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-rw-r--r--src/Curves/Weierstrass/Affine.v6
-rw-r--r--src/Curves/Weierstrass/AffineProofs.v196
-rw-r--r--src/Curves/Weierstrass/Pre.v62
3 files changed, 29 insertions, 235 deletions
diff --git a/src/Curves/Weierstrass/Affine.v b/src/Curves/Weierstrass/Affine.v
index 90bb3bdbc..3a48bf998 100644
--- a/src/Curves/Weierstrass/Affine.v
+++ b/src/Curves/Weierstrass/Affine.v
@@ -11,8 +11,10 @@ Module W.
Program Definition opp (P:@W.point F Feq Fadd Fmul a b) : @W.point F Feq Fadd Fmul a b
:= match W.coordinates P return F*F+_ with
| inl (x1, y1) => inl (x1, Fopp y1)
- | _ => P
+ | inr tt => inr tt
end.
- Next Obligation. destruct P as [[[??]|[]]?]; cbv; trivial; fsatz. Qed.
+ Next Obligation.
+ cbv [W.coordinates]; break_match; trivial; fsatz.
+ Qed.
End W.
End W. \ No newline at end of file
diff --git a/src/Curves/Weierstrass/AffineProofs.v b/src/Curves/Weierstrass/AffineProofs.v
index 81583d88f..be76cee90 100644
--- a/src/Curves/Weierstrass/AffineProofs.v
+++ b/src/Curves/Weierstrass/AffineProofs.v
@@ -18,179 +18,33 @@ Module W.
Local Infix "+" := Fadd. Local Infix "-" := Fsub. Local Infix "*" := Fmul.
Local Notation "4" := (1+1+1+1). Local Notation "27" := (4*4 + 4+4 +1+1+1).
+ Local Ltac Algebra_split :=
+ repeat match goal with
+ | |- Proper _ _ => cbv [Proper respectful]; intros
+ | |- Equivalence _ => split; [intros ? | intros ??? | intros ????? ]
+ | |- monoid => split
+ | |- group => split
+ | |- abelian_group => split
+ | |- is_associative => split; intros ???
+ | |- is_commutative => split; intros ??
+ | |- is_left_inverse => split; intros ?
+ | |- is_right_inverse => split; intros ?
+ | |- is_left_identity => split; intros ?
+ | |- is_right_identity => split; intros ?
+ end.
+
Global Instance commutative_group {discriminant_nonzero:id(4*a*a*a + 27*b*b <> 0)} : abelian_group(eq:=W.eq(a:=a)(b:=b))(op:=W.add(char_ge_3:=char_ge_3))(id:=W.zero)(inv:=W.opp).
Proof using Type.
Time
- repeat match goal with
- | _ => solve [ contradiction | trivial | exact _ ]
- | _ => intro
- | |- Equivalence _ => split
- | |- abelian_group => split | |- group => split | |- monoid => split
- | |- is_associative => split | |- is_commutative => split
- | |- is_left_inverse => split | |- is_right_inverse => split
- | |- is_left_identity => split | |- is_right_identity => split
- | _ => progress destruct_head' @W.point
- | _ => progress destruct_head' sum
- | _ => progress destruct_head' prod
- | _ => progress destruct_head' unit
- | _ => progress destruct_head' and
- | _ => progress cbv [W.opp W.eq W.zero W.add W.coordinates proj1_sig]in*
- | _ => progress break_match
- end.
- (* Finished transaction in 2.098 secs (2.099u,0.s) (successful) *)
- all: try split.
- (* Finished transaction in 0.052 secs (0.053u,0.s) (successful) *)
-
- (* The [discriminant_nonzero] hypothesis makes [fsatz] slow but
- is necessary in some cases. Thus, we wrap it in [id] by detault
- to hide it from [nsatz] but unfold it when normal [fsatz] fails. *)
- (* Variable re-ordering is a micro-optimization *)
- (* TODO: why does par not work here? *)
- Ltac s := abstract (
- match goal with [H:id _ |- _] => move H at bottom end;
- move b at bottom;
- move a at bottom;
- repeat match goal with [H: ?x = Fopp ?y |- _] => is_var x; is_var y; revert H end; intros;
- repeat match goal with [H: ?x = ?y |- _] => is_var x; is_var y; revert H end; intros;
- repeat split;
- solve
- [ fsatz
- | cbv [id] in *; fsatz]
- ).
