By Ryszard Kubiak; Roman Rudzinski; Stefan Sokolowski
A characteristic of recent complicated computing is the useful method of programming. during this e-book, the authors current an advent to the math which underline sensible 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 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 every one laptop 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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Additional info for An introduction to programming with specifications : a mathematical approach
4) provided y does not occur in e 2. The restriction is very important because indiscriminate renaming may cause errors. For instance, LET χ ΞΞ 1 IN LET y = 2 IN χ + y evaluates to 3. But when the variable χ is renamed y the result is LET y = 1 IN LET y = 2 IN y + y which evaluates to 4. When applying α-reduction, it is safe to rename bound variables to arbitrary variables not reserved for other purposes. 5) provided all variables shared by e\ and e2 are free in both and e\ is defined. Again, overlooking the constraints may cause errors.
LOCAL DEFINITIONS in LET χ = y IN LET y = 5 IN χ + y χ is bound and there are two unrelated t/s; this can be equivalently translated to LET χ = y IN LET y' = 5 IN χ + y' wherein y is free and y ' is bound. 3 R e d u c t i o n laws This section introduces a few laws that serve as the means for simplifying the LET expressions, frequently without the necessity of evaluating them. Again, as in the case of conditional expressions, these laws may be used to simplify expressions in the outermost-first or another non-standard order.
5) provided there is no type error and b is defined, states that sometimes the conditionals are superfluous. The requirement of the definedness of b is essential: for instance, the value of IF 1/x = 1 THEN χ ELSE χ does not always coincide with the value of x, namely for χ = 0 the former is undefined while the latter is 0. 11) we assume that all expressions involved are well-typed and all Boolean conditions b (possibly with indices) have defined values. Conditionals satisfy the following form of commutativity: (IF b THEN ei ELSE e 2) = (IF -.