation of expressions of the -calculus and of several styles of explicit substitutions calculi.
Applications of this framework include: the visualisation of the contractions of the -calculus, and of
guided one-step reductions and normalisation via each of the associated substitution calculi. Many useful
facilities are available: reductions can be easily recorded and stored into files, latex output and useful
examples for dealing with, among other things, arithmetic operations and computational operators such
as conditionals and repetitions in the -calculus. The current implementation of SUBSEXPL includes
treatment of three different calculi of explicit substitutions: the , the se and the suspension calculus;
other explicit substitutions calculi can be easily incorporated into the system. An implementation of the
-reduction is provided for each of these explicit substitutions calculi. This system has been of great
help for systematically comparing explicit substitutions calculi, as well as for understanding properties
of explicit substitutions such as the Preservation of Strong Normalisation. In addition, it has been used


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


Collections: Mathematics