Efficiency and Completeness of the Set of Support Strategy in Theorem Proving
Journal of the ACM (JACM)
The Concept of Demodulation in Theorem Proving
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Automatic Theorem Proving with Built-in Theories Including Equality, Partial Ordering, and Sets
Journal of the ACM (JACM)
An Approach for Finding C-Linear Complete Inference Systems
Journal of the ACM (JACM)
Automated Theorem-Proving for Theories with Simplifiers Commutativity, and Associativity
Journal of the ACM (JACM)
Experiment with an automatic theorem-prover having partial ordering inference rules
Communications of the ACM
Equational methods in first order predicate calculus
Journal of Symbolic Computation
History and basic features of the critical-pair/completion procedure
Journal of Symbolic Computation
Journal of Symbolic Computation
Rewrite method for theorem proving in first order theory with equality
Journal of Symbolic Computation
Complexity of matching problems
Journal of Symbolic Computation
Critical pair criteria for completion
Journal of Symbolic Computation
Only prime superpositions need be considered in the Knuth-Bendix completion procedure
Journal of Symbolic Computation
Enumerating outer narrowing derivationsfor constructor-based term rewriting systems
Journal of Symbolic Computation
Journal of Symbolic Computation
Efficient solution of linear diophantine equations
Journal of Symbolic Computation
Unification in commutative theories
Journal of Symbolic Computation
A strong restriction of the inductive completion procedure
Journal of Symbolic Computation
PEPM '91 Proceedings of the 1991 ACM SIGPLAN symposium on Partial evaluation and semantics-based program manipulation
Journal of the ACM (JACM)
POPL '94 Proceedings of the 21st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Using resolution for extending KL-ONE-type languages
CIKM '95 Proceedings of the fourth international conference on Information and knowledge management
Integration of declarative paradigms: benefits and challenges
ACM Computing Surveys (CSUR) - Special issue: position statements on strategic directions in computing research
Experiments with subdivision of search in distributed theorem proving
PASCO '97 Proceedings of the second international symposium on Parallel symbolic computation
Partial evaluation of functional logic programs
ACM Transactions on Programming Languages and Systems (TOPLAS)
Specialization of inductively sequential functional logic programs
Proceedings of the fourth ACM SIGPLAN international conference on Functional programming
Automated Theorem-Proving for Theories with Simplifiers Commutativity, and Associativity
Journal of the ACM (JACM)
Automatic Proofs of Theorems in Analysis Using Nonstandard Techniques
Journal of the ACM (JACM)
Complete Sets of Reductions for Some Equational Theories
Journal of the ACM (JACM)
A Unification Algorithm for Associative-Commutative Functions
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Functional and constraint logic programming
Constraints in computational logics
The narrowing-driven approach to functional logic program specialization
New Generation Computing - Partial evaluation and program transformation
Context-sensitive rewriting strategies
Information and Computation
Cancellative abelian monoids and related structures in refutational theorem proving (Part I)
Journal of Symbolic Computation
Cancellative Superposition Decides the Theory of Divisible Torsion-Free Abelian Groups
LPAR '99 Proceedings of the 6th International Conference on Logic Programming and Automated Reasoning
Decision Procedures and Model Building, or How to Improve Logical Information in Automated Deduction
Selected Papers from Automated Deduction in Classical and Non-Classical Logics
A New Rewrite Method for Convergence of Self-Stabilizing Systems
Proceedings of the 13th International Symposium on Distributed Computing
An implementation of narrowing strategies
Proceedings of the 3rd ACM SIGPLAN international conference on Principles and practice of declarative programming
Refining weakly outermost-needed rewriting and narrowing
Proceedings of the 5th ACM SIGPLAN international conference on Principles and practice of declaritive programming
Higher-order narrowing with definitional trees
Journal of Functional Programming
Leftmost outside-in narrowing calculi
Journal of Functional Programming
Superposition with completely built-in Abelian groups
Journal of Symbolic Computation
ACM SIGSOFT Software Engineering Notes - Proceedings of VERkshop III -- a formal verification workshop
An equational approach to theorem proving in first-order predicate calculus
ACM SIGSOFT Software Engineering Notes - Proceedings of VERkshop III -- a formal verification workshop
ACM SIGART Bulletin
Fast narrowing-driven partial evaluation for inductively sequential programs
