From: Thomas Streicher <streicher@mathematik.tu-darmstadt.de>
To: Andrej Bauer <andrej.bauer@andrej.com>
Cc: categories list <categories@mta.ca>
Subject: Re: A category internal to itself
Date: Fri, 6 Sep 2013 14:33:37 +0200 [thread overview]
Message-ID: <E1VHvsJ-0000yO-62@mlist.mta.ca> (raw)
In-Reply-To: <CAB0nkh3zxgAV4tU1jr5ZTWw0exgQEcjGVSyRDqy=T0XE6DaG6Q@mail.gmail.com>
> The results would be a model of type theory (with ?? and ?? but no Id)
> which models Type : Type. It is not trivial, but all types are
> inhabited (and have the fixed-point property). We can still interpret
> Girard's paradox in it, but it is not really a paradox without
> identity types as the type structure does not collapse. Has something
> like that known? (I fully expect Thomas to pull something out of his
> beard.)
Indeed this was done in the Thesis of Nancy J. McCracken in 1979
supervised by John Reynolds. Its title is
An investigation of programming languages with a polymorphic type
structure.
Cardelli and Wegner got interested in this in the mid 1980s. There are
2 paper on this one can find on the web
Cardelli & Wegner On Understanding Types Data Abstraction and Polymorphism
Computing Surveys, Vol.17 (1985)
Cardelli A Polymorphic Lambda Calculus with Type:Type
a DEC report from 1986
That's what I have wrung out of my beard
Thomas
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next prev parent reply other threads:[~2013-09-06 12:33 UTC|newest]
Thread overview: 10+ messages / expand[flat|nested] mbox.gz Atom feed top
2013-09-04 9:23 Andrej Bauer
2013-09-04 20:04 ` Eduardo J. Dubuc
2013-09-04 22:11 ` Colin McLarty
2013-09-05 8:27 ` Edmund Robinson
2013-09-05 11:30 ` Zhen Lin Low
2013-09-05 13:44 ` Alex Simpson
[not found] ` <20130906080410.GA19753@mathematik.tu-darmstadt.de>
2013-09-06 8:20 ` Zhen Lin Low
[not found] ` <CAB0nkh3zxgAV4tU1jr5ZTWw0exgQEcjGVSyRDqy=T0XE6DaG6Q@mail.gmail.com>
2013-09-06 12:33 ` Thomas Streicher [this message]
[not found] ` <CAOzx82rUa8KRkngePON8Gh1KttzZ1-3AKNpP5DQNY7RfEj1VTQ@mail.gmail.com>
2013-09-05 11:46 ` Colin McLarty
[not found] ` <CAOOzEh-04Cq7L_k7v6qxWTYRhkWZw862kmPzLaSNZUgr8Zvzdw@mail.gmail.com>
2013-09-06 9:48 ` Andrej Bauer
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