Specification of Reactive Hardware/Software Systems - Electronic ...

256 Data Part of POOSL
8.7 Example: Complex Numbers
In this paragraph we give an example of the calculation of the semantics of a configuration
representing the addition of two complex numbers. A definition of a system Sys
which contains a class Complex of complex numbers is as follows:
Sys
data class Complex
instance variables re
im
instance methods init(r¥ i) add(comp)
re : r; ¡ i r res ¡
7
im : i; r : self real (comp real );
self i : self imag (comp imag );
res : new (Complex) init(r¥ i);
real res
re
imag
im
Calculating the sum of complex numbers, say (3+4i) and (8+9i), can be performed by
evaluating
( new (Complex) init(3¥ 4)) add( new (Complex) init(8¥ 9))
Syntactic entities 3, 4, 8, and 9 denote the direct naming of natural numbers 3, 4, 8 and 9.
The evaluation of this expression is reflected by a derivation sequence, starting with
configuration
( new init(3¥ (Complex) 4)) add( new init(8¥ 9))¥ ¤ ¥ ¥ ¤ ¥ Sys
(Complex)
In this configuration we have put brackets around expression new init(3¥ (Complex) 4),
although they are not part of the abstract syntax defined in Section 8.3. Such brackets
are used in ambiguous situations to explain the intended structure of expressions or
statements.
To ease readability we represent functions in a way explained by the following example:
Assume
F : A ¦£ (B ¦£ C)
7 Note that instead of self real and self imag we could have written re respectively im.