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[Gregory Malecha <gmalecha AT gmail.com>]

Would Coercions fit the bill for the nat2mynat idea? Or are they not expressive enough.

On Sun, Feb 21, 2016 at 8:40 PM, Jason Gross <jasongross9 AT gmail.com> wrote:

Jonathan, how does that work on open terms?  It'll work fine for parsing, probably (though I don't really want to be able to do arbitrary computation in the parsing of my numerals, that's perhaps a bit scary, but perhaps useful), but seems kind-of sketchy for printing.

On Sun, Feb 21, 2016 at 9:08 PM, Jonathan Leivent <jonikelee AT gmail.com> wrote:

I was thinking something even stupider than that!  The user gives two functions that map between nats and the user type they want to represent with number notations:

Inductive mynat : Set := ...

Definition nat2mynat(n : nat) : mynat := ...

Definition mynat2nat(m: mynat) : nat := ...

Declare Nat Syntax mynat Using nat2mynat, mynat2nat : M_scope.

The parser would, whenever it sees a number in the scope M_scope, call nat2mynat and use the result.  The printer would, whenever it sees a mynat in the scope M_scope, call mynat2nat, and print the resulting number.

-- Jonathan

On 02/21/2016 06:05 PM, Jason Gross wrote:

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

--

gregory malecha