Parameterized horn clause specifications: proof theory and correctness
The International Joint Conference on theory and practice of software development on TAPSOFT '87
Automatic proofs by induction in theories without constructors
Information and Computation
An overview of rewrite rule laboratory (RRL)
RTA-89 Proceedings of the 3rd international conference on Rewriting Techniques and Applications
Inductive methods for reasoning about abstract data types
POPL '88 Proceedings of the 15th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A strong restriction of the inductive completion procedure
Journal of Symbolic Computation
Extensions to the rippling-out tactic for guiding inductive proofs
CADE-10 Proceedings of the tenth international conference on Automated deduction
CADE-10 Proceedings of the tenth international conference on Automated deduction
UNICOM: a refined completion based inductive theorem prover
CADE-10 Proceedings of the tenth international conference on Automated deduction
Automatic demonstration: rewriting techniques (French)
Automatic demonstration: rewriting techniques (French)
Proofs in parameterized specifications
RTA-91 Proceedings of the 4th international conference on Rewriting techniques and applications
Automating inductionless induction using test sets
Journal of Symbolic Computation
Deduction and declarative programming
Deduction and declarative programming
Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
Using induction and rewriting to verify and complete parameterized specifications
Theoretical Computer Science
Automated theorem proving by test set induction
Journal of Symbolic Computation
Proving termination with multiset orderings
Communications of the ACM
On proving inductive properties of abstract data types
POPL '80 Proceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Fundamentals of Algebraic Specification I
Fundamentals of Algebraic Specification I
Reasoning About Functional Programs in Nuprl
Functional Programming, Concurrency, Simulation and Automated Reasoning: International Lecture Series 1991-1992, McMaster University, Hamilton, Ontario, Canada
Buchberger's Algorithm: A Constraint-Based Completion Procedure
CCL '94 Proceedings of the First International Conference on Constraints in Computational Logics
A Mechanizable Induction Principle for Equational Specifications
Proceedings of the 9th International Conference on Automated Deduction
PVS: A Prototype Verification System
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
On Notions of Inductive Validity for First-Oder Equational Clauses
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Proof by Consistency in Conditional Equational Theories
Proceedings of the 2nd International CTRS Workshop on Conditional and Typed Rewriting Systems
Conditional Rewriting in Focus
Proceedings of the 2nd International CTRS Workshop on Conditional and Typed Rewriting Systems
On generic representation of implicit induction procedures
On generic representation of implicit induction procedures
STeP: The Stanford Temporal Prover (Educational Release) User''s Manual
STeP: The Stanford Temporal Prover (Educational Release) User''s Manual
Automated theorem proving: A logical basis (Fundamental studies in computer science)
Automated theorem proving: A logical basis (Fundamental studies in computer science)
Incorporating decision procedures in implicit induction
Journal of Symbolic Computation - Integrated reasoning and algebra systems
Using the transformational approach to build a safe and generic data synchronizer
GROUP '03 Proceedings of the 2003 international ACM SIGGROUP conference on Supporting group work
A safe and generic model for synchronizing divergent data
UbiMob '04 Proceedings of the 1st French-speaking conference on Mobility and ubiquity computing
Proving correctness of transformation functions in real-time groupware
ECSCW'03 Proceedings of the eighth conference on European Conference on Computer Supported Cooperative Work
Combining Rewriting with Noetherian Induction to Reason on Non-orientable Equalities
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Automated Induction with Constrained Tree Automata
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Log-based transactional workflow mining
Distributed and Parallel Databases
Validation of the JavaCard platform with implicit induction techniques
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
Verifying composite service transactional behavior using event calculus
OTM'07 Proceedings of the 2007 OTM Confederated international conference on On the move to meaningful internet systems: CoopIS, DOA, ODBASE, GADA, and IS - Volume Part I
Integrating implicit induction proofs into certified proof environments
IFM'10 Proceedings of the 8th international conference on Integrated formal methods
Formal analysis of intrusion detection systems for high speed networks
ISPACT'10 Proceedings of the 9th WSEAS international conference on Advances in e-activities, information security and privacy
Automatic 'descente infinie' induction reasoning
TABLEAUX'05 Proceedings of the 14th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
Towards synchronizing linear collaborative objects with operational transformation
FORTE'05 Proceedings of the 25th IFIP WG 6.1 international conference on Formal Techniques for Networked and Distributed Systems
Analysis of composite web services using logging facilities
ICSOC'06 Proceedings of the 4th international conference on Service-oriented computing
Automated certification of implicit induction proofs
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
Applying a theorem prover to the verification of optimistic replication algorithms
Rewriting Computation and Proof
Hi-index | 0.01 |
Cover set induction is known as a proof method that keeps the advantages of explicit induction and proof by consistency. Most implicit induction proof procedures are defined in a cover set induction framework. Contextual cover set (CCS) is a new concept that fully characterizes explicit induction schemes, such as the cover sets, and many simplification techniques as those specific to the "proof by consistency' approach. Firstly, we present an abstract inference system uniformly defined in terms of contextual cover sets as our general framework to build implicit induction provers. Then, we show that it generalizes existing cover set induction procedures. This paper also contributes to the general problem of assembling reasoning systems in a sound manner. Elementary CCSs are generated by reasoning modules that implement various simplification techniques defined for a large class of deduction mechanisms such as rewriting, conditional rewriting and resolution-based methods for clauses. We present a generic and sound integration schema of reasoning modules inside our procedure together with a simple methodology for improvements and incremental sound extensions of the concrete proof procedures. As a case study, the inference system of the SPIKE theorem prover has been shown to be an instance of the abstract inference system integrating reasoning modules based on rewriting techniques defined for conditional theories. Our framework allows for modular and incremental sound extensions of SPIKE when new reasoning techniques are proposed. An extension of the prover, incorporating inductive semantic subsumption techniques, has proved the correctness of the MJRTY algorithm by performing a combination of arithmetic and inductive reasoning. 2001 Academic Press.