Partial Composition and Recursion of Module Specifications

The basic interconnections of module specifications (union, composition and actualization) were studied in earlier papers. Here we introduce partial composition and partial actualization of module specifications, describe the connection with their "total" counterpart and prove that the result of successive partial compositions (or actualizations) is independent of the order. We also introduce a recursive construction first of a single module and then of two modules "recursivety calling" each other. A connection between these two recursions is established, along with compatibility properties with the basic constructions and the expected fixed point equation at the semantical level.