an algebraic theory of recursive definitions and recursive languages
This is the introductory paper in a series devoted to a general algebraic theory of recursive definitions and recursive languages. In this paper we present the fundamental concepts and theorems concerning the basic structure (basic syntax), the semantics and the combination and manipulation of recursive definitions and the closure properties of recursive languages. The development is carried out within the framework of category theory and lattice theory. To illustrate the generality of the approach and our results we show how they apply directly to the specific examples of recursive languages of (generalized) context-free grammars, Turing machines, and flowcharts.
theory recursion definition language paper general concept structure semantic combinational manipulation developer lattice examples grammar  framework  context