diff options
Diffstat (limited to 'plugins/nsatz/Nsatz.v')
| -rw-r--r-- | plugins/nsatz/Nsatz.v | 64 |
1 files changed, 42 insertions, 22 deletions
diff --git a/plugins/nsatz/Nsatz.v b/plugins/nsatz/Nsatz.v index 4f2010f29..6d5ea258b 100644 --- a/plugins/nsatz/Nsatz.v +++ b/plugins/nsatz/Nsatz.v @@ -28,6 +28,8 @@ Require Export Cring. Declare ML Module "nsatz_plugin". +(* Definition of integral domains: commutative ring without zero divisor *) + Class Integral_domain {R : Type}`{Rcr:Cring R} := { integral_domain_product: forall x y, x * y == 0 -> x == 0 \/ y == 0; @@ -278,19 +280,21 @@ Fixpoint interpret3 t fv {struct t}: R := End integral_domain. +Ltac equality_to_goal H x y:= + let h := fresh "nH" in + (assert (h:equality x y); + [solve [cring] | clear H; clear h]) + || (try generalize (@psos_r1 _ _ _ _ _ _ _ _ _ _ _ x y H); clear H) +. + Ltac equalities_to_goal := lazymatch goal with - | H: (_ ?x ?y) |- _ => - try generalize (@psos_r1 _ _ _ _ _ _ _ _ _ _ _ x y H); clear H - | H: (_ _ ?x ?y) |- _ => - try generalize (@psos_r1 _ _ _ _ _ _ _ _ _ _ _ x y H); clear H - | H: (_ _ _ ?x ?y) |- _ => - try generalize (@psos_r1 _ _ _ _ _ _ _ _ _ _ _ x y H); clear H - | H: (_ _ _ _ ?x ?y) |- _ => - try generalize (@psos_r1 _ _ _ _ _ _ _ _ _ _ _ x y H); clear H + | H: (_ ?x ?y) |- _ => equality_to_goal H x y + | H: (_ _ ?x ?y) |- _ => equality_to_goal H x y + | H: (_ _ _ ?x ?y) |- _ => equality_to_goal H x y + | H: (_ _ _ _ ?x ?y) |- _ => equality_to_goal H x y (* extension possible :-) *) - | H: (?x == ?y) |- _ => - try generalize (@psos_r1 _ _ _ _ _ _ _ _ _ _ _ x y H); clear H + | H: (?x == ?y) |- _ => equality_to_goal H x y end. (* lp est incluse dans fv. La met en tete. *) @@ -392,8 +396,8 @@ match goal with let lp := get_lpol g in let lpol := eval compute in (List.rev lp) in (* idtac "polynomes:"; idtac lpol;*) - simpl; intros; - simpl; + (*simpl;*) intros; + (*simpl;*) let SplitPolyList kont := match lpol with | ?p2::?lp2 => kont p2 lp2 @@ -411,28 +415,28 @@ match goal with [ (vm_compute;reflexivity) || idtac "invalid nsatz certificate" | let Hg2 := fresh "Hg" in assert (Hg2: (interpret3 q fv) == 0); - [ simpl; + [ (*simpl*) idtac; generalize (@check_correct _ _ _ _ _ _ _ _ _ _ _ fv lp21 q (lci,lq) Hg); let cc := fresh "H" in - simpl; intro cc; apply cc; clear cc; - simpl; + (*simpl*) idtac; intro cc; apply cc; clear cc; + (*simpl*) idtac; repeat (split;[assumption|idtac]); exact I - | simpl in Hg2; simpl; + | (*simpl in Hg2;*) (*simpl*) idtac; apply Rintegral_domain_pow with (interpret3 c fv) (nat_of_N r); - simpl; + (*simpl*) idtac; try apply integral_domain_one_zero; try apply integral_domain_minus_one_zero; try trivial; try exact integral_domain_one_zero; try exact integral_domain_minus_one_zero - || (simpl) || idtac "could not prove discrimination result" + || ((*simpl*) idtac) || idtac "could not prove discrimination result" ] ] ) ) end end end end . -Ltac nsatz:= +Ltac nsatz_default:= intros; try apply (@psos_r1b _ _ _ _ _ _ _ _ _ _ _); match goal with |- (@equality ?r _ _ _) => @@ -440,11 +444,26 @@ Ltac nsatz:= nsatz_generic 6%N 1%Z (@nil r) (@nil r) end. +Tactic Notation "nsatz" := nsatz_default. + +Tactic Notation "nsatz" "with" + "radicalmax" ":=" constr(radicalmax) + "strategy" ":=" constr(info) + "parameters" ":=" constr(lparam) + "variables" ":=" constr(lvar):= + intros; + try apply (@psos_r1b _ _ _ _ _ _ _ _ _ _ _); + match goal with |- (@equality ?r _ _ _) => + repeat equalities_to_goal; + nsatz_generic radicalmax info lparam lvar + end. + Section test. Context {R:Type}`{Rid:Integral_domain R}. Goal forall x y:R, x == x. -nsatz. +nsatz with radicalmax := 6%N strategy := 1%Z parameters := (@nil R) + variables := (@nil R). Qed. Goal forall x y:R, x == y -> y*y == x*x. @@ -510,8 +529,6 @@ Qed. (* Rational numbers *) Require Import QArith. -Check Q_Setoid. - Instance Qops: (@Ring_ops Q 0%Q 1%Q Qplus Qmult Qminus Qopp Qeq). Instance Qri : (Ring (Ro:=Qops)). @@ -557,3 +574,6 @@ Goal forall x y:Z, x = y -> (x*x-x+1)%Z = ((y*y-y)+1+0)%Z. nsatz. Qed. +Goal forall x y:Z, x = y -> x = x -> (x*x-x+1)%Z = ((y*y-y)+1+0)%Z. +nsatz. +Qed.
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