Download e-book for kindle: A Practical Theory of Programming by Eric C.R. Hehner

By Eric C.R. Hehner

ISBN-10: 0387941061

ISBN-13: 9780387941066

Knowing programming and programming languages calls for wisdom of the underlying theoretical version. This ebook explores points of programming which are amenable to mathematical evidence. the writer describes a programming concept that's a lot easier and extra entire than the present theories up to now. within the theoretical version, a specification is simply a boolean expression and refinement is simply a standard implication. the writer develops a realistic and vast strategy for writing targeted requirements and designing courses whose executions most likely fulfill the standards. starting with preparatory fabric in good judgment, numbers, units, lists, services and family members, the publication advances extra into application conception, the guts of the ebook. next chapters should be chosen or passed over in response to direction emphasis. The textual content can be invaluable to scholars in classes on programming technique or verification on the complex undergraduate or starting graduate point, in addition to for software program engineers within the box. All technical phrases are defined after which verified within the ebook at any place attainable. No complicated mathematical wisdom or programming language is believed. The publication comprises a number of routines and worked-out strategies for particular routines. Transparency masters and strategies for the rest routines can be found from the writer.

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Therefore we consider a higher-order function applied to an argument, as written above, to be an abbreviation for 〈f: (A→B)→ ... ~f ... 〉 {g} and the set brackets { } just make the parameter and argument into The power operator elements, as required, and the content operator ~ then removes the set structure. Here is a predicate whose parameter is a function. 10· even (f n)〉 Let us call this predicate check . 10 . When an argument for check is applied to the first 10 natural numbers, the results must be included in int because they will be tested for evenness.

G applies a higher-order function to a function argument. A parameter stands for an element of the domain, and the Application Law requires the argument to be an element of the domain, but functions are not elements. Therefore we consider a higher-order function applied to an argument, as written above, to be an abbreviation for 〈f: (A→B)→ ... ~f ... 〉 {g} and the set brackets { } just make the parameter and argument into The power operator elements, as required, and the content operator ~ then removes the set structure.

With function 1→21 as left operand, and list [10; 11; 12] as right operand, we get 1→21 | [10; 11; 12] = [10; 21; 12] just as we defined it for lists. We can apply quantifiers to lists. #L· Ln , and conveniently expresses the sum of the items of the list. In some respects, lists and functions differ. Catenation and length apply to lists, not to functions. Order is defined for lists, not for functions. List inclusion and function inclusion do not coincide. 4 Limits and Reals 3 Function Theory optional Let f: nat→rat so that f0; f1; f2; ...

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