A CATEGORICAL FRAMEWORK FOR CODE EVALUATION METHOD

Abstract

In the middle of the seventies Skordev proposed to consider in general the so-called fixpoint complete partially ordered algebras, introduced in [3]. The code evaluation method is an universal method for establishing a fixpoint completeness of such algebras. Its principal result - the code evaluation theorem (or the coding theorem, as it was called before) - implies easily all basic results of algebraic recursion theory. In the present work we give a categorical analysis of code evaluation proofs for operative spaces. Thus we obtain an algebraic formulation of the fundamentals of recursion theory which can be considered as an abstract recursion theory of higher level - by one level higher. compared with the usual theory of operative spaces [1]; and it may be otherwise considered as a generalization of the last theory in a new categorical direction, in which the role of multiplication in partially ordered semigroups is played by some kind of weak tensor product in partially ordered (weak) premonoidal categories.