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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...
In this paper we take a new look at one of the basic principles of abstract data types. Due to this principle the domain of an abstract data type must be generated by the operations. In the initial algebraic approach as well as in the loose case with initial restrictions or data constraints this principle is satisfied because of initiality resp. free construction. Actually initiality makes sure that...
In a wide variety of situations, computer science has found it convenient to define complex object as (fixed-point) solutions of certain equations. This has been done in both algebraic and order-theoretic settings, and has often been contrasted with other approaches. This paper shows how to formulate such solutions in a setting which encompasses both algebraic and order-theoretic aspects, so that...
Many apparently divergent approaches to specifying formal semantics for programming languages are applications of initial algebra semantics. Here we provide an overview of the concept of initial algebra semantics.
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