Change the parser and printer so that they use IZR for real constants.

There are two main issues. First, (-cst)%R is no longer syntactically
equal to (-(cst))%R (though they are still convertible). This breaks some
rewriting rules.

Second, the ring/field_simplify tactics did not know how to refold
real constants. This defect is no longer hidden by the pretty-printer,
which makes these tactics almost unusable on goals containing large
constants.

This commit also modifies the ring/field tactics so that real constant
reification is now constant time rather than linear.

Note that there is now a bit of code duplication between z_syntax and
r_syntax. This should be fixed once plugin interdependencies are supported.

Ideally the r_syntax plugin should just disappear by declaring IZR as a
coercion. Unfortunately the coercion mechanism is not powerful enough yet,
be it for parsing (need the ability for a scope to delegate constant
parsing to another scope) or printing (too many visible coercions left).

1 files changed, 15 insertions, 6 deletions

diff --git a/plugins/setoid_ring/RealField.v b/plugins/setoid_ring/RealField.v
index 293722125..facd2e062 100644
--- a/plugins/setoid_ring/RealField.v
+++ b/plugins/setoid_ring/RealField.v
@@ -59,11 +59,12 @@ Notation Rset := (Eqsth R).
 Notation Rext := (Eq_ext Rplus Rmult Ropp).
 
 Lemma Rlt_0_2 : 0 < 2.
+Proof.
 apply Rlt_trans with (0 + 1).
  apply Rlt_n_Sn.
  rewrite Rplus_comm.
    apply Rplus_lt_compat_l.
-    replace 1 with (0 + 1).
+    replace R1 with (0 + 1).
   apply Rlt_n_Sn.
   apply Rplus_0_l.
 Qed.
@@ -126,9 +127,17 @@ Ltac Rpow_tac t :=
   | _ => constr:(N.of_nat t)
   end.
 
-Add Field RField : Rfield
-   (completeness Zeq_bool_complete, power_tac R_power_theory [Rpow_tac]).
-
-
-
+Ltac IZR_tac t :=
+  match t with
+  | R0 => constr:(0%Z)
+  | R1 => constr:(1%Z)
+  | IZR ?u =>
+    match isZcst u with
+    | true => u
+    | _ => constr:(InitialRing.NotConstant)
+    end
+  | _ => constr:(InitialRing.NotConstant)
+  end.
 
+Add Field RField : Rfield
+   (completeness Zeq_bool_complete, constants [IZR_tac], power_tac R_power_theory [Rpow_tac]).