Galois Connections and Fixed Point Calculus

Galois Connections and Fixed Point Calculus

Number of pages: 105

Recursion is a very powerful problem-solving technique that is used widely in computing science. It is used, for example, in the definition of programming languages, as a fundamental programming structure in functional and logic programming, and in the definition of data structures. A complete understanding of recursion can only be achieved by studying its algebraic properties. This tutorial covers fixed point calculus, which is about the solution of recursive equations defined by a monotonic endofunction on a partially ordered set. It presents the basic theory of fixed point calculus together with a number of applications of direct relevance to the construction of computer programs. The tutorial also presents the theory and application of Galois connections between partially ordered sets. In particular, the intimate relation between Galois connections and fixed point equations is amply demonstrated.

Home page url

Download or read it online for free here:
Download link
(0.5MB, PDF)

Similar books

Book cover: An Introduction to the Theory of ComputationAn Introduction to the Theory of Computation
by - Computer Science Pr
The book explores questions and terminologies concerning programs, computers, and computation. The exploration reduces to a study of mathematical theories, such as those of automata and formal languages, theories interesting in their own right.
Book cover: Languages and MachinesLanguages and Machines
by - Macquarie University
This is a text on discrete mathematics. It includes chapters on logic, set theory and strings and languages. There are some chapters on finite-state machines, some chapters on Turing machines and computability, and a couple of chapters on codes.
Book cover: Rule-based Computation and DeductionRule-based Computation and Deduction
This text first introduces the concept of rewriting which is behind rule-based systems. Then the rewriting logic and the rewriting calculus are defined and shown to be especially suited to describing concurrent and non-deterministic computations.
Book cover: Introduction to Computing: Explorations in Language, Logic, and MachinesIntroduction to Computing: Explorations in Language, Logic, and Machines
by - University of Virginia
An introduction to the most important ideas in computing. It focuses on how to describe information processes by defining procedures, how to analyze the costs required to carry out a procedure, and the limits of what can be computed mechanically.