Sufficient completeness, term rewriting systems and “anti-unification”
Proc. of the 8th international conference on Automated deduction
Ground term confluence in parametric conditional equational specifications
4th Annual Symposium on Theoretical Aspects of Computer Sciences on STACS 87
on Rewriting techniques and applications
Journal of Symbolic Computation
The equational theory of parameterized specifications
Information and Computation - Semantics of Data Types
Simplifying conditional term rewriting systems: Unification, termination and confluence
Journal of Symbolic Computation
Confluence of conditional rewrite systems
1st international workshop on Conditional Term Rewriting Systems
Automatic proofs by induction in theories without constructors
Information and Computation
A strong restriction of the inductive completion procedure
Journal of Symbolic Computation
Tools for proving inductive equalities, relative completeness, and &ohgr;-completeness
Information and Computation
On ground-confluence of term rewriting systems
Information and Computation
Computational aspects of an order-sorted logic with term declarations
Computational aspects of an order-sorted logic with term declarations
A rationale for conditional equational programming
Theoretical Computer Science - Special issue on the international conference on fifth generation computer systems. Tokyo, 1988
Sufficient-completeness, ground-reducibility and their complexity
Acta Informatica
Handbook of theoretical computer science (vol. B)
Handbook of theoretical computer science (vol. B)
An automated tool for analyzing completeness of equational specifications
ISSTA '94 Proceedings of the 1994 ACM SIGSOFT international symposium on Software testing and analysis
Using induction and rewriting to verify and complete parameterized specifications
Theoretical Computer Science
Automated theorem proving by test set induction
Journal of Symbolic Computation
POPL '85 Proceedings of the 12th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Specification and proof in membership equational logic
Theoretical Computer Science - Trees in algebra and programming
Fundamentals of Algebraic Specification I
Fundamentals of Algebraic Specification I
Automata-driven automated induction
Information and Computation
Studies on the Ground Convergence Property of Conditional Theories
AMAST '91 Proceedings of the Second International Conference on Methodology and Software Technology: Algebraic Methodology and Software Technology
Proving Ground Confluence and Inductive Validity in Constructor Based Equational Specifications
TAPSOFT '93 Proceedings of the International Joint Conference CAAP/FASE on Theory and Practice of Software Development
A Confluence Criterion Based on the Generalised Neman Lemma
EUROCAL '85 Research Contributions from the European Conference on Computer Algebra-Volume 2
Completeness in Data Type Specifications
EUROCAL '85 Research Contributions from the European Conference on Computer Algebra-Volume 2
Inductive Proofs by Specification Transformation
RTA '89 Proceedings of the 3rd International Conference on Rewriting Techniques and Applications
Confluence of Terminating Conditional Rewrite Systems Revisited
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
Simultaneous Checking of Completeness and Ground Confluence
ASE '00 Proceedings of the 15th IEEE international conference on Automated software engineering
Stop losing sleep over incomplete data type specifications
POPL '84 Proceedings of the 11th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Proofs by induction in equational theories with constructors
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
A Church-Rosser checker tool for conditional order-sorted equational Maude specifications
WRLA'10 Proceedings of the 8th international conference on Rewriting logic and its applications
Constructors, sufficient completeness, and deadlock freedom of rewrite theories
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
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Algebraic specifications provide a powerful method for the specification of abstract data types in programming languages and software systems. Completeness and ground confluence are fundamental notions for building algebraic specifications in a correct and modular way. Related works for checking ground confluence are based on the completion techniques or on the test that all critical pairs between axioms are valid with respect to a sufficient criterion for ground confluence. It is generally accepted that such techniques may be very inefficient, even for very small specifications. Indeed, the completion procedure often diverges and there often exist many critical pairs of the axioms. In this article, we present a procedure for simultaneously checking completeness and ground confluence for specifications with free/nonfree constructors and parameterized specifications. If the specification is not complete or not ground confluent, then our procedure will output the set of patterns on whose ground instances a function is not defined and it can easily identify the rules that break ground confluence. In contrast to previous work, our method does not rely on completion techniques and does not require the computation of critical pairs of the axioms. The method is entirely implemented and allowed us to prove the completeness and the ground confluence of many specifications in a completely automatic way, where related techniques diverge or generate very complex proofs. Our system offers two main components: (i) a completeness and ground confluence analyzer that computes pattern trees of defined functions and may generate some proof obligations; and (ii) a procedure to prove (joinable) inductive conjectures which is used to discharge these proof obligations.