**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 Theory of Computation**

by

**Anil Maheshwari, Michiel Smid**-

**Carleton University**

This is a textbook for an undergraduate course on the Theory of Computation. Contents: Finite Automata and Regular Languages; Context-Free Languages; Turing Machines and Church-Turing Thesis; Decidable and Undecidable Languages; Complexity Theory.

(

**3527**views)

**Languages and Machines**

by

**C. D. H. Cooper**-

**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.

(

**14391**views)

**Logic and Proof**

by

**Lawrence C Paulson**-

**University of Cambridge**

These lecture notes give a brief introduction to logic, with including the resolution method of theorem-proving and its relation to the programming language Prolog. Formal logic is used for specifying and verifying computer systems.

(

**9108**views)

**An Introduction to the Theory of Computation**

by

**Eitan Gurari**-

**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.

(

**24116**views)