Primitive program algebras. II

Reduction programming in a technological programming environment

“…The closure is a definition of composites as programming concepts, basic object operations, and composite-composite interfaces. In this way, we will build an arithmetic TPS based on the results of compositional programming and studies of the class of computational arithmetic functions and predicates [12,13]. As a programming platform, we will use composite programming and a nominal model of data, functions, and operations, as composites -multiplication operations º, branching IF, cycling WD and the simplest compositions derived from them (in the sense of application operations Ap and n-ary superposition…”

The completeness modulo ideal in functional systems of a program type

“…As Ω one can take the class of Yanov's program schemes with the same sets Ρ and Q [2]. At the end of the article we show the possibility of extension of the concept of the completeness modulo ideal to many-place functions and predicates (for example Redko's program logics [3] or Zaslavskii's graph-schemes with memory [4]).…”

“…As Ω one can take the class of Yanov's program schemes with the same sets Ρ and Q [2]. At the end of the article we show the possibility of extension of the concept of the completeness modulo ideal to many-place functions and predicates (for example Redko's program logics [3] or Zaslavskii's graph-schemes with memory [4]).Generalizing results of investigations of various functional systems Kudryavtsev noted [5] that 'the results on completeness, being negative on the whole from the point of view of their effectiveness, leads us to the necessity to consider various modifications of that problem'. There are some modifications for which criterial systems appear to be simpler than those for the ordinary completeness.…”