**Galois Connections and Fixed Point Calculus**

by Roland Backhouse

2001**Number of pages**: 105

**Description**:

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.

Download or read it online for free here:

**Download link**

(0.5MB, PDF)

## Similar books

**Introduction to Computing: Explorations in Language, Logic, and Machines**

by

**David Evans**-

**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.

(

**11229**views)

**Models of Computation: Exploring the Power of Computing**

by

**John E. Savage**-

**Addison-Wesley**

The book re-examines computer science, giving priority to resource tradeoffs and complexity classifications over the structure of machines and their relationships to languages. This viewpoint is motivated by more realistic computational models.

(

**6431**views)

**Cellular Automata And Complexity: Collected Papers**

by

**Stephen Wolfram**-

**Westview Press**

These original papers on cellular automata and complexity provide a highly readable account of what has become a major new field of science, with important implications for computer science, physics, economics, biology, and many other areas.

(

**10368**views)

**Bayesian Computational Methods**

by

**Christian P. Robert**-

**arXiv**

We will first present the most standard computational challenges met in Bayesian Statistics, focusing primarily on mixture estimation and on model choice issues, and then relate these problems with computational solutions.

(

**6307**views)