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https://github.com/AdaCore/why3.git
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programs: WP code refactored
This commit is contained in:
Jean-Christophe Filliatre
@@ -18,34 +18,43 @@ Parameter old: forall (a:Type), a -> a.
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Implicit Arguments old.
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Definition ref (a:Type) := a.
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Inductive ref (a:Type) :=
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| mk_ref : a -> ref a.
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Implicit Arguments mk_ref.
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Definition contents (a:Type)(u:(ref a)): a :=
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match u with
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| mk_ref contents1 => contents1
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end.
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Implicit Arguments contents.
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Parameter map : forall (a:Type) (b:Type), Type.
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Parameter get: forall (a:Type) (b:Type), (map a b) -> a -> b.
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Parameter mixfix_lbrb: forall (a:Type) (b:Type), (map a b) -> a -> b.
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Implicit Arguments get.
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Implicit Arguments mixfix_lbrb.
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Parameter set: forall (a:Type) (b:Type), (map a b) -> a -> b -> (map a b).
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Parameter mixfix_lblsmnrb: forall (a:Type) (b:Type), (map a b) -> a -> b ->
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(map a b).
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Implicit Arguments set.
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Implicit Arguments mixfix_lblsmnrb.
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Axiom Select_eq : forall (a:Type) (b:Type), forall (m:(map a b)),
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forall (a1:a) (a2:a), forall (b1:b), (a1 = a2) -> ((get (set m a1 b1)
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a2) = b1).
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forall (a1:a) (a2:a), forall (b1:b), (a1 = a2) ->
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((mixfix_lbrb (mixfix_lblsmnrb m a1 b1) a2) = b1).
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Axiom Select_neq : forall (a:Type) (b:Type), forall (m:(map a b)),
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forall (a1:a) (a2:a), forall (b1:b), (~ (a1 = a2)) -> ((get (set m a1 b1)
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a2) = (get m a2)).
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forall (a1:a) (a2:a), forall (b1:b), (~ (a1 = a2)) ->
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((mixfix_lbrb (mixfix_lblsmnrb m a1 b1) a2) = (mixfix_lbrb m a2)).
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Parameter create_const: forall (b:Type) (a:Type), b -> (map a b).
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Parameter const: forall (b:Type) (a:Type), b -> (map a b).
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Set Contextual Implicit.
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Implicit Arguments create_const.
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Implicit Arguments const.
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Unset Contextual Implicit.
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Axiom Const : forall (b:Type) (a:Type), forall (b1:b) (a1:a),
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((get (create_const(b1):(map a b)) a1) = b1).
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((mixfix_lbrb (const(b1):(map a b)) a1) = b1).
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Inductive array (a:Type) :=
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| mk_array : Z -> (map Z a) -> array a.
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@@ -63,17 +72,24 @@ Definition length (a:Type)(u:(array a)): Z :=
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end.
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Implicit Arguments length.
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Definition mixfix_lbrb (a:Type)(a1:(array a)) (i:Z): a := (get (elts a1) i).
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Implicit Arguments mixfix_lbrb.
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Definition mixfix_lbrb1 (a:Type)(a1:(array a)) (i:Z): a :=
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(mixfix_lbrb (elts a1) i).
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Implicit Arguments mixfix_lbrb1.
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Definition mixfix_lblsmnrb1 (a:Type)(a1:(array a)) (i:Z) (v:a): (array a) :=
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match a1 with
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| mk_array xcl0 _ => (mk_array xcl0 (mixfix_lblsmnrb (elts a1) i v))
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end.
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Implicit Arguments mixfix_lblsmnrb1.
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Definition decrease1(a:(array Z)): Prop := forall (i:Z), ((0%Z <= i)%Z /\
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(i < ((length a) - 1%Z)%Z)%Z) -> (((mixfix_lbrb a
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i) - 1%Z)%Z <= (mixfix_lbrb a (i + 1%Z)%Z))%Z.
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(i < ((length a) - 1%Z)%Z)%Z) -> (((mixfix_lbrb1 a
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i) - 1%Z)%Z <= (mixfix_lbrb1 a (i + 1%Z)%Z))%Z.
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Theorem decrease1_induction : forall (a:(array Z)), (decrease1 a) ->
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forall (i:Z) (j:Z), (((0%Z <= i)%Z /\ (i <= j)%Z) /\
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(j < (length a))%Z) -> ((((mixfix_lbrb a
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i) + i)%Z - j)%Z <= (mixfix_lbrb a j))%Z.
