Re: [Ur] Generating fresh name (gensym :: {Unit} -> Name).
On 07/09/2017 05:58 PM, Peter Brottveit Bock wrote:
You mean something like
val lolli_right'' :
n :: Name -> [[n] ~ gamma] =>
t0 ::: Type -> t1 ::: Type -> gamma ::: {Type} ->
(n :: Name -> [[n] ~ gamma] => lin (gamma ++ [n = t0]) t1) ->
lin gamma (lolli t0 t1)
?
Yeah, that would be possible to implement, but it wouldn't really be an
improvement, would it?
Yes, that's what I meant. The added benefit is that you really do have
exactly the proof terms you were looking for; they just have these extra
names tacked on them, but you can ignore those from a formal perspective!
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Re: [Ur] Generating fresh name (gensym :: {Unit} -> Name).
Thanks for the quick reply!
On Sun, 9 Jul 2017, at 23:22, Adam Chlipala wrote:
> Short answer: I can't think of any way to implement that feature, with
> Ur as it stands today.
>
> It seems consistent with the model of Ur in Coq, though the
> representation of rows might need to be extended to allow iteration even
> without a folder (to find a fresh name).
I honestly hadn't thought about the possibility of defining it within Ur, but
that's of course something I should have thought about. Anyway, to extend
Ur so that it is possible would require a non-trivial effort I guess.
> Well, you could combine the two: take in a polymorphic premise, but also
> ask for a concrete disjoint name to be passed at the top level. The
> implementation can instantiate the premise with the concrete name.
You mean something like
val lolli_right'' :
n :: Name -> [[n] ~ gamma] =>
t0 ::: Type -> t1 ::: Type -> gamma ::: {Type} ->
(n :: Name -> [[n] ~ gamma] => lin (gamma ++ [n = t0]) t1) ->
lin gamma (lolli t0 t1)
?
Yeah, that would be possible to implement, but it wouldn't really be an
improvement, would it?
— Peter
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Re: [Ur] Generating fresh name (gensym :: {Unit} -> Name).
On 07/09/2017 05:11 PM, Peter Brottveit Bock wrote:
Is it possible to generate a fresh name relative to some collection of names? I.e. something
of kind "gensym :: {Unit} -> Name".
Short answer: I can't think of any way to implement that feature, with
Ur as it stands today.
Does it break some nice meta-properties of Ur/Web?
It seems consistent with the model of Ur in Coq, though the
representation of rows might need to be extended to allow iteration even
without a folder (to find a fresh name).
I have two possible types which can be used to represent this:
val lolli_right :
t0 ::: Type -> t1 ::: Type -> gamma ::: {Type} ->
(n :: Name -> [[n] ~ gamma] => lin (gamma ++ [n = t0]) t1) ->
lin gamma (lolli t0 t1)
and
val lolli_right' :
n ::: Name -> t0 ::: Type -> t1 ::: Type -> gamma ::: {Type} ->
[[n] ~ gamma] =>
lin (gamma ++ [n = t0]) t1 ->
lin gamma (lolli t0 t1)
The first type is arguably nicer, since when used as a proof term, it actually binds the
name "n" locally. The second
version works, but it's not a binder proper, so it "pushes" the problem of
finding a suitable name further out. Said another way, the first version is modular while
the second is not.
While it is straight forward to implement the second version, I can not
immediately see a way to implement the first one, without a way to generate a
fresh name.
Well, you could combine the two: take in a polymorphic premise, but also
ask for a concrete disjoint name to be passed at the top level. The
implementation can instantiate the premise with the concrete name.
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[Ur] Generating fresh name (gensym :: {Unit} -> Name).
Hello Ur/Web'ers,
Is it possible to generate a fresh name relative to some collection of names?
I.e. something of kind "gensym :: {Unit} -> Name".
Does it break some nice meta-properties of Ur/Web?
To give some context for why I'm thinking about this:
I've played a bit with Ur/Web, and I just tried to embed linear logic into
Ur/Web's type system. I've put some of what I've done
in a github repository here: https://github.com/peterbb/ur-linear.
The basic idea is to define a type "lin :: {Type} -> Type -> Type", where the
intuition of "lin gamma tau" is that an object of
"tau" can be produced linearly from the a record "$gamma" (this is similar to
the box type found in contextual modal type theory). Using Ur/Web's module
system to hide the definition of "lin" and exposing functions correspond to the
rules of inference of linear logic, it seems to me that one gets a faithful
shallow representation of linear logic.
The rules where generation of fresh names would be useful, are rules that have
binders. Consider the inference rule for
lollipop in a two-sided sequent calculus:
Gamma, n : t0 |- t1
-
Gamma |- t0 -o t1
I have two possible types which can be used to represent this:
val lolli_right :
t0 ::: Type -> t1 ::: Type -> gamma ::: {Type} ->
(n :: Name -> [[n] ~ gamma] => lin (gamma ++ [n = t0]) t1) ->
lin gamma (lolli t0 t1)
and
val lolli_right' :
n ::: Name -> t0 ::: Type -> t1 ::: Type -> gamma ::: {Type} ->
[[n] ~ gamma] =>
lin (gamma ++ [n = t0]) t1 ->
lin gamma (lolli t0 t1)
The first type is arguably nicer, since when used as a proof term, it actually
binds the name "n" locally. The second
version works, but it's not a binder proper, so it "pushes" the problem of
finding a suitable name further out. Said another way, the first version is
modular while the second is not.
While it is straight forward to implement the second version, I can not
immediately see a way to implement the first one, without a way to generate a
fresh name.
— Peter Brottveit Bock
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