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 -- You received this message because you are subscribed to the Google Groups "Homotopy Type Theory" group. To unsubscribe from this group and stop receiving emails from it, send an email to HomotopyTypeTheory+unsubscribe@googlegroups.com. For more options, visit https://groups.google.com/d/optout.