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(j < (length a))%Z) -> ((((mixfix_lbrb1 a
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i) + i)%Z - j)%Z <= (mixfix_lbrb1 a j))%Z.
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(* YOU MAY EDIT THE PROOF BELOW *)
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unfold decrease1.
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intros a Ha i j Hij.
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@@ -86,11 +102,11 @@ destruct H4.
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subst x.
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ring_simplify.
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omega.
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apply Zle_trans with (mixfix_lbrb a (x-1) - 1)%Z.
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apply Zle_trans with (mixfix_lbrb1 a (x-1) - 1)%Z.
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assert (i <= x-1 < x)%Z by omega.
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assert (0 <= i <= x-1 /\ x-1 < length a)%Z by omega.
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generalize (H (x-1)%Z H8 H9); clear H; intuition.
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apply Zle_trans with (mixfix_lbrb a (x-1+1))%Z.
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apply Zle_trans with (mixfix_lbrb1 a (x-1+1))%Z.
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apply (Ha (x-1)%Z); omega.
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ring_simplify (x-1+1)%Z.
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omega.
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@@ -3,22 +3,22 @@
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<why3session name="examples/programs/decrease1/why3session.xml">
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<file name="../decrease1.mlw" verified="true" expanded="true">
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<theory name="Decrease1" verified="true" expanded="true">
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<goal name="decrease1_induction" sum="8319c3299f6c5b391aec5943ca151429" proved="true" expanded="true">
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<goal name="decrease1_induction" sum="eb0923143934165c0f02dda5dd1d9064" proved="true" expanded="true">
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<proof prover="coq" timelimit="10" edited="decrease1.mlw_Decrease1_decrease1_induction_2.v" obsolete="false">
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<result status="valid" time="0.75"/>
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<result status="valid" time="0.74"/>
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</proof>
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</goal>
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<goal name="WP_parameter search" expl="correctness of parameter search" sum="46e3d9215dcd11606cc49de64a5a327f" proved="true" expanded="true">
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<transf name="split_goal" proved="true" expanded="true">
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<goal name="WP_parameter search.1" expl="loop invariant init" sum="f5954e0aa354b70603e2561453b4ded0" proved="true" expanded="true">
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<goal name="WP_parameter search" expl="correctness of parameter search" sum="5ecc8b47f440f11c94bcb33eb0c0f5da" proved="true" expanded="false">
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<transf name="split_goal" proved="true" expanded="false">
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<goal name="WP_parameter search.1" expl="loop invariant init" sum="c3003e2b17bd7912bbde842b069e15bc" proved="true" expanded="false">
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<proof prover="alt-ergo" timelimit="10" edited="" obsolete="false">
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<result status="valid" time="0.02"/>
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</proof>
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<proof prover="z3" timelimit="10" edited="" obsolete="false">
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<result status="valid" time="0.02"/>
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<result status="valid" time="0.00"/>
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</proof>
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</goal>
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<goal name="WP_parameter search.2" expl="precondition" sum="f0aee083a6eefd91f49d716bfaf3a741" proved="true" expanded="true">
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<goal name="WP_parameter search.2" expl="precondition" sum="a9e24466223260e82e53917990341c5a" proved="true" expanded="false">
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<proof prover="alt-ergo" timelimit="10" edited="" obsolete="false">
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<result status="valid" time="0.02"/>
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</proof>
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@@ -26,15 +26,7 @@
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<result status="valid" time="0.03"/>
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</proof>
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</goal>
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<goal name="WP_parameter search.3" expl="normal postcondition" sum="c09d1921f62c8a7957bab3179290a800" proved="true" expanded="true">
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<proof prover="alt-ergo" timelimit="10" edited="" obsolete="false">
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<result status="valid" time="0.06"/>
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</proof>
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<proof prover="z3" timelimit="10" edited="" obsolete="false">
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<result status="valid" time="0.03"/>
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</proof>
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</goal>
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<goal name="WP_parameter search.4" expl="precondition" sum="fafef13cd1de3a63dcb73b0bead2cbe7" proved="true" expanded="true">
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<goal name="WP_parameter search.3" expl="normal postcondition" sum="c463c5623e8270cf898748cd4fc200db" proved="true" expanded="false">
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<proof prover="alt-ergo" timelimit="10" edited="" obsolete="false">
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<result status="valid" time="0.02"/>
