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A Complete Calculus for Equational Deduction in Coalgebraic Specification (1997)
| Venue: | Recent Trends in Algebraic Development Techniques, WADT 97, volume 1376 of LNCS |
| Citations: | 20 - 0 self |
BibTeX
@TECHREPORT{Corradini97acomplete,
author = {Andrea Corradini and Andrea Corradini},
title = {A Complete Calculus for Equational Deduction in Coalgebraic Specification},
institution = {Recent Trends in Algebraic Development Techniques, WADT 97, volume 1376 of LNCS},
year = {1997}
}
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Abstract
The use of coalgebras for the specification of dynamical systems with a hidden state space is receiving more and more attention in the years, as a valid alternative to algebraic methods based on observational equivalences. However, to our knowledge, the coalgebraic framework is still lacking a complete equational deduction calculus which enjoys properties similar to those stated in Birkhoff's completeness theorem for the algebraic case. In this paper we present a sound and complete equational calculus for coalgebras of a restricted class of polynomial functors. This restriction allows us to borrow some "algebraic" notions for the formalization of the calculus. Additionally, we discuss the notion of colours as a suitable dualization of variables in the algebraic case. Then the completeness result is extended to the "non-ground" or "coloured" case, which is shown to be expressive enough to deal with equations of hidden sort. Finally we discuss some weaknesses of the proposed results wit...
Keyphrases
coalgebraic specification complete calculus equational deduction algebraic case algebraic notion hidden state space completeness result valid alternative dynamical system suitable dualization polynomial functors completeness theorem complete equational deduction calculus complete equational calculus observational equivalence hidden sort restricted class coalgebraic framework
