From: "Martín Hötzel Escardó" <escardo.martin@gmail.com>
To: Homotopy Type Theory <HomotopyTypeTheory@googlegroups.com>
Subject: [HoTT] Agda formalization question
Date: Wed, 20 Jun 2018 12:43:15 -0700 (PDT) [thread overview]
Message-ID: <f6147773-786c-4f19-950d-60023c5a7294@googlegroups.com> (raw)
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This is really an Agda question, but because it involves HoTT concepts, and
because there are several Agda formalizers here, I prefer to ask it here
rather than in the Agda mailing list.
Forgive me is the question has a simple answer.
Consider the following constructions:
is-set' : ∀ {U} → U ̇ → U ̇
is-set' X = {x y : X} → is-prop(x ≡ y)
is-set' : ∀ {U} → U ̇ → U ̇
is-set' X = (x y : X) → is-prop(x ≡ y)
is-set'-is-set : ∀ {U} {X : U ̇} → is-set' X → is-set X
is-set'-is-set s {x} {y} = s x y
is-set-is-set' : ∀ {U} {X : U ̇} → is-set X → is-set' X
is-set-is-set' s x y = s {x} {y}
is-prop-is-set' : ∀ {U} {X : U ̇} → funext U U → is-prop (is-set' X)
is-prop-is-set' fe = is-prop-exponential-ideal fe
(λ x → is-prop-exponential-ideal fe
(λ y → is-prop-is-prop fe))
Now I am not able to prove that
is-prop-is-set : ∀ {U} {X : U ̇} → funext U U → is-prop (is-set X)
The reason is that funext has explicit parameters, and I don't seem to be
able to get funext with implicit parameters from funext with explicit
parameters. Am I missing something obvious?
(I am tempted to make is-set' the official version and ditch is-set, but
this will involve major rewriting of the Agda code.)
Martin
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next reply other threads:[~2018-06-20 19:43 UTC|newest]
Thread overview: 5+ messages / expand[flat|nested] mbox.gz Atom feed top
2018-06-20 19:43 Martín Hötzel Escardó [this message]
2018-06-20 19:46 ` [HoTT] " Martín Hötzel Escardó
2018-06-26 19:15 ` Favonia
2018-06-26 20:00 ` Martín Hötzel Escardó
2018-06-26 20:42 ` Favonia
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