Keyed unification option, compiling the whole standard library

(but deactivated still).

Set Keyed Unification to activate the option, which changes
subterm selection to _always_ use full conversion _after_ finding a
subterm whose head/key matches the key of the term we're looking for.
This applies to rewrite and higher-order unification in
apply/elim/destruct.

Most proof scripts already abide by these semantics. For those that
don't, it's usually only a matter of using:

Declare Equivalent Keys f g.

This make keyed unification consider f and g to match as keys.
This takes care of most cases of abbreviations: typically Def foo :=
bar and rewriting with a bar-headed lhs in a goal mentioning foo works
once they're set equivalent.
For canonical structures, these hints should be automatically declared.

For non-global-reference headed terms, the key is the constructor name
(Sort, Prod...). Evars and metas are no keys.

INCOMPATIBILITIES:
In FMapFullAVL, a Function definition doesn't go through with keyed
unification on.

4 files changed, 9 insertions, 3 deletions

diff --git a/theories/Numbers/Cyclic/Abstract/NZCyclic.v b/theories/Numbers/Cyclic/Abstract/NZCyclic.v
index 1d5b78ec4..c9f3a774d 100644
--- a/theories/Numbers/Cyclic/Abstract/NZCyclic.v
+++ b/theories/Numbers/Cyclic/Abstract/NZCyclic.v
@@ -126,9 +126,7 @@ Let B (n : Z) := A (ZnZ.of_Z n).
 
 Lemma B0 : B 0.
 Proof.
-unfold B.
-setoid_replace (ZnZ.of_Z 0) with zero. assumption.
-red; zify. apply ZnZ.of_Z_correct. auto using gt_wB_0 with zarith.
+unfold B. apply A0.
 Qed.
 
 Lemma BS : forall n : Z, 0 <= n -> n < wB - 1 -> B n -> B (n + 1).
diff --git a/theories/Numbers/Natural/BigN/NMake_gen.ml b/theories/Numbers/Natural/BigN/NMake_gen.ml
index 8df4b7c64..dc35d087b 100644
--- a/theories/Numbers/Natural/BigN/NMake_gen.ml
+++ b/theories/Numbers/Natural/BigN/NMake_gen.ml
@@ -961,6 +961,11 @@ pr "  end.";
 pr "";
 
 pr " Ltac unfold_red := unfold reduce, %s." (iter_name 1 size "reduce_" ",");
+pr "";
+for i = 0 to size do
+pr " Declare Equivalent Keys reduce reduce_%i." i;
+done;
+pr " Declare Equivalent Keys reduce_n reduce_%i." (size + 1);
 
 pr "
  Ltac solve_red :=
diff --git a/theories/Numbers/Natural/BigN/Nbasic.v b/theories/Numbers/Natural/BigN/Nbasic.v
index 161f523ca..e8a9940bd 100644
--- a/theories/Numbers/Natural/BigN/Nbasic.v
+++ b/theories/Numbers/Natural/BigN/Nbasic.v
@@ -320,6 +320,7 @@ Section CompareRec.
  Let double_to_Z_pos: forall n x, 0 <= double_to_Z n x < double_wB n :=
    (spec_double_to_Z wm_base wm_to_Z wm_to_Z_pos).
 
+ Declare Equivalent Keys compare0_mn compare0_m.
 
  Lemma spec_compare0_mn: forall n x,
    compare0_mn n x = (0 ?= double_to_Z n x).
diff --git a/theories/Numbers/Rational/BigQ/BigQ.v b/theories/Numbers/Rational/BigQ/BigQ.v
index e866a52d6..b304b339b 100644
--- a/theories/Numbers/Rational/BigQ/BigQ.v
+++ b/theories/Numbers/Rational/BigQ/BigQ.v
@@ -88,6 +88,8 @@ exact BigQ.add_opp_diag_r. exact BigQ.neq_1_0.
 exact BigQ.div_mul_inv. exact BigQ.mul_inv_diag_l.
 Qed.
 
+Declare Equivalent Keys pow_N pow_pos.
+
 Lemma BigQpowerth :
  power_theory 1 BigQ.mul BigQ.eq Z.of_N BigQ.power.
 Proof.