fix

.gitignore

@@ -17,6 +17,7 @@
 .depend
 .loadpath
 _CoqProject
+!packages/**/_CoqProject
 *.cache
 *~
 *#

Makefile

+DIST=coq-verif-tweetnacl
+
+# NO_COLOR="\033[0m"
+# RED = "\033[38;5;009m"
+# GREEN = "\033[38;5;010m"
+# YELLOW = "\033[38;5;011m"
+# ORANGE = "\033[38;5;214m"
+# LIGHTPURPLE = "\033[38;5;177m"
+# PURPLE = "\033[38;5;135m"
+# CYAN = "\033[38;5;014m"
+# LIGHTGRAY = "\033[38;5;252m"
+# DARKGRAY = "\033[38;5;242m"
+# BRIGHTRED = "\033[91m"
+# BOLD = "\033[1m"
+#
+# all: coq-tweetnacl-spec coq-tweetnacl-vst
+
+include coq.mk
+
+.PHONY: clean
+clean: clean-spec clean-vst clean-dist
+
+# build paper
+.PHONY: paper
+paper:
+	@cd paper && $(MAKE)
+
+clean-paper:
+	cd paper && $(MAKE) clean
+
+# generate artefact
+$(DIST):
+	@echo $(BOLD)$(ORANGE)"Creating $(DIST)"$(NO_COLOR)$(DARKGRAY)
+	mkdir $(DIST)
+
+$(DIST)/specs_map.pdf:
+	@echo $(BOLD)$(YELLOW)"Building map for specs"$(NO_COLOR)$(DARKGRAY)
+	cd paper && $(MAKE) specs_map.pdf
+	mv specs_map.pdf $(DIST)/specs_map.pdf
+
+dist: clean-dist $(DIST) $(DIST)/specs_map.pdf
+	@echo $(BOLD)$(YELLOW)"Preparing $(DIST)"$(NO_COLOR)$(DARKGRAY)
+	cp -r proofs $(DIST)
+	cd $(DIST)/proofs/spec && $(MAKE) clean
+	cd $(DIST)/proofs/vst && $(MAKE) clean
+	mkdir $(DIST)/packages
+	cp -r packages/coq-compcert $(DIST)/packages/
+	cp -r packages/coq-reciprocity $(DIST)/packages/
+	cp -r packages/coq-ssr-elliptic-curves $(DIST)/packages/
+	cp -r packages/coq-vst $(DIST)/packages/
+	cp repo $(DIST)/
+	cp version $(DIST)/
+	cp README.md $(DIST)/
+	cp coq.mk $(DIST)/Makefile
+	cp opam $(DIST)/
+	@echo $(BOLD)$(LIGHTPURPLE)"Building $(DIST).tar.gz"$(NO_COLOR)$(DARKGRAY)
+	tar -czvf $(DIST).tar.gz $(DIST)
+	@echo $(BOLD)$(GREEN)"Done."$(NO_COLOR)
+
+clean-dist:
+	@echo $(BOLD)$(YELLOW)"removing $(DIST)"$(NO_COLOR)$(DARKGRAY)
+	-rm -r $(DIST)
+	-rm $(DIST).tar.gz
+	@echo $(BOLD)$(GREEN)"Done."$(NO_COLOR)

packages/coq-bignums/coq-bignums.8.8.dev/.gitignore

+BigN/NMake_gen.v
+*.d
+*.o
+*.cmi
+*.cmx
+*.cmxs
+*.vo
+*.glob
+*.aux
+Makefile.coq
+Makefile.coq.conf

packages/coq-bignums/coq-bignums.8.8.dev/BigN/BigN.v

+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016     *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+(** * Efficient arbitrary large natural numbers in base 2^31 *)
+
+(** Initial Author: Arnaud Spiwack *)
+
+Require Export Int31.
