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Boolean algebra is simpler than number algebra, with applications in programming, circuit design, law, specifications, mathematical proof, and reasoning in any domain. So why is number algebra taught in primary school and used routinely by scientists, engineers, economists, and the general public, while boolean algebra is not taught until university, and… (More)
<italic>Programs are given a new semantics with the merit that a specification written as a first-order predicate can be refined, step by step, to a program via the rules of Predicate Calculus. The semantics allows a free mixture of predicate and programming notations, and manipulation of programs.</italic>
Time and space limitations can be specified, and proven, in exactly the same way as functionality. Proofs of time bounds, both implementation-independent and real-time, and of space requirements, both worst-case and average-case, are given in complete detail. ———————————————
This roadmap describes ways that researchers in four areas---specification languages, program generation, correctness by construction, and programming languages---might help further the goal of verified software. It also describes what advances the "verified software" grand challenge might anticipate or demand from work in these areas. That is, the roadmap… (More)
The utility of repetitive constructs is challenged. Recursive refinement is claimed to be semantically as simple, and superior for programming ease and clarity. Some programming examples are offered to support this claim. The relation between the semantics of predicate transformers and “least fixed point” semantics is presented.
The notion of termination is examined, first for its physical observability, then for its part in six semantic formalisms, with emphasis on predicative semantics.
This paper shows how probabilistic reasoning can be applied to the predicative style of programming. 0 Introduction Probabilistic programming refers to programming in which the probabilities of the values of variables are of interest. For example, if we know the probability distribution from which the inputs are drawn, we may calculate the probability… (More)