Handbook of theoretical computer science (vol. B)
The Z notation: a reference manual
The Z notation: a reference manual
Rippling: a heuristic for guiding inductive proofs
Artificial Intelligence
Handbook of logic in artificial intelligence and logic programming
Partial functions and logics: a warning
Information Processing Letters
Constructors can be partial, too
Automated reasoning and its applications
Term rewriting and all that
Approximating the domains of functional and imperative programs
Science of Computer Programming
Inconsistency and Undefinedness in Z - A Practical Guide
ZUM '98 Proceedings of the 11th International Conference of Z Users on The Z Formal Specification Notation
On Mutually Recursive Free Types in Z
ZB '00 Proceedings of the First International Conference of B and Z Users on Formal Specification and Development in Z and B
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
Termination Analysis by Inductive Evaluation
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
On partial-function application in Z
3FACS'98 Proceedings of the 3rd BCS-FACS conference on Northern Formal Methods
Abstract Relations Between Restricted Termination And Confluence Properties Of Rewrite Systems
Fundamenta Informaticae
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Simply-typed set-theoretic languages such as Z and B are widely used for program and system specifications. The main technique for reasoning about such specifications is induction. However, while partiality is an important concept in these languages, many standard approaches to automating induction proofs rely on the totality of all occurring functions. Reinterpreting the second author's recently proposed induction technique for partial functional programs, we introduce in this paper the new principle of "closure induction" for reasoning about the inductive properties of partial functions in simply-typed set-theoretic languages. In particular, closure induction allows us to prove partial correctness, that is, to prove those instances of conjectures for which designated partial functions are explicitly defined.