From: Dimitris Tsementzis <dtse...@princeton.edu>
To: Homotopy Type Theory <HomotopyT...@googlegroups.com>
Subject: A question regarding certain rules
Date: Mon, 9 Oct 2017 13:41:51 -0400 [thread overview]
Message-ID: <01C857D9-9B30-4836-8F22-761A678B5D53@princeton.edu> (raw)
Dear all,
Is there a type theory that has been considered in the literature which includes *both* the following rules
Γ |- t : T
———————— (R1)
Γ |- t : C(T)
Γ |- t : T
———————— (R2)
Γ |- p(t) : C(T)
where C(T) is a type expression, p(t) is a term expression, t is a term expression that must appear in p(t), and T is a type expression that may or may not appear in C(T).
An example of (R1) is (U-CUMUL) as in the HoTT book, i.e. cumulativity of universes.
An example of (R2) is (Nat-intro-2) as in the HoTT book, i.e. the successor for Nat (with C(T) == Nat).
Best,
Dimitris
next reply other threads:[~2017-10-09 17:41 UTC|newest]
Thread overview: 3+ messages / expand[flat|nested] mbox.gz Atom feed top
2017-10-09 17:41 Dimitris Tsementzis [this message]
2017-10-09 17:54 ` [HoTT] " Gaëtan Gilbert
2017-10-10 3:06 ` Dimitris Tsementzis
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