+Require Import CyclicAxioms Cyclic31 Ring31 NSig NSigNAxioms NMake
+  NProperties GenericMinMax.
+
+(** The following [BigN] module regroups both the operations and
+    all the abstract properties:
+
+    - [NMake.Make Int31Cyclic] provides the operations and basic specs
+       w.r.t. ZArith
+    - [NTypeIsNAxioms] shows (mainly) that these operations implement
+      the interface [NAxioms]
+    - [NProp] adds all generic properties derived from [NAxioms]
+    - [MinMax*Properties] provides properties of [min] and [max].
+
+*)
+
+Delimit Scope bigN_scope with bigN.
+
+Module BigN <: NType <: OrderedTypeFull <: TotalOrder :=
+  NMake.Make Int31Cyclic
+  <+ NTypeIsNAxioms
+  <+ NBasicProp [no inline] <+ NExtraProp [no inline]
+  <+ HasEqBool2Dec [no inline]
+  <+ MinMaxLogicalProperties [no inline]
+  <+ MinMaxDecProperties [no inline].
+
+(** Notations about [BigN] *)
+
+Local Open Scope bigN_scope.
+
+Notation bigN := BigN.t.
+Bind Scope bigN_scope with bigN BigN.t BigN.t'.
+Arguments BigN.N0 _%int31.
+Local Notation "0" := BigN.zero : bigN_scope. (* temporary notation *)
+Local Notation "1" := BigN.one : bigN_scope. (* temporary notation *)
+Local Notation "2" := BigN.two : bigN_scope. (* temporary notation *)
+Infix "+" := BigN.add : bigN_scope.
+Infix "-" := BigN.sub : bigN_scope.
+Infix "*" := BigN.mul : bigN_scope.
+Infix "/" := BigN.div : bigN_scope.
+Infix "^" := BigN.pow : bigN_scope.
+Infix "?=" := BigN.compare : bigN_scope.
+Infix "=?" := BigN.eqb (at level 70, no associativity) : bigN_scope.
+Infix "<=?" := BigN.leb (at level 70, no associativity) : bigN_scope.
+Infix "<?" := BigN.ltb (at level 70, no associativity) : bigN_scope.
+Infix "==" := BigN.eq (at level 70, no associativity) : bigN_scope.
+Notation "x != y" := (~x==y) (at level 70, no associativity) : bigN_scope.
+Infix "<" := BigN.lt : bigN_scope.
+Infix "<=" := BigN.le : bigN_scope.
+Notation "x > y" := (y < x) (only parsing) : bigN_scope.
+Notation "x >= y" := (y <= x) (only parsing) : bigN_scope.
+Notation "x < y < z" := (x<y /\ y<z) : bigN_scope.
+Notation "x < y <= z" := (x<y /\ y<=z) : bigN_scope.
+Notation "x <= y < z" := (x<=y /\ y<z) : bigN_scope.
+Notation "x <= y <= z" := (x<=y /\ y<=z) : bigN_scope.
+Notation "[ i ]" := (BigN.to_Z i) : bigN_scope.
+Infix "mod" := BigN.modulo (at level 40, no associativity) : bigN_scope.
+
+(** Example of reasoning about [BigN] *)
+
+Theorem succ_pred: forall q : bigN,
+  0 < q -> BigN.succ (BigN.pred q) == q.
+Proof.
+intros; apply BigN.succ_pred.
+intro H'; rewrite H' in H; discriminate.
+Qed.
+
+(** [BigN] is a semi-ring *)
+
+Lemma BigNring : semi_ring_theory 0 1 BigN.add BigN.mul BigN.eq.
+Proof.
+constructor.
+exact BigN.add_0_l. exact BigN.add_comm. exact BigN.add_assoc.
+exact BigN.mul_1_l. exact BigN.mul_0_l. exact BigN.mul_comm.
+exact BigN.mul_assoc. exact BigN.mul_add_distr_r.
+Qed.