Proceedings of the tenth ACM SIGPLAN international conference on Functional programming
A short survey on the state of the art in matching and unification problems
ACM SIGSAM Bulletin
Matching with multiplication and exponentiation (extended abstract)
Mathematical Structures in Computer Science
Ensuring the quasi-termination of needed narrowing computations
Information Processing Letters
A new generic scheme for functional logic programming with constraints
Higher-Order and Symbolic Computation
Modeling Pointer Redirection as Cyclic Term-graph Rewriting
Electronic Notes in Theoretical Computer Science (ENTCS)
Static Slicing of Rewrite Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
A Transformational Approach to Polyvariant BTA of Higher-Order Functional Programs
Logic-Based Program Synthesis and Transformation
Application of automatic transformations to program verification
IJCAI'81 Proceedings of the 7th international joint conference on Artificial intelligence - Volume 1
The Markgraf Karl refutation procedure
IJCAI'81 Proceedings of the 7th international joint conference on Artificial intelligence - Volume 1
A superposition oriented theorem prover
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 2
An equational approach to theorem proving in first-order predicate calculus
IJCAI'85 Proceedings of the 9th international joint conference on Artificial intelligence - Volume 2
A complete unification algorithm for associative-commutative functions
IJCAI'75 Proceedings of the 4th international joint conference on Artificial intelligence - Volume 1
Associative commutative pattern matching
IJCAI'79 Proceedings of the 6th international joint conference on Artificial intelligence - Volume 1
Constraint Functional Logic Programming Revisited
Electronic Notes in Theoretical Computer Science (ENTCS)
Communications of the ACM
Operational semantics for declarative multi-paradigm languages
Journal of Symbolic Computation
Automatic partial inversion of inductively sequential functions
IFL'06 Proceedings of the 18th international conference on Implementation and application of functional languages
Improving offline narrowing-driven partial evaluation using size-change graphs
LOPSTR'06 Proceedings of the 16th international conference on Logic-based program synthesis and transformation
Compiling and verifying security protocols
LPAR'00 Proceedings of the 7th international conference on Logic for programming and automated reasoning
Multi-paradigm declarative languages
ICLP'07 Proceedings of the 23rd international conference on Logic programming
Termination of narrowing in left-linear constructor systems
FLOPS'08 Proceedings of the 9th international conference on Functional and logic programming
An integrated framework for the diagnosis and correction of rule-based programs
Theoretical Computer Science
Journal of Visual Languages and Computing
Digital Ecosystems: Ecosystem-Oriented Architectures
Natural Computing: an international journal
Goal-directed and relative dependency pairs for proving the termination of narrowing
LOPSTR'09 Proceedings of the 19th international conference on Logic-Based Program Synthesis and Transformation
Lazy narrowing with simplification
Computer Languages
Using semantics specified in maude to generate test cases
ICTAC'12 Proceedings of the 9th international conference on Theoretical Aspects of Computing
Using narrowing to test maude specifications
WRLA'12 Proceedings of the 9th international conference on Rewriting Logic and Its Applications
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To prove really difficult theorems, resolution principle programs need to make better inferences and to make them faster. An approach is presented for taking advantage of the structure of some special theories. These are theories with simplifiers, commutativity, and associativity, which are valuable concepts to build in, since they so frequently occur in important theories, for example, number theory (plus and times) and set theory (union and intersection). The object of the approach is to build in such concepts in a (refutation) complete, valid, efficient (in time) manner by means of a “natural” notation and/or new inference rules. Some of the many simplifiers that can be built in are axioms for (left and right) identities, inverses, and multiplication by zero.As for results, commutativity is built in by a straightforward modification to the unification (matching) algorithm. The results for simplifiers and associativity are more complicated. These theoretical results can be combined with one another and/or extended to either C-linear refutation completeness or theories with partial ordering, total ordering, or sets. How these results can serve as the basis of practical computer programs is discussed.