# Some fundamentals of order-algebraic semantics

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## Abstract

The order-theoretic enrichment of the algebraic approach to theoretical computer science, and to the theory of programming in particular, can be accomplished rather directly and elegantly, and appears to have a wide range of applications. This paper presents mathematical fundamentals of order-algebraic semantics. The principal new results concern free continuous algebraic theories and minimal conditions for solving general "systems of (recursive) equations" in algebraic theories.

## Keywords

Minimum Element Partial Function Category Theory Rational Theory Algebraic Theory
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## Copyright information

© Springer-Verlag Berlin Heidelberg 1976