+
+Lemma BigNeqb_correct : forall x y, (x =? y) = true -> x==y.
+Proof. now apply BigN.eqb_eq. Qed.
+
+Lemma BigNpower : power_theory 1 BigN.mul BigN.eq BigN.of_N BigN.pow.
+Proof.
+constructor.
+intros. red. rewrite BigN.spec_pow, BigN.spec_of_N.
+rewrite Zpower_theory.(rpow_pow_N).
+destruct n; simpl. reflexivity.
+induction p; simpl; intros; BigN.zify; rewrite ?IHp; auto.
+Qed.
+
+Lemma BigNdiv : div_theory BigN.eq BigN.add BigN.mul (@id _)
+ (fun a b => if b =? 0 then (0,a) else BigN.div_eucl a b).
+Proof.
+constructor. unfold id. intros a b.
+BigN.zify.
+case Z.eqb_spec.
+BigN.zify. auto with zarith.
+intros NEQ.
+generalize (BigN.spec_div_eucl a b).
+generalize (Z_div_mod_full [a] [b] NEQ).
+destruct BigN.div_eucl as (q,r), Z.div_eucl as (q',r').
+intros (EQ,_). injection 1 as EQr EQq.
+BigN.zify. rewrite EQr, EQq; auto.
+Qed.
+
+
+(** Detection of constants *)
+
+Ltac isStaticWordCst t :=
+ match t with
+ | W0 => constr:(true)
+ | WW ?t1 ?t2 =>
+   match isStaticWordCst t1 with
+   | false => constr:(false)
+   | true => isStaticWordCst t2
+   end
+ | _ => isInt31cst t
+ end.
+
+Ltac isBigNcst t :=
+ match t with
+ | BigN.N0 ?t => isStaticWordCst t
+ | BigN.N1 ?t => isStaticWordCst t
+ | BigN.N2 ?t => isStaticWordCst t
+ | BigN.N3 ?t => isStaticWordCst t
+ | BigN.N4 ?t => isStaticWordCst t
+ | BigN.N5 ?t => isStaticWordCst t
+ | BigN.N6 ?t => isStaticWordCst t
+ | BigN.Nn ?n ?t => match isnatcst n with
+   | true => isStaticWordCst t
+   | false => constr:(false)
+   end
+ | BigN.zero => constr:(true)
+ | BigN.one => constr:(true)
+ | BigN.two => constr:(true)
+ | _ => constr:(false)
+ end.
+
+Ltac BigNcst t :=
+ match isBigNcst t with
+ | true => constr:(t)
+ | false => constr:(NotConstant)
+ end.
+
+Ltac BigN_to_N t :=
+ match isBigNcst t with
+ | true => eval vm_compute in (BigN.to_N t)
+ | false => constr:(NotConstant)
+ end.
+
+Ltac Ncst t :=
+ match isNcst t with
+ | true => constr:(t)
+ | false => constr:(NotConstant)
+ end.
+
+(** Registration for the "ring" tactic *)
+
+Add Ring BigNr : BigNring
+ (decidable BigNeqb_correct,
+  constants [BigNcst],
+  power_tac BigNpower [BigN_to_N],
+  div BigNdiv).
+
+Section TestRing.
+Let test : forall x y, 1 + x*y^1 + x^2 + 1 == 1*1 + 1 + y*x + 1*x*x.
+intros. ring_simplify. reflexivity.
+Qed.
+End TestRing.
+
+(** We benefit also from an "order" tactic *)
+
+Ltac bigN_order := BigN.order.
+
+Section TestOrder.
+Let test : forall x y : bigN, x<=y -> y<=x -> x==y.
+Proof. bigN_order. Qed.
+End TestOrder.
+
+(** We can use at least a bit of (r)omega by translating to [Z]. *)
+
+Section TestOmega.
+Let test : forall x y : bigN, x<=y -> y<=x -> x==y.
