Integrating constraints and concurrent objects in musical applications: A calculus and its visual language

We propose PiCO, a calculus integrating concurrent objects and constraints, as a base for music composition tools. In contrast with calculi such as [5], [9] or TyCO [16], both constraints and objects are primitive notions in PiCO. In PiCO a base object model is extended with constraints by orthogonally adding the notion of constraint system found in the ρ-calculus [12]. Concurrent processes make use of a constraint store to synchronize communications either via the ask and tell operations of the constraint model or the standard message-passing mechanism of the object model. A message delegation mechanism built into the calculus allows encoding of general forms of inheritance. This paper includes encodings in PiCO of the concepts of class and sub-class. These allow us to represent complex partially defined objects such as musical structures in a compact way. We illustrate the transparent interaction of constraints and objects by a musical example involving harmonic and temporal relations. The relationship between Cordial, a visual language for music composition applications, and its underlying model PiCO is described.