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[Jason Gross <jasongross9 AT gmail.com>]

I was thinking something stupider: you pass in terms that are treated as constructors and required to have the appropriate type signature (a type "NAT", an "O : NAT", and an "S : NAT -> NAT" (hopefully the code can be parametric over how many universes NAT uses, and whether its polymorphic or not, etc), and then notations get translated to applications of S and O, and applications of S and O get translated back, and if S and O happen to unfold to other things, then unfolding them breaks the notation (which is not the end of the world).

Even better would be to generalize the nat_syntax_plugin to handle things like [trunc_index], i.e., things where the base case should be displayed as 1 or as -2, etc.

I do not think that we should have to trust Ltac code to get syntax for custom natural numbers.

On Sun, Feb 21, 2016 at 5:49 PM, Pierre-Marie Pédrot <pierre-marie.pedrot AT inria.fr> wrote:

On 21/02/2016 23:31, Jason Gross wrote:
> How hard would it be to set up the syntax plugins already in Coq so that
> they registered vernaculars such as [Declare NatSyntax for nat in
> nat_scope [O S].] and similarly for notations for negative numbers,
> ascii, strings, etc?

Not that difficult, I believe. Yet, we need to rely on a meta-language
to pattern-match over terms. Ltac would fit the bill, but I personally
find this use a little bit ugly.  The vernacular would probably look like:

Parameter myNat : Type.

Ltac reify_myNat n :=
match n with
(* insert a code producing a Z from a myNat here *)
end.

Declare Nat Syntax myNat reify_myNat.

PMP