+Proof. intros x y. BigN.zify. omega. Qed.
+End TestOmega.
+
+(** Todo: micromega *)

packages/coq-bignums/coq-bignums.8.8.dev/BigN/Nbasic.v

+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016     *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+(*            Benjamin Gregoire, Laurent Thery, INRIA, 2007             *)
+(************************************************************************)
+
+Require Import ZArith Ndigits.
+Require Import BigNumPrelude.
+Require Import Max.
+Require Import DoubleType.
+Require Import DoubleBase.
+Require Import CyclicAxioms.
+Require Import DoubleCyclic.
+
+Arguments mk_zn2z_ops [t] ops.
+Arguments mk_zn2z_ops_karatsuba [t] ops.
+Arguments mk_zn2z_specs [t ops] specs.
+Arguments mk_zn2z_specs_karatsuba [t ops] specs.
+Arguments ZnZ.digits [t] Ops.
+Arguments ZnZ.zdigits [t] Ops.
+
+Lemma Pshiftl_nat_Zpower : forall n p,
+  Zpos (Pos.shiftl_nat p n) = Zpos p * 2 ^ Z.of_nat n.
+Proof.
+ intros.
+ rewrite Z.mul_comm.
+ induction n. simpl; auto.
+ transitivity (2 * (2 ^ Z.of_nat n * Zpos p)).
+ rewrite <- IHn. auto.
+ rewrite Z.mul_assoc.
+ rewrite Nat2Z.inj_succ.
+ rewrite <- Z.pow_succ_r; auto with zarith.
+Qed.
+
+(* To compute the necessary height *)
+
+Fixpoint plength (p: positive) : positive :=
+  match p with
+    xH => xH
+  | xO p1 => Pos.succ (plength p1)
+  | xI p1 => Pos.succ (plength p1)
+  end.
+
+Theorem plength_correct: forall p, (Zpos p < 2 ^ Zpos (plength p))%Z.
+assert (F: (forall p, 2 ^ (Zpos (Pos.succ p)) = 2 * 2 ^ Zpos p)%Z).
+intros p; replace (Zpos (Pos.succ p)) with (1 + Zpos p)%Z.
+rewrite Zpower_exp; auto with zarith.
+rewrite Pos2Z.inj_succ; unfold Z.succ; auto with zarith.
+intros p; elim p; simpl plength; auto.
+intros p1 Hp1; rewrite F; repeat rewrite Pos2Z.inj_xI.
+assert (tmp: (forall p, 2 * p = p + p)%Z);
+  try repeat rewrite tmp; auto with zarith.
+intros p1 Hp1; rewrite F; rewrite (Pos2Z.inj_xO p1).
+assert (tmp: (forall p, 2 * p = p + p)%Z);
+  try repeat rewrite tmp; auto with zarith.
+rewrite Z.pow_1_r; auto with zarith.
+Qed.
+
+Theorem plength_pred_correct: forall p, (Zpos p <= 2 ^ Zpos (plength (Pos.pred p)))%Z.
+intros p; case (Pos.succ_pred_or p); intros H1.
+subst; simpl plength.
+rewrite Z.pow_1_r; auto with zarith.
+pattern p at 1; rewrite <- H1.
+rewrite Pos2Z.inj_succ; unfold Z.succ; auto with zarith.
+generalize (plength_correct (Pos.pred p)); auto with zarith.
+Qed.
+
+Definition Pdiv p q :=
+  match Z.div (Zpos p) (Zpos q) with
+    Zpos q1 => match (Zpos p) - (Zpos q) * (Zpos q1) with
+                 Z0 => q1
+               | _ => (Pos.succ q1)
+               end
+  |  _ => xH
+  end.
+
+Theorem Pdiv_le: forall p q,
+  Zpos p <= Zpos q * Zpos (Pdiv p q).
+intros p q.
+unfold Pdiv.
