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ETA-RULES IN MARTIN-LÖF TYPE THEORY

Published online by Cambridge University Press:  22 July 2019

ANSTEN KLEV
ANSTEN KLEV*
Affiliation:
INSTITUTE OF PHILOSOPHY CZECH ACADEMY OF SCIENCES JILSKÁ 1, PRAGUE 1, 110 00, CZECH REPUBLIC E-mail:klev@flu.cas.cz
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Abstract

The eta rule for a set A says that an arbitrary element of A is judgementally identical to an element of constructor form. Eta rules are not part of what may be called canonical Martin-Löf type theory. They are, however, justified by the meaning explanations, and a higher order eta rule is part of that type theory. The main aim of this article is to clarify this somewhat puzzling situation. It will be argued that lower order eta rules do not, whereas the higher order eta rule does, accord with the understanding of judgemental identity as definitional identity. A subsidiary aim is to clarify precisely what an eta rule is. This will involve showing how such rules relate to various other notions of type theory, proof theory, and category theory.

Keywords

03B1503A05type theorydefinitional identityjustification of logical laws
Type
Articles
Information
Bulletin of Symbolic Logic , Volume 25 , Issue 3 , September 2019 , pp. 333 - 359
Copyright
Copyright © The Association for Symbolic Logic 2019 

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