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

By Ryszard Kubiak; Roman Rudzinski; Stefan Sokolowski

A function of contemporary complex computing is the useful method of programming. during this e-book, the authors current an advent to the math which underline practical programming, emphasizing the certainty of definition and specification--a prerequisite of excellent programming and challenge fixing with a working laptop or computer. The e-book is self-contained, requiring a low point of mathematical sophistication and will be used as an advent to the maths 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 each 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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LOCAL DEFINITIONS LET α ΞΞ abs IN LET s ΞΞ IN a ( s ( - l ) ) 3. Find an example of three expressions e, e i and e 2 with a variable χ such that the value of e\ is equal to the value of e 2 under any valuation of variables but the values of e\[e/x] and e 2[ e / x ] differ for some valuations. 4. Find free and bound variables in the following expressions and simplify the expressions using the a - and /3-reductions: a. LET χ = LET y ΞΞ χ IN y IN y b. LET χ = y + ζ IN LET y = χ - ζ IN χ + y c. LET χ = χ + 1 IN 2x + 1 + (LET χ ΞΞ 2x IN 2x + 1) 5.

2) is a n e w n a m e w e i n t r o d u c e for t h e c o n c e p t d e n o t e d e x p r e s s i o n . T h e l a t t e r h a s t o b e e x p r e s s e d in o l d t e r m s , w h i c h in p a r t i c u l a r m e a n s t h a t it m u s t n o t refer t o definiendum. ΞΞ is t h e s o - c a l l e d defining equality, T h e sign t h e c o u n t e r p a r t of t h e w o r d s "is" a n d "means" in t h e e x a m p l e s w e h a v e s e e n s o far. 1). It serves t o i n t r o d u c e n e w n o t i o n s i n t o our v o c a b u l a r y .

2. e. SPECIFICATIONS Λ Vz : Int. g(i) = 2 · g(0) h : Να* χ JVa£ Nat χ TVai Vn, k : Nat. ea/. (/c(x)) + 9 Real 2 dom(k) 4. AND g : Int —> Int 0 e dom(g) d. ON DEFINITIONS < 6 · fc(x) E x p l a i n in plain E n g l i s h w h a t o b j e c t s are d e s c r i b e d by t h e following specifications: a. a : Real 3k : Int. a — k b. ( m , n ) : Int χ Int Va : TVai. a • m = η c. d. Vx : Real. \/(iJ) : Int χ Jra*. / ( z , j ) < fc 5. Let / b e defined as follows: / : Real —> Real ί{χ) = χ 2 D o e s / satisfy t h e following specifications?

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