The Semantics of CLEAR, A Specification Language
Proceedings of the Abstract Software Specifications, 1979 Copenhagen Winter School
How to Prove Algebraic Inductive Hypotheses Without Induction
Proceedings of the 5th Conference on Automated Deduction
The specification and application to programming of abstract data types.
The specification and application to programming of abstract data types.
Remarks on remarks on many-sorted equational logic
ACM SIGPLAN Notices
A complete calculus for the multialgebraic and functional semantics of nondeterminism
ACM Transactions on Programming Languages and Systems (TOPLAS)
Complete Categorical Equational Deduction
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
Specification of abstract data types with partially defined operations
ICSE '82 Proceedings of the 6th international conference on Software engineering
On the equality of probabilistic terms
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
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The rules of deduction which are usually used for many-sorted equational logic in computer science, for example in the study of abstract data types, are not sound. Correcting these rules by introducing explicit quantifiers yields a system which, although it is sound, is not complete; some new rules are needed for the addition and deletion of quantifiers. This note is intended as an informal, but precise, introduction to the main issues and results. It gives an example showing the unsoundness of the usual rules; it also gives a completeness theorem for our new rules, and gives necessary and sufficient conditions for the old rules to agree with the new.