more proofs updated

examples/WP_revisited/formula/why3session.xml

@@ -5,14 +5,14 @@
 <prover id="1" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="0"/>
 <prover id="2" name="Vampire" version="0.6" timelimit="5" steplimit="0" memlimit="0"/>
 <prover id="3" name="Alt-Ergo" version="0.99.1" timelimit="5" steplimit="0" memlimit="0"/>
-<file name="../formula.why">
-<theory name="Formula" sum="d41d8cd98f00b204e9800998ecf8427e" expanded="true">
+<file name="../formula.why" expanded="true">
+<theory name="Formula" sum="d41d8cd98f00b204e9800998ecf8427e">
 </theory>
-<theory name="PropositionalCalculus" sum="8e90228c74fc9a58ce016c323f7a8bff" expanded="true">
+<theory name="PropositionalCalculus" sum="006c6d79ffb672881234e4a2aa8e3016" expanded="true">
  <goal name="Test1" expanded="true">
  <proof prover="1"><result status="valid" time="0.01"/></proof>
  <proof prover="2"><result status="valid" time="0.19"/></proof>
- <proof prover="3"><result status="valid" time="0.05" steps="46"/></proof>
+ <proof prover="3"><result status="valid" time="0.05" steps="48"/></proof>
  </goal>
 </theory>
 </file>

examples/WP_revisited/imp_n.why

@@ -186,7 +186,7 @@ function subst_expr (e:expr) (x:ident) (t:expr) : expr =
   end
 
 lemma eval_subst_expr:
-  forall s:state, e:expr, x:ident, t:expr.
+  forall s:state, e "induction":expr, x:ident, t:expr.
     eval_expr s (subst_expr e x t) =
       eval_expr (IdMap.set s x (eval_expr s t)) e
 

