On the completeness of the inductive assertion method

win and sin : predicate transformers for concurrency

“…As observed by de Bakker and Meertens [4], the operator sp is a dual of wlp; for every property of wlp there is a corresponding dual property of sp. For example, the following are the duals of WLP2 and WLP3.…”

Completeness with Finite Systems of Intermediate Assertions for Recursive Program Schemes

“…From the proof we can extract all intermediate assertions about atomic substatements of the original program. Since proofs are finite, we obtain a finite system of intermediate assertions, thus apparently contradicting the result of [2]. Also [ 4] and [6] avoid the necessity of an infinite number of assertions by using an extension of the inductive assertion method.…”

“…The purpose of this paper is to investigate this issue in the 'relational framework of [2] and to obtain, within that framework, a unification of the (essence of the) results of [2] and of [ 4], [5] and [6]. The solution of the apparent contradiction lies in the fact that in [4], [5] and [6] auxiliary variables are used (to store the initial values of variables).…”

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[2] shows that for W one could also take the set of all so-called index-triple sequences, so that these two completeness results differ only in the choice of the extended state space. Our choice is both more economical and easier to use in the concrete proofs.

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Natural Quantum Operational Semantics with Predicates

“…The weakest-precondition was developed by (de Bakker and de Roever, 1972;de Bakker and Meertens, 1975) and popularised by Dijkstra (1976). This notion is connected with the Hoare triple {f 1 }P {f 2 } (Hoare, 1969), where f 1 and f 2 denote some predicates and P is a program.…”