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Theories of Programming and Formal Methods
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This study is clearly not immediately related to any application. Instead we definitely and only consider the fundamental mathematical structure modeling mechanical computations. As pointed out in [12] and in other scientific disciplines as well, it appears to be very important to develop some mathematical models for our main concept, that is in our case that of computation. In doing so, we intend to be able to understand not only the well known existing mechanisms at work in computations today but also those we might encounter in the future. This topic is by no means new. In fact, a variety of computational models have been proposed in the literature. This is carefully reviewed by Nelson in [19]. He made a clear distinction between models dealing with relations on predicate [13], relations on states [14], predicate transformers [5], or simply predicates [12]. The approach presented here deals with relations on states and with set transformers (the set-theoretic equivalent to predicate transformers). For this, I use set theory rather than predicate calculus. To the best of my knowledge, it has not been done so far systematically in this way. The reason why I favor set the- ory over predicate calculus as a medium for such a theoretical development is certainly one of personal taste: I prefer to quantify over sets (or better, over all subsets of a certain set) than over predicates, and I think that set complementation is more convenient than predicate negation for theoretical developments and in mechanized proofs as well.
Zhiming Liu and Jim Woodcock and HuibiaoZhu(Eds.) - Personal Name
978-3-642-39697-7
NONE
Information Technology
English
1998
1-422
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