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Datatype laws without signatures

Published online by Cambridge University Press:  04 March 2009

Maarten M. Fokkinga
Maarten M. Fokkinga
Affiliation:
University of Twente, dept. INF, P.O. Box 217, 7500 AE Enschede, The Netherlands Email: fokkinga@cs.utwente.nl
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Abstract

Using the well-known categorical notion of ‘functor’, one may define the concept of datatype (algebra) without being forced to introduce a signature (that is, names and typings for the individual sorts (types) and operations involved). This has proved to be advantageous for those theory developments where one is not interested in the syntactic appearance of an algebra.

The categorical notion of ‘transformer’ developed in this paper allows the same approach to laws: without using signatures one can define the concept of law for datatypes (lawful algebras), and investigate the equational specification of datatypes in a syntax-free manner. A transformer is a special kind of functor and also a natural transformation on the level of dialgebras. Transformers are quite expressive, satisfy several closure properties, and are related to naturality and Wadler'' Theorems For Free Theorem. In fact, any colimit is an initial lawful algebra.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 6 , Issue 1 , February 1996 , pp. 1 - 32
Copyright
Copyright © Cambridge University Press 1996

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