Verifying the unification algorithm in LCF
Science of Computer Programming - Ellis Horwood series in artificial intelligence
The foundations of program verification (2nd ed.)
The foundations of program verification (2nd ed.)
Proof by induction using test sets
Proc. of the 8th international conference on Automated deduction
Artificial Intelligence
Initial computability, algebraic specifications, and partial algebras
Initial computability, algebraic specifications, and partial algebras
Partial algebras flow from algebraic specifications
14th International Colloquium on Automata, languages and programming
Journal of Symbolic Computation
Efficient tests for top-down termination of logical rules
Journal of the ACM (JACM)
A mechanical proof of the Church-Rosser theorem
Journal of the ACM (JACM)
Journal of Automated Reasoning
Automatic proofs by induction in theories without constructors
Information and Computation
CADE-10 Proceedings of the tenth international conference on Automated deduction
CADE-10 Proceedings of the tenth international conference on Automated deduction
Termination proofs for logic programs
Termination proofs for logic programs
Introduction to HOL: a theorem proving environment for higher order logic
Introduction to HOL: a theorem proving environment for higher order logic
Rippling: a heuristic for guiding inductive proofs
Artificial Intelligence
A type-theoretical alternative to ISWIM, CUCH, OWHY
Theoretical Computer Science - A collection of contributions in honour of Corrado Bo¨hm on the occasion of his 70th birthday
Handbook of logic in artificial intelligence and logic programming
On proving the termination of algorithms by machine
Artificial Intelligence
Constructors can be partial, too
Automated reasoning and its applications
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Approximating the domains of functional and imperative programs
Science of Computer Programming
Communications of the ACM
Abstract data types and the development of data structures
Communications of the ACM
Recursive functions of symbolic expressions and their computation by machine, Part I
Communications of the ACM
Partial Functions in a Total Setting
Journal of Automated Reasoning
Termination of Nested and Mutually Recursive Algorithms
Journal of Automated Reasoning
The Use of Sorts in Algebraic Specifications
Selected papers from the 8th Workshop on Specification of Abstract Data Types Joint with the 3rd COMPASS Workshop on Recent Trends in Data Type Specification
Automating Induction over Mutually Recursive Functions
AMAST '96 Proceedings of the 5th International Conference on Algebraic Methodology and Software Technology
HOL'92 Proceedings of the IFIP TC10/WG10.2 Workshop on Higher Order Logic Theorem Proving and its Applications
Boyer-Moore Automation for the HOL System
HOL'92 Proceedings of the IFIP TC10/WG10.2 Workshop on Higher Order Logic Theorem Proving and its Applications
Derivation and Use of Induction Schemes in Higher-Order Logic
TPHOLs '97 Proceedings of the 10th International Conference on Theorem Proving in Higher Order Logics
Termination Analysis for Functional Programs using Term Orderings
SAS '95 Proceedings of the Second International Symposium on Static Analysis
RTA '97 Proceedings of the 8th International Conference on Rewriting Techniques and Applications
Automated Termination Proofs with Measure Functions
KI '95 Proceedings of the 19th Annual German Conference on Artificial Intelligence: Advances in Artificial Intelligence
A Mechanizable Induction Principle for Equational Specifications
Proceedings of the 9th International Conference on Automated Deduction
On Notions of Inductive Validity for First-Oder Equational Clauses
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
More Church-Rosser Proofs (in Isabelle/HOL)
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
Termination Analysis by Inductive Evaluation
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
Termination Analysis for Partial Functions
SAS '96 Proceedings of the Third International Symposium on Static Analysis
A Mechanization of Strong Kleene Logic for Partial Functions
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Mathematical Theory of Computation
Mathematical Theory of Computation
Simplification Orderings: History Of Results
Fundamenta Informaticae
Journal of Automated Reasoning
Partial and Nested Recursive Function Definitions in Higher-order Logic
Journal of Automated Reasoning
Reasoning about incompletely defined programs
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
A Two-Valued Logic for Properties of Strict Functional Programs Allowing Partial Functions
Journal of Automated Reasoning
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In this paper we present a method for automated induction proofs about partial functions. We show that most well-known techniques developed for (explicit) induction theorem proving are unsound when dealing with partial functions. But surprisingly, by slightly restricting the application of these techniques, it is possible to develop a calculus for automated induction proofs with partial functions. In particular, under certain conditions one may even generate induction schemes from the recursions of nonterminating algorithms. The need for such induction schemes and the power of our calculus have been demonstrated on a large collection of nontrivial theorems (including Knuth and Bendix's critical pair lemma). In this way, existing induction theorem provers can be directly extended to partial functions without major changes of their logical framework.