examples/WP_revisited/imp_n/why3session.xml

@@ -4,67 +4,66 @@
 <why3session shape_version="4">
 <prover id="0" name="Coq" version="8.6" timelimit="3" steplimit="0" memlimit="0"/>
 <prover id="1" name="CVC3" version="2.4.1" timelimit="3" steplimit="0" memlimit="0"/>
-<prover id="5" name="Z3" version="3.2" timelimit="3" steplimit="0" memlimit="0"/>
-<prover id="6" name="Alt-Ergo" version="0.99.1" timelimit="3" steplimit="0" memlimit="0"/>
-<prover id="7" name="Z3" version="4.3.2" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="4" name="Alt-Ergo" version="1.30" timelimit="5" steplimit="0" memlimit="1000"/>
 <file name="../imp_n.why" expanded="true">
-<theory name="Imp" sum="c5b2f605219b1db882298415fdd56cc4" expanded="true">
+<theory name="Imp" sum="5dd0f4706664ed444265b03d0a9e3322" expanded="true">
  <goal name="ident_eq_dec">
- <proof prover="6"><result status="valid" time="0.00" steps="0"/></proof>
+ <proof prover="4"><result status="valid" time="0.00" steps="1"/></proof>
  </goal>
  <goal name="check_skip">
- <proof prover="6"><result status="valid" time="0.00" steps="1"/></proof>
+ <proof prover="4"><result status="valid" time="0.00" steps="2"/></proof>
  </goal>
  <goal name="Test13">
- <proof prover="6"><result status="valid" time="0.02" steps="4"/></proof>
+ <proof prover="4"><result status="valid" time="0.01" steps="3"/></proof>
  </goal>
  <goal name="Test42">
- <proof prover="6"><result status="valid" time="0.02" steps="2"/></proof>
+ <proof prover="4"><result status="valid" time="0.01" steps="3"/></proof>
  </goal>
  <goal name="Test55">
- <proof prover="6"><result status="valid" time="0.02" steps="25"/></proof>
+ <proof prover="4"><result status="valid" time="0.00" steps="17"/></proof>
  </goal>
  <goal name="Ass42">
- <proof prover="6"><result status="valid" time="0.09" steps="90"/></proof>
+ <proof prover="4"><result status="valid" time="0.04" steps="128"/></proof>
  </goal>
  <goal name="If42">
- <proof prover="5" timelimit="5" memlimit="1000"><result status="valid" time="0.06"/></proof>
- <proof prover="6" timelimit="5" memlimit="1000"><result status="valid" time="0.29" steps="489"/></proof>
- <proof prover="7"><result status="valid" time="0.08"/></proof>
+ <proof prover="4"><result status="valid" time="0.13" steps="543"/></proof>
  </goal>
  <goal name="progress">
  <proof prover="0" edited="imp_n_Imp_progress_1.v"><result status="valid" time="0.31"/></proof>
  </goal>
  <goal name="steps_non_neg">
- <proof prover="0" edited="imp_n_Imp_steps_non_neg_1.v"><result status="valid" time="0.30"/></proof>
+ <proof prover="0" edited="imp_n_Imp_steps_non_neg_1.v"><result status="valid" time="0.50"/></proof>
  </goal>
  <goal name="many_steps_seq">
  <proof prover="0" edited="imp_n_Imp_many_steps_seq_1.v"><result status="valid" time="0.36"/></proof>
  </goal>
  <goal name="eval_subst_expr">
- <proof prover="0" edited="imp_n_Imp_eval_subst_expr_1.v"><result status="valid" time="0.34"/></proof>
+ <transf name="induction_ty_lex">
+  <goal name="eval_subst_expr.1" expl="1.">
+  <proof prover="4"><result status="valid" time="0.02" steps="113"/></proof>
+  </goal>
+ </transf>
  </goal>
  <goal name="eval_subst">
- <proof prover="0" edited="imp_n_Imp_eval_subst_1.v"><result status="valid" time="0.35"/></proof>
+ <proof prover="0" edited="imp_n_Imp_eval_subst_1.v"><result status="valid" time="0.51"/></proof>
  </goal>
  <goal name="skip_rule">
- <proof prover="6"><result status="valid" time="0.04" steps="113"/></proof>
+ <proof prover="4"><result status="valid" time="0.04" steps="148"/></proof>
  </goal>
  <goal name="assign_rule">
- <proof prover="0" edited="imp_n_Imp_assign_rule_1.v"><result status="valid" time="0.33"/></proof>
+ <proof prover="4"><result status="valid" time="1.39" steps="1910"/></proof>
  </goal>
  <goal name="seq_rule">
- <proof prover="0" edited="imp_n_Imp_seq_rule_1.v"><result status="valid" time="0.33"/></proof>
+ <proof prover="4"><result status="valid" time="3.09" steps="7135"/></proof>
  </goal>
  <goal name="if_rule">
  <proof prover="0" edited="imp_n_Imp_if_rule_1.v"><result status="valid" time="0.33"/></proof>
  </goal>
  <goal name="while_rule">
- <proof prover="0" edited="imp_n_Imp_while_rule_1.v"><result status="valid" time="0.33"/></proof>
+ <proof prover="0" edited="imp_n_Imp_while_rule_1.v"><result status="valid" time="0.57"/></proof>
  </goal>
  <goal name="consequence_rule">
  <proof prover="1"><result status="valid" time="0.05"/></proof>
- <proof prover="5"><result status="timeout" time="2.98"/></proof>
  </goal>
 </theory>
 </file>

