From cdae9d225576146dc88902a466173170ee7e9dc1 Mon Sep 17 00:00:00 2001
From: Adam Chlipala <adam@chlipala.net>
Date: Wed, 28 Oct 2015 14:07:05 -0400
Subject: Tiny module-system tweaks in PointFormats

---
 .gitignore                |  1 +
 src/Curves/PointFormats.v | 24 ++++++++++++++----------
 2 files changed, 15 insertions(+), 10 deletions(-)

diff --git a/.gitignore b/.gitignore
index ae784f4a5..cec91e9a6 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,2 +1,3 @@
+bedrock
 fiat
 *~
diff --git a/src/Curves/PointFormats.v b/src/Curves/PointFormats.v
index 7af310257..baa6bd2a7 100644
--- a/src/Curves/PointFormats.v
+++ b/src/Curves/PointFormats.v
@@ -78,8 +78,8 @@ Module PointFormats.
   End CompleteTwistedEdwardsPointFormat.
 
   Module CompleteTwistedEdwardsFacts (Import ta:TwistedA) (Import td:TwistedD).
-    Module M := CompleteTwistedEdwardsSpec ta td.
-    Import M.
+    Module Import Spec := CompleteTwistedEdwardsSpec ta td.
+
     Lemma twistedAddCompletePlus : forall (P1 P2:point)
       (oc1:onCurve P1) (oc2:onCurve P2),
       let x1 := projX P1 in
@@ -131,7 +131,7 @@ Module PointFormats.
 
 
   Module CompleteTwistedEdwardsSpecPointFormat (ta:TwistedA) (td:TwistedD)
-      <: (CompleteTwistedEdwardsPointFormat ta td).
+      <: CompleteTwistedEdwardsPointFormat ta td.
     Module Spec := CompleteTwistedEdwardsSpec ta td.
     Definition point := Spec.point.
     Definition mkPoint := Spec.mkPoint.
@@ -178,16 +178,18 @@ Module PointFormats.
     End ta.
     Import ta.
 
-    Module M := CompleteTwistedEdwardsSpec ta td.
+    Module Spec := CompleteTwistedEdwardsSpec ta td.
 
     Module Format <: CompleteTwistedEdwardsPointFormat ta td.
-      Module Spec := CompleteTwistedEdwardsSpec ta td.
+      Module Import Facts := CompleteTwistedEdwardsFacts ta td.
+
       (** [projective] represents a point on an elliptic curve using projective
       * Edwards coordinates for twisted edwards curves with a=-1 (see
       * <https://hyperelliptic.org/EFD/g1p/auto-edwards-projective.html>
       * <https://en.wikipedia.org/wiki/Edwards_curve#Projective_homogeneous_coordinates>) *)
       Record projective := mkProjective {projectiveX : GF; projectiveY : GF; projectiveZ : GF}.
       Local Notation "'(' X ',' Y ',' Z ')'" := (mkProjective X Y Z).
+
       Definition twistedToProjective (P : Spec.point) : projective :=
         let x := Spec.projX P in
         let y := Spec.projY P in
@@ -205,11 +207,6 @@ Module PointFormats.
       Lemma twistedProjectiveInv : forall P,
         projectiveToTwisted (twistedToProjective P) = P.
       Proof.
-    (* FIXME: this is copied from CompleteTwistedEdwardsFacts because I don't know how to get it to be in scope here *)
-    Ltac twisted := autounfold; intros;
-                    repeat match goal with
-                               | [ x : Spec.point |- _ ] => destruct x
-                           end; simpl; repeat (ring || f_equal); field.
         twisted.
       Qed.
 
@@ -246,6 +243,7 @@ Module PointFormats.
       Qed.
 
       Lemma twistedToExtendedValid : forall (P : Spec.point), extendedValid (twistedToExtended P).
+      Proof.
         autounfold.
         destruct P.
         simpl.
@@ -255,6 +253,7 @@ Module PointFormats.
       Definition rep (P:point) (rP:Spec.point) : Prop :=
         extendedToTwisted P = rP /\ extendedValid P.
       Lemma mkPoint_rep : forall x y, rep (mkPoint x y) (Spec.mkPoint x y).
+      Proof.
         split.
         apply twistedExtendedInv.
         apply twistedToExtendedValid.
@@ -268,9 +267,11 @@ Module PointFormats.
                                | [ x : rep ?a ?b |- _ ] => destruct x
                                end).
       Lemma projX_rep : forall P rP, P ~= rP -> projX P = Spec.projX rP.
+      Proof.
         rep.
       Qed.
       Lemma projY_rep : forall P rP, P ~= rP -> projY P = Spec.projY rP.
+      Proof.
         rep.
       Qed.
 
@@ -353,10 +354,13 @@ Module PointFormats.
 
       Lemma unifiedAdd_rep: forall P Q rP rQ, Spec.onCurve rP -> Spec.onCurve rQ ->
         P ~= rP -> Q ~= rQ -> (unifiedAdd P Q) ~= (Spec.unifiedAdd rP rQ).
+      Proof.
         split; rep.
         apply unifiedAddToTwisted; auto.
         apply unifiedAddCon; auto.
       Qed.
+
+      Module Spec := Spec.
     End Format.
   End Minus1Twisted.
 
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