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</proof>
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@@ -42,44 +34,36 @@
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<result status="valid" time="0.03"/>
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</proof>
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</goal>
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<goal name="WP_parameter search.5" expl="precondition" sum="60fccac213582dacf78a1595c1a07a68" proved="true" expanded="true">
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<goal name="WP_parameter search.4" expl="precondition" sum="c9ffe9627c38578519b5fb654bc2311b" proved="true" expanded="false">
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<proof prover="alt-ergo" timelimit="10" edited="" obsolete="false">
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<result status="valid" time="0.02"/>
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</proof>
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<proof prover="z3" timelimit="10" edited="" obsolete="false">
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<result status="valid" time="0.03"/>
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<result status="valid" time="0.00"/>
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</proof>
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</goal>
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<goal name="WP_parameter search.6" expl="loop invariant preservation" sum="f4703704714fb12b1cfc7e1f7033703a" proved="true" expanded="true">
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<proof prover="z3" timelimit="10" edited="" obsolete="false">
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<result status="valid" time="0.10"/>
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</proof>
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</goal>
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<goal name="WP_parameter search.7" expl="loop variant decreases" sum="fbefe9d12ef4966b8e4cd42008951924" proved="true" expanded="true">
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<proof prover="alt-ergo" timelimit="10" edited="" obsolete="false">
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<result status="valid" time="0.03"/>
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</proof>
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<proof prover="z3" timelimit="10" edited="" obsolete="false">
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<result status="valid" time="0.03"/>
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</proof>
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</goal>
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<goal name="WP_parameter search.8" expl="loop invariant preservation" sum="7c213b031c337fec29d0003aec1f4dc0" proved="true" expanded="true">
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<goal name="WP_parameter search.5" expl="precondition" sum="87f27d100b565712984fd9fda61cce4e" proved="true" expanded="false">
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<proof prover="alt-ergo" timelimit="10" edited="" obsolete="false">
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<result status="valid" time="0.02"/>
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</proof>
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<proof prover="z3" timelimit="10" edited="" obsolete="false">
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<result status="valid" time="0.06"/>
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<result status="valid" time="0.00"/>
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</proof>
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</goal>
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<goal name="WP_parameter search.9" expl="loop variant decreases" sum="c65a3f1470a58687f3ba32fd10a257dc" proved="true" expanded="true">
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<goal name="WP_parameter search.6" expl="loop invariant preservation" sum="726cc05d33c2e38e4510462e1e7605e2" proved="true" expanded="false">
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<proof prover="alt-ergo" timelimit="10" edited="" obsolete="false">
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<result status="valid" time="0.02"/>
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<result status="timeout" time="10.35"/>
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</proof>
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<proof prover="z3" timelimit="10" edited="" obsolete="false">
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<result status="valid" time="0.03"/>
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</proof>
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</goal>
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<goal name="WP_parameter search.10" expl="normal postcondition" sum="aed189de59d328d4a7873cf4ad31f1ee" proved="true" expanded="true">
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<goal name="WP_parameter search.7" expl="loop variant decreases" sum="2b005062b036872b0521075f47993799" proved="true" expanded="false">
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<proof prover="z3" timelimit="10" edited="" obsolete="false">
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<result status="valid" time="0.02"/>
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</proof>
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</goal>
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<goal name="WP_parameter search.8" expl="loop invariant preservation" sum="8c2b5cf695743e9c3d5c78cda24518fe" proved="true" expanded="false">
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<proof prover="alt-ergo" timelimit="10" edited="" obsolete="false">
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<result status="valid" time="0.03"/>
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</proof>
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@@ -87,11 +71,27 @@
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<result status="valid" time="0.03"/>
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</proof>
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</goal>
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<goal name="WP_parameter search.9" expl="loop variant decreases" sum="6180bf4f47e0f340cb46853306f6bf48" proved="true" expanded="false">
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<proof prover="alt-ergo" timelimit="10" edited="" obsolete="false">
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<result status="valid" time="0.02"/>
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</proof>