examples/vacid_0_sparse_array/vacid_0_sparse_array_2_SparseArray_permutation_1.v

-(* This file is generated by Why3's Coq driver *)
-(* Beware! Only edit allowed sections below    *)
-Require Import BuiltIn.
-Require BuiltIn.
-Require HighOrd.
-Require int.Int.
-Require map.Map.
-Require map.Occ.
-Require map.MapInjection.
-
-(* Why3 assumption *)
-Definition unit := unit.
-
-Axiom array : forall (a:Type), Type.
-Parameter array_WhyType : forall (a:Type) {a_WT:WhyType a},
-  WhyType (array a).
-Existing Instance array_WhyType.
-
-Parameter elts: forall {a:Type} {a_WT:WhyType a}, (array a) -> (Z -> a).
-
-Parameter length: forall {a:Type} {a_WT:WhyType a}, (array a) -> Z.
-
-Axiom array'invariant : forall {a:Type} {a_WT:WhyType a}, forall (self:(array
-  a)), (0%Z <= (length self))%Z.
-
-(* Why3 assumption *)
-Definition mixfix_lbrb {a:Type} {a_WT:WhyType a} (a1:(array a)) (i:Z): a :=
-  ((elts a1) i).
-
-Parameter mixfix_lblsmnrb: forall {a:Type} {a_WT:WhyType a}, (array a) ->
-  Z -> a -> (array a).
-
-Axiom mixfix_lblsmnrb_spec : forall {a:Type} {a_WT:WhyType a},
-  forall (a1:(array a)) (i:Z) (v:a), ((length (mixfix_lblsmnrb a1 i
-  v)) = (length a1)) /\ ((elts (mixfix_lblsmnrb a1 i
-  v)) = (map.Map.set (elts a1) i v)).
-
-Axiom sparse_array : forall (a:Type), Type.
-Parameter sparse_array_WhyType : forall (a:Type) {a_WT:WhyType a},
-  WhyType (sparse_array a).
-Existing Instance sparse_array_WhyType.
-
-Parameter values: forall {a:Type} {a_WT:WhyType a}, (sparse_array a) ->
-  (array a).
-
-Parameter index: forall {a:Type} {a_WT:WhyType a}, (sparse_array a) -> (array
-  Z).
-
-Parameter back: forall {a:Type} {a_WT:WhyType a}, (sparse_array a) -> (array
-  Z).
-
-Parameter card: forall {a:Type} {a_WT:WhyType a}, (sparse_array a) -> Z.
-
-Parameter def: forall {a:Type} {a_WT:WhyType a}, (sparse_array a) -> a.
-
-Axiom sparse_array'invariant : forall {a:Type} {a_WT:WhyType a},
-  forall (self:(sparse_array a)), ((0%Z <= (card self))%Z /\
-  (((card self) <= (length (values self)))%Z /\
-  ((length (values self)) <= 1000%Z)%Z)) /\
-  ((((length (values self)) = (length (index self))) /\
-  ((length (index self)) = (length (back self)))) /\ forall (i:Z),
-  ((0%Z <= i)%Z /\ (i < (card self))%Z) -> (((0%Z <= (mixfix_lbrb (back self)
-  i))%Z /\ ((mixfix_lbrb (back self) i) < (length (values self)))%Z) /\
-  ((mixfix_lbrb (index self) (mixfix_lbrb (back self) i)) = i))).
-
-(* Why3 assumption *)
-Definition is_elt {a:Type} {a_WT:WhyType a} (a1:(sparse_array a))
-  (i:Z): Prop := ((0%Z <= (mixfix_lbrb (index a1) i))%Z /\
-  ((mixfix_lbrb (index a1) i) < (card a1))%Z) /\ ((mixfix_lbrb (back a1)
-  (mixfix_lbrb (index a1) i)) = i).
-
-Parameter value: forall {a:Type} {a_WT:WhyType a}, (sparse_array a) -> Z ->
-  a.
-
-Axiom value_def : forall {a:Type} {a_WT:WhyType a}, forall (a1:(sparse_array
-  a)) (i:Z), ((is_elt a1 i) -> ((value a1 i) = (mixfix_lbrb (values a1)
-  i))) /\ ((~ (is_elt a1 i)) -> ((value a1 i) = (def a1))).
-
-(* Why3 assumption *)
-Definition length1 {a:Type} {a_WT:WhyType a} (a1:(sparse_array a)): Z :=
-  (length (values a1)).
-
-Require Import Why3.
-Ltac ae := why3 "Alt-Ergo,0.99.1," timelimit 5; admit.
-
-(* Why3 goal *)
-Theorem permutation : forall {a:Type} {a_WT:WhyType a},
-  forall (a1:(sparse_array a)), (((0%Z <= (card a1))%Z /\
-  (((card a1) <= (length (values a1)))%Z /\
-  ((length (values a1)) <= 1000%Z)%Z)) /\
-  ((((length (values a1)) = (length (index a1))) /\
-  ((length (index a1)) = (length (back a1)))) /\ forall (i:Z),
-  ((0%Z <= i)%Z /\ (i < (card a1))%Z) -> (((0%Z <= (mixfix_lbrb (back a1)
-  i))%Z /\ ((mixfix_lbrb (back a1) i) < (length (values a1)))%Z) /\
-  ((mixfix_lbrb (index a1) (mixfix_lbrb (back a1) i)) = i)))) ->
-  (((card a1) = (length1 a1)) -> forall (i:Z), ((0%Z <= i)%Z /\
-  (i < (length1 a1))%Z) -> (is_elt a1 i)).
-(* Why3 intros a a_WT a1 ((h1,(h2,h3)),((h4,h5),h6)) h7 i (h8,h9). *)
-intros a _a a1.
-destruct a1 as ((n0, a_values), (n1, a_index), (n2, a_back), a_card, a_def); simpl.
-unfold is_elt, length1, get; simpl.
-intro H; decompose [and] H; clear H.
-subst n1 n2.
-intros. subst a_card.
-assert (inj: MapInjection.injective a_back n0) by ae.
-assert (rng: MapInjection.range a_back n0) by ae.
-generalize (MapInjection.injective_surjective a_back n0 inj rng); intro surj.
-destruct (surj i H1) as (j, (hj1, hj2)).
-ae.
-Admitted.
-