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Variable types, sets and values

Definition 1   A variable type denotes a borned set of values taken by a one dimensional variable. If $\Omega$ is a set of variables $\{X_1,X_2,\ldots X_m\}$ with $\omega = \{X_1=x_1,X_2=x_2,\ldots X_m=x_m\} \in \Omega$ then we call $\Omega$ a variable set or space and $\omega$ a variable value of $\Omega$.

At the current version ProBT contains three variable types: the integer type (plIntegerType), the real type (plRealType) and the sparce type (plSparseType). Other types will be available in further ProBT versions. Examples of types are: $[1,2,\ldots100]\subset I\!\!N$, $[-1,1]\subset I\!\!R$ or $\{2, 5.6, 7.8\}$ counterexamples are: $I\!\!N$, $[1,2,\ldots100]^2 \subset I\!\!N^2$ or $[-1,1]^2\subset I\!\!R^2$.

A variable set is represented in ProBT by an abstract object class called plVariableSet and it has three derived classes : plSymbol, plArray and plVariable. A symbol is defined as a variable set containing one and only one unidimensional variable. Examples of symbols are :

$$\begin{array}{l} \{age\} \mbox{ with } age\in[0,1,\ldots,140... ...\{distance\} \mbox{ with } distance \in [0.5,23.5] \end{array}$$

An plArray is variable set containing $n$ unidimensional variables of the same type. Examples of this variable set are:

$${\small \begin{array}{l} \{price(0),price(1),\ldots,price(m)... ...n_z)\} \mbox{ with }point(i,j,k) \in [-200,200] \end{array} }$$

Defining multiple type variable sets is also possible in ProBT by using the object class plVariable. At the end of this chapter we give an example showing the use of the ``$\land$'' operator in order to create a multi type variable set such as:

$$\begin{eqnarray*} \{ age, height, sex\} &\mbox{with}& age\in[0,1,\ldots,130], height\in [0.15,3.0], sex \in [1,0] \\ \end{eqnarray*}$$

AVariable values stores the values of a given variable and they are called merely values (plValues) in ProBT. Examples of values are :

$$\begin{array}{l} \{age=24\} \\ \{distance=34.83\} \\ \{ima... ...},n_{c})=109\} \\ \{ age=27, height=1.77, sex=0\} \end{array}$$