A Unified Mathematical Model of Programs

Despite the rich depository of empirical knowledge on programming and software engineering, the theoretical model of programs is still unknown. This paper presents an embedded relational model (ERM) for describing the nature of programs. ERM provides a unified mathematical treatment of programs, which reveals that a program is a large and finite set of embedded binary relations between a given current statement and all previous ones that formed the semantic context or environment of computing. According to the ERM model, a program is a composed listing and a logical combination of multiple statements according to certain composing rules. A set of 17 meta statements and a set of 17 compositional relations in computing are elicited in real-time process algebra (RTPA). Based on the ERM model, a set of mathematical laws of programming is formally established