+assert (H1: Zpos q > 0); auto with zarith.
+assert (H1b: Zpos p >= 0); auto with zarith.
+generalize (Z_div_ge0 (Zpos p) (Zpos q) H1 H1b).
+generalize (Z_div_mod_eq (Zpos p) (Zpos q) H1); case Z.div.
+  intros HH _; rewrite HH; rewrite Z.mul_0_r; rewrite Z.mul_1_r; simpl.
+case (Z_mod_lt (Zpos p) (Zpos q) H1); auto with zarith.
+intros q1 H2.
+replace (Zpos p - Zpos q * Zpos q1) with (Zpos p mod Zpos q).
+  2: pattern (Zpos p) at 2; rewrite H2; auto with zarith.
+generalize H2 (Z_mod_lt (Zpos p) (Zpos q) H1); clear H2;
+  case Z.modulo.
+  intros HH _; rewrite HH; auto with zarith.
+  intros r1 HH (_,HH1); rewrite HH; rewrite Pos2Z.inj_succ.
+  unfold Z.succ; rewrite Z.mul_add_distr_l; auto with zarith.
+  intros r1 _ (HH,_); case HH; auto.
+intros q1 HH; rewrite HH.
+unfold Z.ge; simpl Z.compare; intros HH1; case HH1; auto.
+Qed.
+
+Definition is_one p := match p with xH => true | _ => false end.
+
+Theorem is_one_one: forall p, is_one p = true -> p = xH.
+intros p; case p; auto; intros p1 H1; discriminate H1.
+Qed.
+
+Definition get_height digits p :=
+  let r := Pdiv p digits in
+   if is_one r then xH else Pos.succ (plength (Pos.pred r)).
+
+Theorem get_height_correct:
+  forall digits N,
+   Zpos N <= Zpos digits * (2 ^ (Zpos (get_height digits N) -1)).
+intros digits N.
+unfold get_height.
+assert (H1 := Pdiv_le N digits).
+case_eq (is_one (Pdiv N digits)); intros H2.
+rewrite (is_one_one _ H2) in H1.
+rewrite Z.mul_1_r in H1.
+change (2^(1-1))%Z with 1; rewrite Z.mul_1_r; auto.
+clear H2.
+apply Z.le_trans with (1 := H1).
+apply Z.mul_le_mono_nonneg_l; auto with zarith.
+rewrite Pos2Z.inj_succ; unfold Z.succ.
+rewrite Z.add_comm; rewrite Z.add_simpl_l.
+apply plength_pred_correct.
+Qed.
+
+Definition zn2z_word_comm : forall w n, zn2z (word w n) = word (zn2z w) n.
+ fix zn2z_word_comm 2.
+ intros w n; case n.
+  reflexivity.
+  intros n0;simpl.
+  case (zn2z_word_comm w n0).
+  reflexivity.
+Defined.
+
+Fixpoint extend (n:nat) {struct n} : forall w:Type, zn2z w -> word w (S n) :=
+ match n return forall w:Type, zn2z w -> word w (S n) with
+ | O => fun w x => x
+ | S m =>
+   let aux := extend m in
+   fun w x => WW W0 (aux w x)
+ end.
+
+Section ExtendMax.
+
+Open Scope nat_scope.
+
+Fixpoint plusnS (n m: nat) {struct n} : (n + S m = S (n + m))%nat :=
+  match n return  (n + S m = S (n + m))%nat with
+  | 0 => eq_refl (S m)
+  | S n1 =>
+      let v := S (S n1 + m) in
+      eq_ind_r (fun n => S n = v) (eq_refl v) (plusnS n1 m)
+  end.
+
+Fixpoint plusn0 n : n + 0 = n :=
+  match n return (n + 0 = n) with
+  | 0 => eq_refl 0
+  | S n1 =>
+      let v := S n1 in
+      eq_ind_r (fun n : nat => S n = v) (eq_refl v) (plusn0 n1)
+  end.
