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A theory of mixin modules: algebraic laws and reduction semantics

Published online by Cambridge University Press:  17 January 2003

DAVIDE ANCONA  and
ELENA ZUCCA
DAVIDE ANCONA
Affiliation:
Dipartimento di Informatica e Scienze dell'Informazione, Via Dodecaneso, 35, 16146 Genova (Italy) Email: davide@disi.unige.it, zucca@disi.unige.it
ELENA ZUCCA
Affiliation:
Dipartimento di Informatica e Scienze dell'Informazione, Via Dodecaneso, 35, 16146 Genova (Italy) Email: davide@disi.unige.it, zucca@disi.unige.it
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Abstract

Mixins are modules that may contain deferred components, that is, components not defined in the module itself; moreover, in contrast to parameterised modules (like ML functors), they can be mutually dependent and allow their definitions to be overridden. In a preceding paper we defined a syntax and denotational semantics of a kernel language of mixin modules. Here, we take instead an axiomatic approach, giving a set of algebraic laws expressing the expected properties of a small set of primitive operators on mixins. Interpreting axioms as rewriting rules, we get a reduction semantics for the language and prove the existence of normal forms. Moreover, we show that the model defined in the earlier paper satisfies the given axiomatisation.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 12 , Issue 6 , December 2002 , pp. 701 - 737
Copyright
2002 Cambridge University Press

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Footnotes

Partially supported by Murst (Tecniche formali per la specifica, l'analisi, la verifica, la sintesi e la trasformazione di sistemi software) and CNR (Formalismi per la specifica e la descrizione di sistemi ad oggetti).