Turning an Abstract Function into a Concrete Function

This mode of writing gives the basic structure of such a mapping but tells nothing about the details how such a function works. To transform such an abstract connection into a concrete working function one has therefore to make additional assumptions, e.g.:

$$POP \subseteq RealNumbers$$ (3.3)

$$ChR \subseteq RealNumbers$$ (3.4)

$$\textbf{mul} : RelNumbers \times RealNUmbers \longmapsto RealNumbers$$ (3.5)

$$\textbf{add} : RelNumbers \times RealNUmbers \longmapsto RealNumbers$$ (3.6)

$$mul := multiplication$$ (3.7)

$$add := addition$$ (3.8)

$$\textbf{f1} = add(POP, mul(POP, ChR))$$ (3.9)

Figure 3.5: Turn an abstract function into a concrete function

This can again be represented in a diagram by opening the box of the dependency $f1$ as abstract function and filling the content of the f1-box up with already known functions like $add()$ and $mul()$. Doing this we give the abstract function $f1$ an operational meaning (cf. figure 3.5).