Mazzola, Guerino / Noll, Thomas / Lluis-Puebla, Emilio: Perspectives in Mathematical and Computational Music Theory

Boxes represent functional calls while connections represent functional composition. Figure 2 shows the editor of a patch computing the expression (3 * 5) + 2.

Figure 2:

Example of patch.

Boxes are placed in patches and allow other meta-objects to be involved in the calculus. Boxes consist of an icon and an ordered set of inlets and outlets. There are different types of boxes depending on the referential meta-object. The user may create boxes in a patch by dragging meta-objects into it. Boxes and connections in a patch can be seen as a graph of functional compositions. By clicking on the output of a box, an evaluation from the corresponding point into the graph is triggered. The evaluation of a box can give rise to other box evaluations and it may create a chain corresponding to the execution of a program.

The patch abstraction mechanism is very straightforward. Abstractions in a patch are made by adding input and output boxes. When a patch icon is dropped in a patch editor, it appears as a patch invocation box. Inputs and outputs eventually belonging to the patch appear then as small inlets and outlets of the box. Therefore, patches can be used again in other patches, even in a recursive way (see Figure 3).

Figure 3:

Factorial definition and invocation.

Patches offer several original features, such as reflexivity, meta-programming capacities and persistence. We do not describe here patches in detail. For a complete formalization of the visual language see (Agon, 1998). For the purpose of this paper, we must keep in mind the idea that patches denote composition processes.