Summary: SUBSEXPL: a tool for simulating and
comparing explicit substitutions calculi1
F. L. C. de Moura * -- M. Ayala-Rincón * -- F. Kamareddine**
1 Work supported by funds from CNPq (CT-INFO) 50.6598/04-7.
Supported by the Brazilian Ministry Educational Council CAPES.
Partially supported by the Brazilian Research Council CNPq.
* Departamento de Matemática, Universidade de Brasília
70900-910 Brasília D.F., Brasil
** School of Mathematical and Computer Sciences
Heriot-Watt University, Edinburgh EH14 4AS, Scotland
ABSTRACT. We present the system SUBSEXPL used for simulating and comparing explicit sub-
stitutions calculi. The system allows the manipulation of expressions of the -calculus and of
three different styles of explicit substitutions: the , the se and the suspension calculus. A
variation of the suspension calculus, which allows for combination of steps of -contraction
is included too. Implementations of the -reduction are provided for each style. Other explicit
substitutions calculi can be easily incorporated into the system due to its modular structure. The
uses of the system include: the visualization of the contractions of the -calculus in de Bruijn
notation, and of guided one-step reductions as well as normalization via each of the associ-