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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