In this paper we define a graph-theoretic formalization of programs with procedures and show how to approximate the classes of such programs by the algebraic models of programs with procedures. This approximation is achieved in two steps. First, we introduce a model of standard schemata with procedures that extend a well known model of standard (first-order) programs. We prove that to analyze the behavior of standard program schemata with procedures it is sufficient to consider on free (Herbrand) interpretations. At the next step we study algebraic models of programs of procedures and establish its relationship with standard model of programs with procedures. Thus, we arrive at the conclusion that the class of algebraic models of programs approximate programs with procedures.

model of programs, subroutine, approximation relation, algebraic model of programs

Mathematical problems and theory of numerical methods