Numeral Notation (for inductive types)

 This is a portion of roglo's PR#156 introducing a Numeral Notation
 command : we deal here with inductive types via conversion fonctions
 from/to Z written in Coq.

 For an example, see plugins/syntax/NatSyntaxViaZ.v

 This commit does not include the part about printing via some ltac.
 Using ltac was meant for dealing with real numbers, let's see first what
 become PR#415 about a compact representation for real literals.

1 files changed, 56 insertions, 0 deletions

diff --git a/plugins/syntax/NatSyntaxViaZ.v b/plugins/syntax/NatSyntaxViaZ.v
new file mode 100644
index 0000000000..adee347d90
--- /dev/null
+++ b/plugins/syntax/NatSyntaxViaZ.v
@@ -0,0 +1,56 @@
+Declare ML Module "numeral_notation_plugin".
+Require Import BinNums.
+
+(** ** Parsing and Printing digit strings as type nat *)
+
+Fixpoint pos_pred_double x :=
+  match x with
+  | xI p => xI (xO p)
+  | xO p => xI (pos_pred_double p)
+  | xH => xH
+  end.
+
+Definition nat_of_Z x :=
+  match x with
+  | Z0 => Some O
+  | Zpos p =>
+      let fix iter p a :=
+        match p with
+        | xI p0 => a + iter p0 (a + a)
+        | xO p0 => iter p0 (a + a)
+        | xH => a
+        end
+      in
+      Some (iter p (S O))
+  | Zneg p => None
+  end.
+
+Fixpoint pos_succ x :=
+  match x with
+  | xI p => xO (pos_succ p)
+  | xO p => xI p
+  | xH => xO xH
+  end.
+
+Definition Z_succ x :=
+  match x with
+  | Z0 => Zpos xH
+  | Zpos x => Zpos (pos_succ x)
+  | Zneg x =>
+      match x with
+      | xI p => Zneg (xO p)
+      | xO p => Zneg (pos_pred_double p)
+      | xH => Z0
+      end
+  end.
+
+Fixpoint Z_of_nat_loop n :=
+  match n with
+  | O => Z0
+  | S p => Z_succ (Z_of_nat_loop p)
+  end.
+
+Definition Z_of_nat n := Some (Z_of_nat_loop n).
+
+Numeral Notation nat nat_of_Z Z_of_nat : nat_scope
+  (warning after 5000).