Complexity Theory and the Operational Structure of Algebraic Programming Systems

An algebraic programming system is a language built from a fixed algebraic data abstraction and a selection of deterministic, and non-deterministic, assignment and control constructs. First, we give a detailed analysis of the operational structure of an algebraic data type, one which is designed to classify programming systems in terms of the complexity of their implementations. Secondly, we test our operational description by comparing the computations in deterministic and non-deterministic programming systems under certain space and time restrictions

Los conceptos de biología adquiridos en el proceso de aprendizaje

AbstractAn extensive survey is given of the properties of various specification mechanisms based on initial algebra semantics

Partial arithmetical data types of rational numbers and their equational specification

Upon adding division to the operations of a field we obtain a meadow. It is conventional to view division in a field as a partial function, which complicates considerably its algebra and logic. But partiality is one out of a plurality of possible design decisions regarding division. Upon adding a partial division function ÷ to a field Q of rational numbers we obtain a partial meadow Q (÷) of rational numbers that qualifies as a data type. Partial data types bring problems for specifying and programming that have led to complicated algebraic and logical theories – unlike total data types. We discuss four different ways of providing an algebraic specification of this important arithmetical partial data type Q (÷) via the algebraic specification of a closely related total data type. We argue that the specification method that uses a common meadow of rational numbers as the total algebra is the most attractive and useful among these four options. We then analyse the problem of equality between expressions in partial data types by examining seven notions of equality that arise from our methods alone. Finally, based on the laws of common meadows, we present an equational calculus for working with fracterms that is of general interest outside programming theory