By D. John Cooke

ISBN-10: 1852338202

ISBN-13: 9781852338206

Crucial to Formal tools is the so-called Correctness Theorem which relates a specification to its right Implementations. This theorem is the aim of conventional application checking out and, extra lately, of application verification (in which the theory has to be proved). Proofs are tricky, although in spite of using strong theorem provers. This quantity explains and illustrates another strategy, which permits the development of (necessarily right) algorithms from a specification utilizing algebraic adjustments and refinement suggestions which stop the advent of mistakes. in accordance with instructing fabric used generally at Loughborough college, John Cooke introduces the fundamentals, utilizing uncomplicated examples and many targeted operating (which can frequently be re-used). developing right software program will supply precious interpreting for college kids and practitioners of laptop technology and software program Engineering to whom correctness of software program is of top value.

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**Additional info for Constructing Correct Software (Formal Approaches to Computing and Information Technology)**

**Example text**

But the development of a software system does not start with the specification of the operations that it might perform but from a statement of the requirements that it should meet. To do this we need new logical forms with which to state these requirements and another level of design (between requirements and specifications), associated notions of refinement and so on. We cannot deal with these topics in this book, but we include a brief discussion of the ideas that need to be considered within the formal synthesis of software systems.

I|m) i divides m and .... ” We will not go into all the details but pick out some of the relevant factors used in the proper mathematical calculation (of the program scheme, not the answer to the gcd problem). 13 14 Also called the Highest Common Factor (HCF). Types are also called ‘sorts’ or ‘kinds’, but we shall not use these terms for types. , m is a multiple of i) with i,j: . Similarly, if i|n then n = i*k (for some k: ). Moreover and 1 ≤ i ≤ m, 1≤j≤m 1 ≤ i ≤ n, 1 ≤ k ≤ n. Obviously, if we were only asked to find any divisor of m and n, the number 1 would do; 1|m since m = 1*m etc.

4). It is also convenient here to give the definition of the graph of a function. The distinction between a function and its graph is often blurred, but here goes. Given a function f of type X — Y, the graph of f is the relation (which is of type (X Ù Y) ) consisting of the pairs ”x, f(x)’ for all x for which f(x) exists. ] Suppose now that x, the input value for R1, is known to be greater than 2. This is OK since “if x > 2 then x > 1” and the wp condition is met, but so we don’t spend effort working out a result for x = 2 (which will never be used) we can use the relation {”x,y’: X Ù X | x > 2 and x = y + 1} Of course, and is a logical connective, a logical operator, and we shall say much more about such things later.

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