sessions: more updates for Coq 8.5

examples/bellman_ford/bellman_ford_Graph_long_path_decomposition_1.v

@@ -241,6 +241,9 @@ Axiom long_path_decomposition_pigeon3 : forall (l:(list vertex)) (v:vertex),
   exists l3:(list vertex),
   (l = (Init.Datatypes.app l1 (Init.Datatypes.cons n (Init.Datatypes.app l2 (Init.Datatypes.cons n l3)))))).
 
+Require Import Why3.
+Ltac ae := why3 "Alt-Ergo,0.99.1," timelimit 5; admit.
+
 (* Why3 goal *)
 Theorem long_path_decomposition : forall (l:(list vertex)) (v:vertex), (path
   s l v) -> (((cardinal vertices) <= (list.Length.length l))%Z ->
@@ -252,11 +255,8 @@ Theorem long_path_decomposition : forall (l:(list vertex)) (v:vertex), (path
 (* Why3 intros l v h1 h2. *)
 intuition.
 
-Require Why3.
-Ltac ae := why3 "alt-ergo".
-
 apply long_path_decomposition_pigeon3.
 apply long_path_decomposition_pigeon2 ; ae.
 
-Qed.
+Admitted.
 

examples/bellman_ford/bf_Graph_key_lemma_1_1.v

@@ -258,7 +258,8 @@ Definition negative_cycle (v:vertex): Prop := (mem v vertices) /\
   ((exists l1:(list vertex), (path s l1 v)) /\ exists l2:(list vertex), (path
   v l2 v) /\ ((path_weight l2 v) < 0%Z)%Z).
 
-Require Import Why3. Ltac ae := why3 "alt-ergo".
+Require Import Why3. 
+Ltac ae := why3 "Alt-Ergo,0.99.1," timelimit 5; admit.
 
 Require Import list.Length.
 
@@ -342,5 +343,5 @@ assert (path_weight ln v =
 assert (path_weight l' v = path_weight l1 u + path_weight (cons u l3) v)%Z.
   ae.
 omega.
-Qed.
+Admitted.
 

examples/bellman_ford/bf_Graph_simple_path_1.v

@@ -249,7 +249,8 @@ Axiom long_path_decomposition : forall (l:(list vertex)) (v:vertex), (path s
   exists l3:(list vertex),
   (l = (Init.Datatypes.app l1 (Init.Datatypes.cons n (Init.Datatypes.app l2 (Init.Datatypes.cons n l3))))))).
 
-Require Import Why3. Ltac ae := why3 "alt-ergo".
+Require Import Why3. 
+Ltac ae := why3 "Alt-Ergo,0.99.1," timelimit 5; admit.
 
 Require Import list.Length.
 
@@ -299,5 +300,5 @@ assert (0 <= length (app l1 (cons u l3)) < z)%Z.
 apply (IH (length (app l1 (cons u l3))) H1 (app l1 (cons u l3))).
 omega.
 assumption.
-Qed.
+Admitted.
 

examples/bellman_ford/bf_WP_BellmanFord_WP_parameter_bellman_ford_17.v

@@ -354,8 +354,9 @@ Axiom key_lemma_2 : forall (m:(map.Map.map vertex t)), (inv1 m
   edges) -> forall (v:vertex), ~ (negative_cycle v)).
 
 Require Import Why3.
-Ltac Z3 := why3 "z3".
-Ltac ae := why3 "alt-ergo".
+Ltac Z3 := why3 "Z3,4.4.0,"; admit.
+Ltac ae := why3 "Alt-Ergo,0.99.1,"; admit.
+Ltac cvc3 := why3 "CVC3,2.4.1,"; admit.
 
 (* Why3 goal *)
 Theorem WP_parameter_bellman_ford : let o := ((cardinal vertices) - 1%Z)%Z in
@@ -412,7 +413,9 @@ intros o h1 m i (h2,h3) h4 es h5 es1 m1 (h6,h7) o1 h8 h9 h10 v h11 x
         h12 l hpath hlength.
 destruct (path_right_inversion s v l hpath) as [(hg1,hg2) | (y, (l', (hg1, (hg2, hg3))))].
 (* Nil *)
-subst. simpl. why3 "cvc3".
+cvc3.
+subst. simpl. cvc3.
+(*
 (* Cons *)
 rewrite hg3; rewrite path_weight_right_extension.
 generalize (h10 v h11); clear h10.
@@ -423,5 +426,6 @@ assert (Length.length l = Length.length l' + 1)%Z.
 subst l. rewrite Append.Append_length.
 auto.
 ae.
-Qed.
+*)
+Admitted.
 

examples/bellman_ford/bf_WP_BellmanFord_WP_parameter_bellman_ford_18.v

@@ -354,7 +354,7 @@ Axiom key_lemma_2 : forall (m:(map.Map.map vertex t)), (inv1 m
   edges) -> forall (v:vertex), ~ (negative_cycle v)).
 
