* [HoTT] A setoid model of extensional Martin-Löf type theory in Agda
@ 2019-03-02 21:33 Erik Palmgren
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From: Erik Palmgren @ 2019-03-02 21:33 UTC (permalink / raw)
To: constructivenews, homotopytypetheory, Agda List
you may be interested in this development. It has been presented (in
preliminary form) at seminars at HIM Bonn, Göteborg and Stockholm during
"A setoid model of extensional Martin-Löf type theory in Agda"
Abstract. We present details of an Agda formalization of a setoid model
of Martin-Löf type theory with Pi, Sigma, extensional identity types,
natural numbers and an infinite hiearchy of universe à la Russell. A
crucial ingredient is the use of Aczel's type V of iterative sets as an
extensional universe of setoids, which allows for a well-behaved
interpretation of type equality.
(Not mentioned in the talks: There is also a formalized set-theoretic
model of the calculus of constructions in Coq by Bruno Barras which
however use classical logic.)
The the following link contains the Agda development (surely in need of
some cleaning up):
The README file should tell where to start.
A write up of this is being prepared. Comments are welcome.
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