[Agda] Why no impredicative prop?

[Thorsten Altenkirch]

Actually why do you need an impredicative universe?

>From a purely pragmatic point it is a bit strange if one universe behaves different from the other one. But having two impredicative universes is already unsound.

More on the philosphical side: impredicativity is basically a classical idea which arises from the identification of Prop and Bool. I don’t know an intuitionistic justification of impredicativity.

Thorsten

From: <agda-bounces at lists.chalmers.se<mailto:agda-bounces at lists.chalmers.se>> on behalf of Timothy Carstens <intoverflow at gmail.com<mailto:intoverflow at gmail.com>>
Date: Tuesday, 29 December 2015 17:19
To: "agda at lists.chalmers.se<mailto:agda at lists.chalmers.se>" <agda at lists.chalmers.se<mailto:agda at lists.chalmers.se>>
Subject: [Agda] Why no impredicative prop?

Hello,

I'm a relatively new Agda user, coming from a background using Coq for the past few years. As is well known, Coq has an impredicative Prop sort, while Agda does not.

Why not? Is it simply a matter of project goals, or is there something about Agda's underlying theory which is incompatible with having an impredicative sort at the bottom of the universe hierarchy?

Forgive me if this is an old topic or has an obvious answer; I'm not a logician, but I use proof assistants at work.
-t





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