 Require Import Why3.
-Ltac ae := why3 "alt-ergo" timelimit 30.
+Ltac ae := why3 "Alt-Ergo,0.99.1," timelimit 30; admit.
 
 (* Why3 goal *)
 Theorem WP_parameter_bellman_ford : let o := ((cardinal vertices) - 1%Z)%Z in
@@ -421,5 +421,5 @@ assert (i <= Length.length l')%Z by ae.
 assert (Length.length l = Length.length l' + 1)%Z.
 subst l. apply Append.Append_length.
 ae.
-Qed.
+Admitted.
 

examples/bellman_ford/bf_WP_BellmanFord_WP_parameter_bellman_ford_19.v

@@ -7,15 +7,12 @@ Require list.Length.
 Require int.Int.
 Require list.Mem.
 Require map.Map.
+Require map.Const.
 Require list.Append.
 
 (* Why3 assumption *)
 Definition unit := unit.
 
-Axiom qtmark : Type.
-Parameter qtmark_WhyType : WhyType qtmark.
-Existing Instance qtmark_WhyType.
-
 Axiom set : forall (a:Type), Type.
 Parameter set_WhyType : forall (a:Type) {a_WT:WhyType a}, WhyType (set a).
 Existing Instance set_WhyType.
@@ -116,6 +113,10 @@ Axiom cardinal_remove : forall {a:Type} {a_WT:WhyType a}, forall (x:a),
 Axiom cardinal_subset : forall {a:Type} {a_WT:WhyType a}, forall (s1:(set a))
   (s2:(set a)), (subset s1 s2) -> ((cardinal s1) <= (cardinal s2))%Z.
 
+Axiom subset_eq : forall {a:Type} {a_WT:WhyType a}, forall (s1:(set a))
+  (s2:(set a)), (subset s1 s2) -> (((cardinal s1) = (cardinal s2)) ->
+  (infix_eqeq s1 s2)).
+
 Axiom cardinal1 : forall {a:Type} {a_WT:WhyType a}, forall (s:(set a)),
   ((cardinal s) = 1%Z) -> forall (x:a), (mem x s) -> (x = (choose s)).
 
@@ -353,7 +354,7 @@ Axiom key_lemma_2 : forall (m:(map.Map.map vertex t)), (inv1 m
   edges) -> forall (v:vertex), ~ (negative_cycle v)).
 
 Require Import Why3.
-Ltac ae := why3 "alt-ergo".
+Ltac ae := why3 "Alt-Ergo,0.99.1," timelimit 5; admit.
 
 (* Why3 goal *)
 Theorem WP_parameter_bellman_ford : let o := ((cardinal vertices) - 1%Z)%Z in
@@ -366,6 +367,7 @@ Theorem WP_parameter_bellman_ford : let o := ((cardinal vertices) - 1%Z)%Z in
   forall (v:vertex), (mem v vertices) -> forall (x:Z), ((map.Map.get m
   v) = (Finite x)) -> forall (l:(list vertex)), (path s l v) ->
   (x <= (path_weight l v))%Z)))).
+(* Why3 intros o h1 m h2 h3 es h4 es1 (h5,h6) o1 h7 h8 h9 v h10 x h11 l h12. *)
 intros o _ m _ hinv1 _ _ _ _ _ _ _ hinv2 v hv z Heqt0 l hl.
 assert (case: (z <= path_weight l v \/ path_weight l v < z)%Z) by omega.
 destruct case; auto.
@@ -374,5 +376,5 @@ generalize (hinv1 v hv); clear hinv1 hinv2.
 rewrite Heqt0; ae.
 exists l; intuition.
 ae.
-Qed.
+Admitted.
 

examples/bellman_ford/bf_WP_BellmanFord_WP_parameter_bellman_ford_20.v

@@ -354,7 +354,7 @@ Axiom key_lemma_2 : forall (m:(map.Map.map vertex t)), (inv1 m
   edges) -> forall (v:vertex), ~ (negative_cycle v)).
 
 Require Import Why3.
-Ltac ae := why3 "alt-ergo".
+Ltac ae := why3 "Alt-Ergo,0.99.1,"; admit.
 
