[Agda] A setoid model of extensional Martin-Löf type theory in Agda

[Erik Palmgren]

Dear all,

you may be interested in this development. It has been presented (in 
preliminary form) at seminars at HIM Bonn, Göteborg and Stockholm during 
2018.

"A setoid model of extensional Martin-Löf type theory in Agda"

Erik Palmgren

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):

http://staff.math.su.se/palmgren/From-type-theory-to-setoids-and-back.zip

The README file should tell where to start.

A write up of this is being prepared. Comments are welcome.



    Erik Palmgren