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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).
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