By Dr D. John Cooke (auth.)
Constructing right software program - The Basics illustrates and explains the confident method of software program improvement. This strategy consists of calculating a solution from the preliminary assertion of necessities or specification, instead of "guessing" a solution after which trying out no matter if it really works. It makes use of an analogous simple idea as conventional thoughts, yet is far swifter and more uncomplicated as no "wrong solutions" are bought, and as a result no unsuitable paintings has to be discarded. John Cooke has dependent this e-book on fabric which has been used to educate the subject broadly at Loughborough collage. it's been rigorously written to be obtainable to someone with a suitable uncomplicated historical past wisdom of formal tools. it truly is meant for 3rd/4th yr undergraduate and postgraduate scholars on formal tools and software program engineering classes, and software program builders in who desire a extra pragmatic, but totally formal, method of software program improvement.
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Extra info for Constructing Correct Software: The Basics
In relation Rt, the input value, x, is of type X. X is the source of Rt (the set from which input values may be selected). Similarly, Y is the target of R 1 (the set of potential results). It is important to know these sets - even if they are the same as each other, as in R4 - different source and target sets can give rise to different relations even when the 'same formula' is used in the definition. 6 The interpretation here is quite straightforward. The dot at intersection of lines representing x 2 and y 1 represents the arrow from 2 to 1 and indicates that (2,1) E Rt.
3y:Y) ((x,y)ER) means "that there is - usually written without the gap in the middle - value of type Y, we call it 'y', such that the expression '(x,y)ER' is True". som~ [As we shall see the logical notion of "existential quantification" - the symbol 3 works in exacdy the same way as local variables in block-structured programming languages. No more, no less. ] 41 SPECIFICATION OF FUNCTIONS 1 Also defined- and quite often seen in specifications- is the mirror-image concept of the range of the relation R.
Notice also that plq represents the exact fractional answer but the answer to the div(p, q) function evaluation is n, an integer. Infact n=p+q Notice how we use "fi" to close the 'if then else' construct. This avoids ambiguity in other similar situations. 7 CONSTRUCTING CORRECT SOFIWARE 18 so 3 +2 = 1 2+ 3 = o 7 +3 = 2 remainder 1 remainder2 remainder 1 etc .. e. multiplying through by 2, and in general 1*2 = 2 s; 3 < 4 = 2*2 n*q :5 p < (n+1) *q Similarly, 0*3 s; 2 < (0+ 1) * 3 and 2*3 s; 7 < (2+1) * 3.