Download PDF by Eric C.R. Hehner: A Practical Theory of Programming

By Eric C.R. Hehner

ISBN-10: 0387941061

ISBN-13: 9780387941066

ISBN-10: 3540941061

ISBN-13: 9783540941064

There are a number of theories of programming. the 1st usable concept, known as ''Hoare's Logic'', continues to be the most widely recognized. In it, a specification is a couple of predicates: a precondition and postcondition (these and all technical phrases should be outlined in due course). one other well known and heavily comparable concept by way of Dijkstra makes use of the weakest precondition predicate transformer, that is a functionality from courses and postconditions to preconditions. lones's Vienna improvement technique has been used to virtue in a few industries; in it, a specification is a couple of predicates (as in Hoare's Logic), however the moment predicate is a relation. Temporal common sense is one more formalism that introduces a few unique operators and quantifiers to explain a few points of computation. the speculation during this ebook is easier than any of these simply pointed out. In it, a specification is simply a boolean expression. Refinement is simply usual implication. This conception can be extra common than these simply pointed out, using to either terminating and nonterminating computation, to either sequential and parallel computation, to either stand-alone and interactive computation. And it comprises time bounds, either for set of rules type and for tightly restricted real-time functions

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In addition to the notations already presented, we add two more. = σ′=σ ok = x′=x ∧ y′=y ∧ ... x:= e = = (substitute e for x in ok ) x′=e ∧ y′=y ∧ ... The notation ok specifies that the final values of all variables equal the corresponding initial values. A computer can satisfy this specification by doing nothing. The assignment x:= e is pronounced “ x is assigned e ”, or “ x gets e ”, or “ x becomes e ”. In the assignment notation, x is any unprimed state variable and e is any unprimed expression in the domain of x .

When that is so, there is no need for any other specification, and no need for refinement. However, the programming notations are only part of the specification notations: those that happen to be implemented. Specifiers should use whatever notations help to make their specifications clear, including but not limited to programming notations. 0 Refinement Laws Once we have a specification, we refine it until we have a program. We have only five programming notations to choose from when we refine.

We have only five programming notations to choose from when we refine. Two of them, ok and assignment, are programs and require no further refinement. The other three solve the given refinement problem by raising new problems to be solved by further refinement. When these new problems are solved, their solutions will contribute to the solution of the original problem, according to the first of our refinement laws. Refinement by Steps (Stepwise Refinement) (monotonicity, transitivity) If A ⇐ if b then C else D and C ⇐ E and D ⇐ F are theorems, then A ⇐ if b then E else F is a theorem.

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