Axiomatisation des tests (Q1062748)

This paper extends one of the completeness theorems of \textit{S. L. Bloom} and \textit{R. Tindell} [SIAM J. Comput. 12, 677-707 (1983; Zbl 0518.68010)] to the case of ordered algebras equipped with the constants tt and ff and the conditional: \([p,x,y]=x\) if \(p=tt\); y if \(p=ff;\perp\) otherwise. One of the main results shows that the set of if-then-else equations valid in a variety K of ordered algebras is the same as those valid in the collection of flat algebras in K. In a forthcoming paper [''Equational bases for if-then-else''] \textit{A. Mekler} and \textit{E. Nelson} show that the proof here is incorrect. A correct version (for many sorted continuous algebras) is given in ''On axiomatizations of if-then-else'', by \textit{J. Meseguer} and \textit{I. Guessarian} [SIAM J. Comput. (to appear)].