The Coq mailing list

[Altenkirch Thorsten <psztxa AT exmail.nottingham.ac.uk>]

Isn't an impredicative Prop nothing else but a universe which is closed under impredicative Pi-types (I.e. Pi-types whose domain is on the same level as the whole Pi-type)?

One argument against a universe closed under impredicative Pi is that you only have it once, I.e. you cannot have two universes Type(0), Type(1) with Type(0) : Type(1) and both of them closed under impredicative Pi-types.

Thorsten

From: "Benjamin C. Pierce" <bcpierce AT cis.upenn.edu>
Date: Tue, 31 Jul 2012 16:07:01 +0100
To: Arnaud Spiwack <aspiwack AT lix.polytechnique.fr>
Cc: Bas Spitters <spitters AT cs.ru.nl>, "coq-club AT inria.fr" <coq-club AT inria.fr>
Subject: Re: [Coq-Club] Simplest example of impredicative Prop?

Very interesting.  Just to check: this is saying that we need a universe *instead of* impredicative Prop for this example?

   - B

On Jul 31, 2012, at 3:16 AM, Arnaud Spiwack wrote:

Mmm, very clever.

My bad then. I'll have to retract my example.

On 30 July 2012 15:40, Bas Spitters <spitters AT cs.ru.nl> wrote:

> surjectivity is equivalent to being epi in the category of setoids

You need at least a universe to prove this statement:
http://www2.math.uu.se/research/pub/Wilander2.pdf

but if you have a universe the statement can be proved.

Bas

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