An introduction to programming with specifications : a by Ryszard Kubiak; Roman Rudzinski; Stefan Sokolowski

By Ryszard Kubiak; Roman Rudzinski; Stefan Sokolowski

A characteristic of contemporary complex computing is the practical method of programming. during this e-book, the authors current an creation to the math which underline practical programming, emphasizing the knowledge of definition and specification--a prerequisite of fine programming and challenge fixing with a working laptop or computer. The ebook is self-contained, requiring a low point of mathematical sophistication and should be used as an creation to the maths of programming.

Provides an advent to the useful method of programming**Emphasizes the matter to be solved, no longer the programming language**Takes the view that each one desktop courses are a definition of a function**Includes routines for every chapter**Can be used as a pre-programming language advent to the math of computing.

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W i t h a g e n u i n e b r o w n i e s t a n d i n g in p l a c e of t h e d o t s . T h e s p e c i f i c a t i o n of b r o w n i e s is o b v i o u s l y difficult t o realize. If y o u are over s i x years of a g e y o u are p r o b a b l y c o n v i n c e d it is unsatisfiable. It is w o r t h n o t i c i n g t h a t b o t h a c t i v i t i e s , s p e c i f y i n g a n d realizing a s p e c ­ ification, require skill a n d ingenuity. O n t h e o n e h a n d , it is e a s y t o w r i t e a specification t h a t d o e s n o t a d e q u a t e l y reflect o n e ' s i n t u i t i v e l y p e r c e i v e d n e e d s a n d a d m i t s trivial s o l u t i o n s .

For instance, (a + 6 ) [ ( c + l ) / 6 ] = a + ( c + l ) (Vn : Nat. (3x η > k)[l/k] : Real, x 2 = (Vn : Nat. = 0)[0/x] = (3x η > 1) 2 : Real, x = 0) Note that there are no free xs in the last formula. A warning regarding the operation of substitution is due. This is a syntactic operation and the value of the resulting expression may depend not only on the value of the expression in which the substitution is performed, but also on its syntactic shape. In other words, even if e\ and e 2 are equal for any valuations the values of e\\ejx\ and e2[e/x] are not necessarily equal (see Exercise 3 to this chapter).

Tortoise m e a n s zolw. — b o t h are perfect definitions p r o v i d e d y o u u n d e r s t a n d t h e defining t e r m s . If y o u k n o w w h a t are E n g l a n d , W a l e s , S c o t l a n d a n d N o r t h e r n Ireland, a n d also y o u are familiar w i t h t h e o p e r a t i o n "union" t h a t t a k e s a n u m b e r of countries a n d delivers a ( c o m p o s i t e ) country, t h e n t h e former definition u n i q u e l y tells y o u w h a t t h e U n i t e d K i n g d o m is. T h e l a t t e r definition is similar: if y o u k n o w w h a t z o l w is, w h i c h y o u p r o b a b l y d o not u n l e s s y o u s p e a k P o l i s h , t h e definition e x p l a i n s a d e q u a t e l y t h e c o n c e p t of t o r t o i s e .

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