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Summary: Towards Observational Type Theory
Thorsten Altenkirch and Conor McBride
School of Computer Science and Information Technology
University of Nottingham
{txa,ctm}@cs.nott.ac.uk
Abstract
Observational Type Theory (OTT) combines benefi-
cial aspects of Intensional and Extensional Type Theory
(ITT/ETT). It separates definitional equality, decidable as in
ITT, and a substitutive propositional equality, capturing ex-
tensional equality of functions, as in ETT. Moreover, canon-
icity holds: any closed term is definitionally reducible to a
canonical value.
Building on previous work by each author, this article
reports substantial progress in the form of a simplified the-
ory with a straightforward syntactic presentation, which we
have implemented.
As well as simplifying reasoning about functions, OTT
offers potential foundational benefits, e.g. it gives rise to a
closed type theory encoding inductive datatypes.
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