Multialgebras, Power Algebras and Complete Calculi of Identities and Inclusions

After motivating the introduction of nondeterministic operators into algebraic specifications, a language L with two primitive predicates, identity and inclusion, for specifying nondeterministic operations is introduced. It is given a multialgebraic semantics which captures the singular (call-time-choice) strategy of passing nondeterministic parameters. A calculus NEQ, with restricted substitutivity rules, is introduced. NEQ is sound and complete wrt. the multialgebraic semantics.

[1]  Matthew Hennessy,et al.  The Semantics of Call-By-Value and Call-By-Name in a Nondeterministic Environment , 1980, SIAM J. Comput..

[2]  J.J.S.P. Cabral.  Introduction to algorithms — A creative approach: Udi Manber, Addison-Wesley, Reading, Massachusetts, 1989 , 1992 .

[3]  Wim H. Hesselink,et al.  A mathematical approach to nondeterminism in data types , 1988, TOPL.

[4]  D. Kapur.  TOWARDS A THEORY FOR ABSTRACT DATA TYPES , 1980 .

[5]  Peter D. Mosses.  Unified Algebras and Action Semantics , 1989, STACS.

[6]  Richard L. Schwartz,et al.  An Aximatic Treatment of Algol 68 Routines , 1979, ICALP.

[7]  José Meseguer,et al.  Remarks on remarks on many-sorted equational logic , 1987, SIGP.

[8]  Peter D. Mosses,et al.  Unified Algebras and Action Semantics , 1988, STACS.

[9]  N. Ward.  A refinement calculus for nondeterministic expressions , 1994 .

[10]  Allen Goldberg,et al.  Referential opacity in nondeterministic data refinement , 1993, LOPL.

[11]  William B. Ackerman,et al.  Scenarios: A Model of Non-Determinate Computation , 1981, ICFPC.

[12]  José Meseguer,et al.  Conditioned Rewriting Logic as a United Model of Concurrency , 1992, Theor. Comput. Sci..

[13]  Peter D. Mosses,et al.  Unified Algebras and Institutions , 1989 .

[14]  J. A. Goguen,et al.  Completeness of many-sorted equational logic , 1981, SIGP.

[15]  William D. Clinger.  Nondeterministic call by need is neither lazy nor by name , 1982, LFP '82.

[16]  Heinrich Hussmann,et al.  Nondeterminism in Algebraic Specifications and Algebraic Programs , 1993 .

[17]  Robert M. Keller,et al.  Denotational Models for Parallel Programs with Indeterminate Operators , 1977, Formal Description of Programming Concepts.

[18]  G. Huet,et al.  Equations and rewrite rules: a survey , 1980 .

[19]  José Meseguer,et al.  Conditional Rewriting Logic: Deduction, Models and Concurrency , 1990, CTRS.

[20]  Robin Milner,et al.  Communication and concurrency , 1989, PHI Series in computer science.

[21]  Udi Manber,et al.  Introduction to algorithms , 1989 .

[22]  Joost Engelfriet,et al.  IO and OI. I , 1977, J. Comput. Syst. Sci..

[23]  Cliff B. Jones,et al.  Specifications are not (necessarily) executable , 1989 .

[24]  Peter D. Mosses,et al.  Unified algebras and institutions , 1989, [1989] Proceedings. Fourth Annual Symposium on Logic in Computer Science.

[25]  C. A. R. Hoare,et al.  Communicating sequential processes , 1978, CACM.