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predicate transformer semantics
Predicate transformer semantics were introduced by Dijkstra in his seminal paper "Guarded commands, nondeterminacy and formal derivation of programs". They define the semantics of an imperative programming paradigm by assigning to each ''statement'' in this language a corresponding ''predicate transformer'': a total function between two ''predicates'' on the state space of the statement. In this sense, predicate transformer semantics are a kind of denotational semantics. Actually, in guarded commands, Dijkstra uses only one kind of predicate transformer: the well-known weakest preconditions (see below).
Moreover, predicate transformer semantics are a reformulation of Floyd–Hoare logic. Whereas Hoare logic is presented as a deductive system, predicate transformer semantics (either by weakest-preconditions or by strongest-postconditions see below) are complete strategies to build valid deductions of Hoare logic. In other words, they provide an effective algorithm to reduce the problem of verifying a Hoare triple to the problem of proving a first-order formula. Technically, predicate transformer semantics perform a kind of symbolic execution of statements into predicates: execution runs ''backward'' in the case of weakest-preconditions, or runs ''forward'' in the case of strongest-postconditions.
== Weakest preconditions ==
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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