Mathematical Theory of Program Correctness
Mathematical Theory of Program Correctness
First-Order Dynamic Logic
Axiomatic definitions of programming languages: a theoretical assessment (preliminary report)
POPL '80 Proceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Computability and completeness in logics of programs (Preliminary Report)
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
Effective Axiomatizations of Hoare Logics
Journal of the ACM (JACM)
A good Hoare axiom system for an ALGOL-like language
POPL '84 Proceedings of the 11th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
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The termination assertion pq means that whenever the formula p is true, there is an execution of the possibly nondeterministic program S which terminates in a state in which q is true. Termination assertions are more tractable technically than the partial correctness assertions usually treated in the literature. Termination assertions are studied for a programming language which includes local variable declarations, calls to undeclared global procedures, and nondeterministic recursive procedures with call-by-address and call-by-value parameters. By allowing formulas p and q to place conditions on global procedures, we provide a method for reasoning about programs with calls to global procedures based on hypotheses about procedure input-output behavior. The set of first-order termination assertions valid over all interpretations is completely axiomatizable without reference to the theory of any interpretation. Although uninterpreted assertions have limited expressive power, the set of valid termination assertions defines the semantics of recursive programs in the sense of Meyer and Halpern [10]. Thus the axiomatization constitutes an axiomatic definition of the semantics of recursive programs.