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345e24d7
Commit
345e24d7
authored
Aug 12, 2019
by
Ralf Jung
Committed by
Robbert Krebbers
Aug 12, 2019
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fix typo in -d> docs
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74858b88
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theories/algebra/ofe.v
theories/algebra/ofe.v
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theories/algebra/ofe.v
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345e24d7
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@@ -1105,11 +1105,19 @@ Proof.
Qed
.
(** Dependently-typed functions over a discrete domain *)
(** We make [discrete_fun] a definition so that we can register it as a
canonical structure. Note that non-dependent functions over a discrete domain,
[discrete_fun (λ _, A) B] (or [A -d> B] following the notation we introduce
below) are isomorphic to [leibnizO A -n> B]. In other words, since the domain
is discrete, we get non-expansiveness for free. *)
(** This separate notion is useful whenever we need dependent functions, and
whenever we want to avoid the hassle of the bundled non-expansive function type.
Note that non-dependent functions over a discrete domain, [A -d> B] (following
the notation we introduce below) are non-expansive if they are
[Proper ((≡) ==> (≡))]. In other words, since the domain is discrete,
non-expansiveness and respecting [(≡)] are the same. If the domain is moreover
Leibniz ([LeibnizEquiv A]), we get both for free.
We make [discrete_fun] a definition so that we can register it as a canonical
structure. We do not bundle the [Proper] proof to keep [discrete_fun] easier to
use. It turns out all the desired OFE and functorial properties do not rely on
this [Proper] instance. *)
Definition
discrete_fun
{
A
}
(
B
:
A
→
ofeT
)
:
=
∀
x
:
A
,
B
x
.
Section
discrete_fun
.
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