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Structural subtyping for inductive types with functorial equality rules†

Published online by Cambridge University Press:  01 October 2008

ZHAOHUI LUO  and
ROBIN ADAMS
ZHAOHUI LUO
Affiliation:
Department of Computer Science, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom Email: zhaohui@cs.rhul.ac.uk
ROBIN ADAMS
Affiliation:
Department of Computer Science, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom Email: robin@cs.rhul.ac.uk
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Abstract

In this paper we study subtyping for inductive types in dependent type theories in the framework of coercive subtyping. General structural subtyping rules for parameterised inductive types are formulated based on the notion of inductive schemata. Certain extensional equality rules play an important role in proving some of the crucial properties of the type system with these subtyping rules. In particular, it is shown that the structural subtyping rules are coherent and that transitivity is admissible in the presence of the functorial rules of computational equality.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 18 , Special Issue 5: Theory and applications of subtyping , October 2008 , pp. 931 - 972
Copyright
Copyright © Cambridge University Press 2008

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