By Ryszard Kubiak; Roman Rudzinski; Stefan Sokolowski

A function of recent complicated computing is the practical method of programming. during this publication, 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 booklet is self-contained, requiring a low point of mathematical sophistication and should be used as an advent to the maths of programming.

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

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

**Sample text**

5) where A and Β are types and the right-hand side of the equality may refer to / . 1. 5) in the sense that it has the least domain, and all other solutions have to coincide with it over this domain. 6) is not a valid definition since the notions "evaluation generated by a specification for an argument" and "result of evaluation" have not been formally introduced. In fact, not every specification of the form gives rise to evaluations. For instance, the specification / : Int —> Int Mi : Int. f(i) = (IF / is increasing THEN -i ELSE i) does not.

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. 2, e a c h specification is in fact a definition of a set. In particular, a f u n c t i o n specification s h o u l d define a set of f u n c t i o n s . For i n s t a n c e , a s p e c i f i c a t i o n of i n c r e a s i n g f u n c t i o n s from Nat t o Nat m a y b e g i v e n b y t h e following set comprehension: ss = {s : Nat —• Nat | Vn : Nat.

12) that abs(x — y) + abs(x + y) = 2max(abs(x), abs(y)) 9. How many functions do satisfy the following specifications? a. / : Real —• Real dom(f) = Real A Vx,y : Real. IF χ > y THEN f(x) ELSE f{x) = b. g : Nat -+ dom(g) f(y) Bool = Nat A Vn : Ato. 1 I n t r o d u c t i o n t o local definitions Compare the following occurrences of definitions in fictitious mathematical texts: • By a quadrangle we mean a polygon with exactly four angles. A quadrangle with four right angles is termed a rectangle.