An introduction to programming with specifications : a - download pdf or read online

An introduction to programming with specifications : a - download pdf or read online

By Ryszard Kubiak; Roman Rudzinski; Stefan Sokolowski

ISBN-10: 0124276202

ISBN-13: 9780124276208

A function of recent complex computing is the practical method of programming. during this booklet, the authors current an creation to the maths which underline sensible programming, emphasizing the knowledge of definition and specification--a prerequisite of excellent programming and challenge fixing with a working laptop or computer. The publication is self-contained, requiring a low point of mathematical sophistication and will be used as an creation to the math of programming.

Provides an advent to the sensible method of programming**Emphasizes the matter to be solved, now not the programming language**Takes the view that every one desktop courses are a definition of a function**Includes workouts for every chapter**Can be used as a pre-programming language creation to the math of computing.

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Extra resources for An introduction to programming with specifications : a mathematical approach

Sample text

T h e c u s t o m e r w o u l d p r o b a b l y b e dissatisfied w i t h t h i s s o l u t i o n , y e t h e w o u l d h a v e t o a c c e p t it since it m e e t s his specification. O n t h e o t h e r h a n d , a s p e c i f i c a t i o n d o e s n o t generally give a n y h i n t s h o w t o realize it, so t h e p r o g r a m m e r ' s t a s k t a k e s talent too. 3 Function specifications a n d realizations P a r t i a l f u n c t i o n s are t h e o b j e c t s w e are g o i n g t o specify a n d define in t h i s b o o k m o r e often t h a n a n y t h i n g else.

IFx>yTHEN(x,2/) ELSE IF χ = y THEN χ ELSE ( y , x ) for x, y : Real c. 2 2 IF (a > 6) Λ ( a > 6 ) THEN (a, 6) ELSE (6, a) for a, 6 : /tea/ d. IF x 2 > y 2 THEN {false, y) ELSE (x, irue) for χ, ι/ : Nat e. IF η = 1 THEN abs ELSE sgn for η : 7n£ 38 3. CONDITIONAL EXPRESSIONS 3. In the absence of logical connectives, the conditional expressions provide a means for defining them. : a Bool x Bool —• Bool b = IF a THEN b ELSE true Define the remaining connectives, ->, V and Λ , alike. 4. 12) and the solution of Exercise 3 above that a.

Vy. 3y. / ( x ) + /(j/) = 5 6. D o t h e following f u n c t i o n s m e e t t h e c o r r e s p o n d i n g specifications? a. function: c : Int —> Int 2 c(i) = i specification: h : Int —> Int Vz : Int. 5. b. Exercises 29 function: specification: q : Int χ Int —> Nat 2 2 χ Να£ ρ : Int χ Int —• Afa£ χ iVa£ g(i,j)^(z ,j ) c. p(l,2)=p(-2,-l) function: g : A t o χ Real —• £ 0 0 / specification: / : Afai χ iteaZ —> £ooZ g(n, x) = ( ^ / x > 0) Vx > 0. / ( 2 , x ) 7. R e a l i z e t h e following specifications a n d prove t h e r e a l i z a t i o n s correct.

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


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