by Andrea Corradini, Fabio Gadducci
Recent Trends in Algebraic Development Techniques, volume 1589 of LNCS
http://www.di.unipi.it/~gadducci/papers/WADT98-2.ps
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Abstract:
Abstract. Multi-algebras allow to model nondeterminism in an algebraic framework by interpreting operators as functions from individual arguments to sets of possible results. We propose a functorial presentation of various categories of multi-algebras and partial algebras, analogous to the classical presentation of algebras over a signature \Sigma as cartesian functors from the algebraic theory of \Sigma, Th(\Sigma), to Set. The functors we introduce are based on variations of the notion of theory, having a structure weaker than cartesian, and their target is Rel, the category of sets and relations. We argue that this functorial presentation provides an original abstract syntax for partial and multi-algebras. 1
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