Operational Specifications with Built-Ins

We present a framework for studying equational specifications that partially specify functions over built-in structures. Using an order-sorted approach we are able to suitably assign semantics to such specifications in a denotational as well as an operational way. The operationalization, based on a combination of order-sorted and constraint based reasoning, enables us to generalize some basic results from classical rewrite theory.

[1]  Sergei G. Vorobyov,et al.  Conditional Rewrite Rule Systems with Built-In Arithmetic and Induction , 1989, RTA.

[2]  Nachum Dershowitz,et al.  Completion for Rewriting Modulo a Congruence , 1987, Theor. Comput. Sci..

[3]  Deepak Kapur,et al.  Inductive Reasoning with Incomplete Specifications (Preliminary Report) , 1986, LICS.

[4]  Joxan Jaffar,et al.  Constraint logic programming , 1987, POPL '87.

[5]  Nachum Dershowitz,et al.  Decidable Matching for Convergent Systems (Preliminary Version) , 1992, CADE.

[6]  Gérard P. Huet,et al.  Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems , 1980, J. ACM.

[7]  C. Kirchner,et al.  Deduction with symbolic constraints , 1990 .

[8]  Martin Wirsing,et al.  Algebraic Specification , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[9]  J. Van Leeuwen,et al.  Handbook of theoretical computer science - Part A: Algorithms and complexity; Part B: Formal models and semantics , 1990 .

[10]  Bernhard Gramlich,et al.  A Constructor-Based Approach to Positive/Negative-Conditional Equational Specifications , 1994, J. Symb. Comput..

[11]  Klaus Becker.  Proving Ground Confluence and Inductive Validity in Constructor Based Equational Specifications , 1993, TAPSOFT.

[12]  Nachum Dershowitz,et al.  A Rationale for Conditional Equational Programming , 1990, Theor. Comput. Sci..

[13]  J. Goguen,et al.  Order-Sorted Equational Computation , 1989 .

[14]  Manfred Broy,et al.  A Systematic Study of Models of Abstract Data Types , 1984, Theor. Comput. Sci..

[15]  Christine Choppy,et al.  Abstract Rewriting with Concrete Operations , 1989, RTA.

[16]  Manfred Broy,et al.  Generalized Heterogeneous Algebras and Partial Interpretations , 1983, CAAP.

[17]  Gerard Huet,et al.  Conflunt reductions: Abstract properties and applications to term rewriting systems , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[18]  Hélène Kirchner,et al.  Completion of a Set of Rules Modulo a Set of Equations , 1986, SIAM J. Comput..