Davide Ancona An Algebraic Approach to Mixins and Modularity

State Machines (alias evolving algebras as defined by Y. Gurevich) have been used to specify languages (e.g. Prolog, C++, VHDL) and architectures (e.g. PVM, APE100, Transputer, DLX), to validate standard language implementations (e.g. of Prolog, Occam), to verify numerous distributed and real-time protocols, etc.. See [2] for a recent survey and general discussion of the approach. In this talk, we explain the use the software designer can make of ASMs for a systematic modular development of well documented programs. We exemplify the method by an ASM solution of the production cell control problem (posed in the case study book Formal Development of Reactive Systems edited by C. Lewerentz and T. Lindner, Springer LNCS 891, 1995). As starting point we present the ground model which faithfully reflects the production cell as informally specified by C. Lewerentz and T. Lindner op. cit. We explain how the information hiding and abstraction mechanisms of ASMs allow the designer to formulate the ground model as an appropriate interface to the customer; this provides a possibility to discuss and negotiate with the customer, in rigorous yet simple terms of traditional mathematical language, so that one can come to a common understanding of the contract (i.e. of what the informal description really means) and of the conditions on its being met eventually by the algorithmic design. The modularity capabilities of ASMs are used to reflect in a direct way the distributed nature of the production cell. Starting from this abstract model of the system we define a series of refined models all the way to executable C code (which controls successfully the production cell simulation environment, running at FZI Karlsruhe). The ability of ASMs to reflect arbitrary abstraction levels facilitates the modular