On the Most Suitable Axiomatization of Signed Integers
Résumé
The standard mathematical definition of signed integers, based on set theory, is not well-adapted to the needs of computer science. For this reason, many formal specification languages and theorem provers have designed alternative definitions of signed integers based on term algebras , by extending the Peano-style construction of unsigned naturals using "zero" and "succ" to the case of signed integers. We compare the various approaches used in CADP, CASL, Coq, Isabelle/HOL, KIV, Maude, mCRL2, PSF, SMT-LIB, TLA+, etc. according to objective criteria and suggest an "optimal" definition of signed integers.
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