- Time s. (* Finished transaction in 0.099 secs (0.096u,0.003s) (successful) *)
- Time s. (* Finished transaction in 0.094 secs (0.093u,0.s) (successful) *)
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- (* Total: 414.396 seconds, roughly 7 minutes*)
-
- Time Qed. (* Finished transaction in 390.998 secs (390.783u,0.276s) (successful) *)
+ cbv [W.opp W.eq W.zero W.add W.coordinates proj1_sig];
+ repeat match goal with
+ | _ => progress Algebra_split
+ | H: _ /\ _ |- _ => destruct H
+ | |- _ /\ _ => split
+ | _ => progress break_match
+ | _ => progress break_match_hyps
+ end; try contradiction; trivial.
+ Time par: abstract (fsatz || (cbv [id] in *; fsatz)).
+ Time Qed.
End W.
End W.
diff --git a/src/Curves/Weierstrass/Pre.v b/src/Curves/Weierstrass/Pre.v
deleted file mode 100644
index 6647d8e76..000000000
--- a/src/Curves/Weierstrass/Pre.v
+++ /dev/null
@@ -1,62 +0,0 @@
-Require Import Coq.Classes.Morphisms. Require Coq.Setoids.Setoid.
-Require Import Crypto.Algebra.Field.
-Require Import Crypto.Util.Tactics.DestructHead.
-Require Import Crypto.Util.Tactics.BreakMatch.
-Require Import Crypto.Util.Notations.
-Require Import Crypto.Util.Decidable.
-Import BinNums.
-
-Local Open Scope core_scope.
-
-Section Pre.
- Context {F Feq Fzero Fone Fopp Fadd Fsub Fmul Finv Fdiv}
- {field:@Algebra.Hierarchy.field F Feq Fzero Fone Fopp Fadd Fsub Fmul Finv Fdiv}
- {char_ge_3:@Ring.char_ge F Feq Fzero Fone Fopp Fadd Fsub Fmul (BinNat.N.succ_pos (BinNat.N.two))}
- {eq_dec: DecidableRel Feq}.
- Local Infix "=" := Feq. Local Notation "a <> b" := (not (a = b)).
- Local Infix "=" := Feq : type_scope. Local Notation "a <> b" := (not (a = b)) : type_scope.
- Local Notation "0" := Fzero. Local Notation "1" := Fone.
- Local Infix "+" := Fadd. Local Infix "*" := Fmul.
- Local Infix "-" := Fsub. Local Infix "/" := Fdiv.
- Local Notation "- x" := (Fopp x).
- Local Notation "x ^ 2" := (x*x). Local Notation "x ^ 3" := (x*x^2).
- Local Notation "'∞'" := unit : type_scope.
- Local Notation "'∞'" := (inr tt) : core_scope.
- Local Notation "2" := (1+1). Local Notation "3" := (1+2).
- Local Notation "( x , y )" := (inl (pair x y)).
-
- Context {a:F}.
- Context {b:F}.
-
- (* the canonical definitions are in Spec *)
- Let onCurve (P:F*F + ∞) := match P with
- | (x, y) => y^2 = x^3 + a*x + b
- | ∞ => True
- end.
- Let add (P1' P2':F*F + ∞) : F*F + ∞ :=
- match P1', P2' return _ with
- | (x1, y1), (x2, y2) =>
- if dec (x1 = x2)
- then
- if dec (y2 = -y1)
- then ∞
- else let k := (3*x1^2+a)/(2*y1) in
- let x3 := k^2-x1-x1 in
- let y3 := k*(x1-x3)-y1 in
- (x3, y3)
- else let k := (y2-y1)/(x2-x1) in
- let x3 := k^2-x1-x2 in
- let y3 := k*(x1-x3)-y1 in
- (x3, y3)
- | ∞, ∞ => ∞
- | ∞, _ => P2'
- | _, ∞ => P1'
- end.
-
- Lemma add_onCurve P1 P2 (_:onCurve P1) (_:onCurve P2) :
- onCurve (add P1 P2).
- Proof using a b char_ge_3 eq_dec field.
- destruct_head' sum; destruct_head' prod;
- cbv [onCurve add] in *; break_match; trivial; [|]; fsatz.
- Qed.
-End Pre.
generated by cgit v1.2.3 (git 2.39.1) at 2024-06-01 11:02:01 +0000