composed from abstract statements operating on abstract data structures) we observe the phenomenon of "joint refinement". Why is this so? %��������� The programmer’s task is to present such complete Edsger Dijkstra, a pioneer in computer science, once said, “Program testing can be used to show the presence of bugs, but never to show their absence!” Yet, many embedded projects mistakenly interpret the absence of test failures as proof of quality. The top pearl describes the program in its most abstract form, in all lower pearls one or more concepts used above are explained (refined) in terms of concepts to be explained (refined) in pearls below it, while the bottom pearl eventually explains what still has to be explained in terms of a standard interface (=machine). The only difference is that now the programmer must invent his own concepts (analogous to the "ready-made" integer) and his own operations upon them (analogous to the "ready-made" arithmetic operations).4.1) In the refinement of an abstract program (i.e. 14.6k Likes, 36 Comments - David Daneman (@thedanemen) on Instagram: “"Program testing can be used to show the presence of bugs, but never show their absence!" Program testing can be used very e ectively to show the presence of bugs but never to show their absence. My willingness to confine my attention to such "well-structured programs" (as a subset of the set of all possible programs) is based on my belief that we can find such a well structured subset satisfying our programming needs, i.e. This white paper presents a … which is a variant of the fact that "absence of evidence is not evidence of the absence". 2.2) By a number of people it has been shown that program correctness can be proved. The abstraction process involved in this mapping turns out (not, amazingly, as an afterthought!) Even the simplest of programs has billions of possible inputs. programs not written with a proof procedure in mind. that for each programmable task this subset contains enough realistic programs.2.4) This what I call "constructive approach to the problem of program correctness" can be taken a step further. “Program testing can be used to show the presence of bugs, but never to show their absence. Some interesting discussions are related to the famous statement: "program testing can be used to show the presence of bugs, but never to show their absence!

I would like to stress that this order may be radically different from the order (in time) in which they are designed.6.1) Pearls have emerged as program modules when I tried to map upon each other as completely as possible, the numerous members of a class of related programs. but on the questions "for what program structures can we give correctness proofs without undue labour, even if the programs get large?" This manual serves as an interface between the two parts of the necklace. Although I tried to do it, I feel that I have given but little recognition to the requirements of program development such as is needed when one wishes to employ a large crowd; I have no experience with the Chinese Army approach, nor am I convinced of its virtues. --Edsger…” To quote Edsger Dijkstra, “Program testing can be used to show the presence of bugs, but never to show their absence!”1 Or, as Albert Einstein reputedly once said, "No amount of experimentation can ever prove me right; a single experiment can prove me wrong." and, as a sequel, "How do we make, for a given task, such a well-structured program?". the number of different computations for which the assertions claim to hold is so fantastically high that demonstration of correctness by sampling is completely out of the question. 4 0 obj
to be the same as the one that can be used to reduce the amount of intellectual labour involved in correctness proofs.

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