Axiomatic criteria for quotients and subobjects for higher-order data types

Authors:
Jo Hannay
Affiliations:
Department of Software Engineering, Simula Research Laboratory, Lysaker, Norway
Venue:
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Year:
2003

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Abstract

Axiomatic criteria are given for the existence of higher-order maps over subobjects and quotients. These criteria are applied in showing the soundness of a method for proving specification refinement up to observational equivalence. This generalises the method to handle data types with higher-order operations, using standard simulation relations. We also give a direct setoid-based model satisfying the criteria. The setting is the second-order polymorphic lambda calculus and the assumption of relational parametricity.