+
+ Fixpoint diff (m n: nat) {struct m}: nat * nat :=
+   match m, n with
+     O, n => (O, n)
+   | m, O => (m, O)
+   | S m1, S n1 => diff m1 n1
+   end.
+
+Fixpoint diff_l (m n : nat) {struct m} : fst (diff m n) + n = max m n :=
+  match m return fst (diff m n) + n = max m n with
+  | 0 =>
+      match n return (n = max 0 n) with
+      | 0 => eq_refl _
+      | S n0 => eq_refl _
+      end
+  | S m1 =>
+      match n return (fst (diff (S m1) n) + n = max (S m1) n)
+      with
+      | 0 => plusn0 _
+      | S n1 =>
+          let v := fst (diff m1 n1) + n1 in
+          let v1 := fst (diff m1 n1) + S n1 in
+          eq_ind v (fun n => v1 = S n)
+            (eq_ind v1 (fun n => v1 = n) (eq_refl v1) (S v) (plusnS _ _))
+            _ (diff_l _ _)
+      end
+  end.
+
+Fixpoint diff_r (m n: nat) {struct m}: snd (diff m n) + m = max m n :=
+  match m return (snd (diff m n) + m = max m n) with
+  | 0 =>
+      match n return (snd (diff 0 n) + 0 = max 0 n) with
+      | 0 => eq_refl _
+      | S _ => plusn0 _
+      end
+  | S m =>
+      match n return (snd (diff (S m) n) + S m = max (S m) n) with
+      | 0 => eq_refl (snd (diff (S m) 0) + S m)
+      | S n1 =>
+          let v := S (max m n1) in
+          eq_ind_r (fun n => n = v)
+            (eq_ind_r (fun n => S n = v)
+               (eq_refl v) (diff_r _ _)) (plusnS _ _)
+      end
+  end.
+
+ Variable w: Type.
+
+ Definition castm (m n: nat) (H: m = n) (x: word w (S m)):
+     (word w (S n)) :=
+ match H in (_ = y) return (word w (S y)) with
+ | eq_refl => x
+ end.
+
+Variable m: nat.
+Variable v: (word w (S m)).
+
+Fixpoint extend_tr (n : nat) {struct n}: (word w (S (n + m))) :=
+  match n  return (word w (S (n + m))) with
+  | O => v
+  | S n1 => WW W0 (extend_tr n1)
+  end.
+
+End ExtendMax.
+
+Arguments extend_tr [w m] v n.
+Arguments castm     [w m n] H x.
+
+
+
+Section Reduce.
+
+ Variable w : Type.
+ Variable nT : Type.
+ Variable N0 : nT.
+ Variable eq0 : w -> bool.
+ Variable reduce_n : w -> nT.
+ Variable zn2z_to_Nt : zn2z w -> nT.
+
+ Definition reduce_n1 (x:zn2z w) :=
+  match x with
+  | W0 => N0
+  | WW xh xl =>
+    if eq0 xh then reduce_n xl
+    else zn2z_to_Nt x
+  end.
+
+End Reduce.
+
+Section ReduceRec.
+
+ Variable w : Type.
+ Variable nT : Type.
+ Variable N0 : nT.
+ Variable reduce_1n : zn2z w -> nT.
+ Variable c : forall n, word w (S n) -> nT.
+
+ Fixpoint reduce_n (n:nat) : word w (S n) -> nT :=
+  match n return word w (S n) -> nT with
+  | O => reduce_1n
+  | S m => fun x =>
+    match x with
+    | W0 => N0
+    | WW xh xl =>
+      match xh with
+      | W0 => @reduce_n m xl
+      | _ => @c (S m) x
+      end
+    end
+  end.
+
+End ReduceRec.
+
+Section CompareRec.
+
+ Variable wm w : Type.
+ Variable w_0 : w.
+ Variable compare : w -> w ->