Download Conception, evolution, and application of functional by Hudak P. PDF

By Hudak P.

The principles of practical programming languages are tested from either historic and technical views. Their evolution is traced via numerous serious sessions: early paintings on lambda calculus and combinatory calculus, Lisp, Iswim, FP, ML, and sleek useful languages comparable to Miranda1 and Haskell. the basic premises on which the useful programming method stands are severely analyzed with appreciate to philosophical, theoretical, and pragmatic issues. specific cognizance is paid to the most positive factors that signify sleek practical languages: higher-order features, lazy assessment, equations and trend matching, robust static typing and sort inference, and information abstraction. furthermore, present learn areas-such as parallelism, nondeterminism, input/output, and state-oriented computations-are tested with the target of predicting the longer term improvement and alertness of practical languages.

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Also note that the rule only holds if P is stronger than QŒxnE. If this is not the case, the rule may not be invoked! P; S; Q/, then we should seek out some intermediate predicate M that we believe to be more easily attainable from the precondition state, P . This intermediate state then serves as a sort of half-way house from which to find some other code that will enable us to arrive at the required postcondition, Q. 4 Refinement Rules 39 The rule is best stated in Hoare triple notation, but relying on the extended notation previously introduced.

But a little thought will convince otherwise. xC1 > 5/ should hold. x > 5/Œxnx C 1. e. x > 4/, the weakest precondition. x > 4/, the weakest precondition, etc. x > 4/. 3 Guarded Command Language 25 So, counter-intuitive as it may initially be, the precondition given above for assignment does indeed make sense. Readers who are not fully convinced should verify this for a variety of other scenarios. This will confirm that assignment’s precondition is as stated. Here we have started off with a notion of what assignment means, and proposed and verified its weakest precondition.

7 This means that if a loop has a variant, then the loop will definitely terminate eventually. As an example, consider the following (rather trivial) loop. i > 0/ ! i WD i 1 od A variant for this loop is the expression i . This is an expression in one of the variables in the loop; it starts with value 10; and it always decreases (by 1) in every iteration. Because of the loop’s guard, it is also bounded below by 0—the value of the variant can never legitimately be less than 0 in the loop. As a result, we can confidently state that the loop will terminate.

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