 (* Why3 goal *)
 Theorem WP_parameter_bellman_ford : (((cardinal vertices) - 1%Z)%Z < 1%Z)%Z ->
@@ -377,7 +377,7 @@ Theorem WP_parameter_bellman_ford : (((cardinal vertices) - 1%Z)%Z < 1%Z)%Z ->
       vertex t)) s (Finite 0%Z))
       result1) with
       | Infinite => True
-      | (Finite y) => ((x + (weight result result1))%Z < y)%Z
+      | (Finite x1) => ((x + (weight result result1))%Z < x1)%Z
       end
   end -> exists v:vertex, (negative_cycle v)))))).
 (* Why3 intros h1 h2 es h3 es1 (h4,h5) o h6 h7 h8 es2 result result1 result2
@@ -395,8 +395,12 @@ assert (v = s) by ae. subst v.
 rewrite Map.Select_eq; auto.
 intros hneg.
 exists s. red.
-split. ae.
-split. exists nil; ae.
-exists (cons s nil); ae.
-Qed.
+split. 
+- ae.
+- split. 
+  + exists nil; ae.
+  + exists (cons s nil); split.
+    apply Path_cons with s; ae.
+    ae.
+Admitted.
 

examples/bellman_ford/bf_WP_BellmanFord_WP_parameter_relax_7.v

@@ -354,7 +354,7 @@ Axiom key_lemma_2 : forall (m:(map.Map.map vertex t)), (inv1 m
   edges) -> forall (v:vertex), ~ (negative_cycle v)).
 
 Require Import Why3.
-Ltac ae := why3 "alt-ergo".
+Ltac ae := why3 "Alt-Ergo,0.99.1,"; admit.
 Require Import Classical.
 
 (* Why3 goal *)
@@ -379,7 +379,7 @@ Theorem WP_parameter_relax : forall (m:(map.Map.map vertex t)) (u:vertex)
   | (Finite x) => match (map.Map.get m
       v) with
       | Infinite => True
-      | (Finite y) => ((x + (weight u v))%Z < y)%Z
+      | (Finite x1) => ((x + (weight u v))%Z < x1)%Z
       end
   end -> forall (m1:(map.Map.map vertex t)), (m1 = (map.Map.set m v
   match (map.Map.get m
@@ -400,5 +400,5 @@ destruct H as (lu, (hu1, hu2)).
 exists (app lu (cons u nil)); ae.
 subst m1. rewrite Map.Select_neq; auto.
 ae.
-Qed.
+Admitted.
 

examples/bellman_ford/bf_WP_BellmanFord_key_lemma_2_1.v

@@ -350,8 +350,8 @@ Definition inv2 (m:(map.Map.map vertex t)) (via:(set (vertex*
   (le (map.Map.get m v) (add1 (map.Map.get m u) (Finite (weight u v)))).
 
 Require Import Why3.
-Ltac ae := why3 "alt-ergo" timelimit 60.
-Ltac Z3 := why3 "z3" timelimit 10.
+Ltac ae := why3 "alt-ergo" timelimit 60; admit.
+Ltac Z3 := why3 "z3" timelimit 10; admit.
 
 Require Import list.Length.
 
@@ -400,5 +400,5 @@ unfold le, add1; destruct (Map.get m v) as [] _eqn.
 ae.
 absurd (Map.get m v = Infinite); auto.
 ae.
-Qed.
+Admitted.
 

examples/euler002.mlw

@@ -41,14 +41,17 @@ theory FibSumEven "sum of even-valued Fibonacci numbers"
 
 end
 
-theory FibOnlyEven
+module FibOnlyEven
 
   use import int.Int
   use import int.ComputerDivision
   use import int.Fibonacci
 
-  lemma fib_even_3n : forall n:int. n >= 0 ->
-    mod (fib n) 2 = 0 <-> mod n 3 = 0
+  let rec lemma fib_even_3n (n:int)
+    requires { n >= 0 }
+    variant { n }
+    ensures { mod (fib n) 2 = 0 <-> mod n 3 = 0 }
+  = if n > 2 then fib_even_3n (n-3)
 
   function fib_even (n: int) : int = fib (3 * n)
 

examples/euler002/euler002_FibOnlyEven_fib_even_1.v

-(* This file is generated by Why3's Coq 8.4 driver *)
-(* Beware! Only edit allowed sections below    *)
-Require Import BuiltIn.
-Require Import ZOdiv.
-Require BuiltIn.
-Require int.Int.
-Require int.Abs.
-Require int.ComputerDivision.
-
-Parameter fib: Z -> Z.
-
-Axiom fib0 : ((fib 0%Z) = 0%Z).
-
-Axiom fib1 : ((fib 1%Z) = 1%Z).
-
-Axiom fibn : forall (n:Z), (2%Z <= n)%Z ->
-  ((fib n) = ((fib (n - 1%Z)%Z) + (fib (n - 2%Z)%Z))%Z).
-
-Require Import Why3.
-
-(* Why3 goal *)
-Theorem fib_even_3n : forall (n:Z), (0%Z <= n)%Z ->
-  (((ZOmod (fib n) 2%Z) = 0%Z) <-> ((ZOmod n 3%Z) = 0%Z)).
-Proof.
-intros n h1.
-generalize h1; pattern n.
-apply Z_lt_induction; auto.
-why3 "cvc3" timelimit 10.
-Qed.