The model works in two modes: in Mode 1, it displays the union and intersection of a given input pair of subsets; in Mode 2, it displays the decreasing subset associated with a selected element of the free distributive lattice FDL3. (The screenshot superimposes an inset of the display in Mode 1 upon the display in Mode 2.)
To operate the model in Mode 1:
The input values for x and y (entered through the screen interface) refer to subsets of {1,2,3} within the boolean lattice: they are specified as lists. The values of x and y can also be entered from the tkeden input window thus:
%eden
x=[1,2];
y=[2,3];
writeln (uxy);
writeln(ixy);
If the model is already in Mode 1, then entering values for x and y and pressing Go is sufficient to highlight the union [uxy] of the subsets x and y (in red) and their intersection [ixy] (in green). If the model is not in Mode 1 when the Go button is pressed, it is necessary to click on the 'Boolean Lattice 3' window, and wait whilst the necessary relations are computed. (This computational activity can be monitored in the output window.)
To operate the model in Mode 2:
Select an element in the free distributive lattice using the mouse, and the corresponding decreasing subset of the boolean lattice will be displayed as a set of blue nodes. Notice that clicking in the FDL window with no element selected returns the cutset for x||y||z as the default: this means that failure to select a node accurately also results in this default. (Element selection in FDL3 results in redefinition of the monotone boolean function referred to as fx in tkeden - its current value can be inspected to confirm this account of the model behaviour in Mode 2.)
The general screen layout can be improved by introducing the supplementary definitions that are recorded in the auxiliary file wmbsupp.script