Abstract
Abstract : Three kinds of mathematical objects are considered which can be designated as the 'meaning or 'semantics' of programs: binary relations between initial and final states, binary relations on predicates (partial correctness semantics), and functionals from predicates to predicates (predicate transformers). We exhibit various formal specification mechanisms: induction on program syntax, axioms, and deductive systems. We show that each kind of semantics can be specified by several different mechanisms. As long as arbitrary predicates on states are permitted, each kind of semantics uniquely determines the others -- with the sole exception of the weakest pre-condition semantics for nondeterministic programs.
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