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<proof prover="z3" timelimit="10" edited="" obsolete="false">
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<result status="valid" time="0.02"/>
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</proof>
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</goal>
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<goal name="WP_parameter search.10" expl="normal postcondition" sum="df0f4238e9b7a001efd85670c5738437" proved="true" expanded="false">
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<proof prover="alt-ergo" timelimit="10" edited="" obsolete="false">
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<result status="valid" time="0.02"/>
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</proof>
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<proof prover="z3" timelimit="10" edited="" obsolete="false">
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<result status="valid" time="0.03"/>
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</proof>
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</goal>
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</transf>
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</goal>
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<goal name="WP_parameter search_rec" expl="correctness of parameter search_rec" sum="9fb29a60c6f5cf8d6b537c46b8c3ba87" proved="true" expanded="true">
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<transf name="split_goal" proved="true" expanded="true">
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<goal name="WP_parameter search_rec.1" expl="precondition" sum="e99d8b29c61d5561f42de7428f854f98" proved="true" expanded="true">
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<goal name="WP_parameter search_rec" expl="correctness of parameter search_rec" sum="e89966a62cd9e50970addcdec10b6caa" proved="true" expanded="false">
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<transf name="split_goal" proved="true" expanded="false">
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<goal name="WP_parameter search_rec.1" expl="precondition" sum="129dba47026aaf884be22c8cbc1d4a1a" proved="true" expanded="false">
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<proof prover="alt-ergo" timelimit="10" edited="" obsolete="false">
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<result status="valid" time="0.02"/>
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</proof>
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@@ -99,7 +99,31 @@
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<result status="valid" time="0.03"/>
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</proof>
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</goal>
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<goal name="WP_parameter search_rec.2" expl="normal postcondition" sum="d0e9788d6a49388120275a1794f251ca" proved="true" expanded="true">
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<goal name="WP_parameter search_rec.2" expl="normal postcondition" sum="c7add74865ef8eb3cc7e152b836f6394" proved="true" expanded="false">
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<proof prover="alt-ergo" timelimit="10" edited="" obsolete="false">
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<result status="valid" time="0.03"/>
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</proof>
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<proof prover="z3" timelimit="10" edited="" obsolete="false">
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<result status="valid" time="0.03"/>
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</proof>
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</goal>
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<goal name="WP_parameter search_rec.3" expl="precondition" sum="752cd932517186cc6711edbfdc9cdcc5" proved="true" expanded="false">
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<proof prover="alt-ergo" timelimit="10" edited="" obsolete="false">
|
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<result status="valid" time="0.02"/>
|
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</proof>
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<proof prover="z3" timelimit="10" edited="" obsolete="false">
|
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<result status="valid" time="0.00"/>
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</proof>
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</goal>
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<goal name="WP_parameter search_rec.4" expl="precondition" sum="70200655836e750408cd8a5996962583" proved="true" expanded="false">
|
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<proof prover="alt-ergo" timelimit="10" edited="" obsolete="false">
|
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<result status="valid" time="0.02"/>
|
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</proof>
|
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<proof prover="z3" timelimit="10" edited="" obsolete="false">
|
||||
<result status="valid" time="0.00"/>
|
||||
</proof>
|
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</goal>
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<goal name="WP_parameter search_rec.5" expl="precondition" sum="3c0ace1c9d0462dad22f9a3def392d80" proved="true" expanded="false">
|
||||
<proof prover="alt-ergo" timelimit="10" edited="" obsolete="false">
|
||||
<result status="valid" time="0.02"/>
|
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</proof>
|
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@@ -107,7 +131,12 @@
|
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<result status="valid" time="0.03"/>
|
||||
</proof>
|
||||
</goal>
|
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<goal name="WP_parameter search_rec.3" expl="precondition" sum="81a8eda76bb9fc55426d0d2c779fb747" proved="true" expanded="true">
|
||||
<goal name="WP_parameter search_rec.6" expl="normal postcondition" sum="5e4e50fa7d00a3e211e6c765447598ac" proved="true" expanded="false">
|
||||
<proof prover="z3" timelimit="10" edited="" obsolete="false">
|
||||
<result status="valid" time="0.04"/>
|
||||
</proof>
|
||||
</goal>
|
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<goal name="WP_parameter search_rec.7" expl="precondition" sum="59fbd71468455b495415851791a881e4" proved="true" expanded="false">
|
||||
<proof prover="alt-ergo" timelimit="10" edited="" obsolete="false">
|
||||
<result status="valid" time="0.02"/>
|
||||
</proof>
|
||||
@@ -115,44 +144,15 @@
|
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<result status="valid" time="0.03"/>
|
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</proof>
|
||||
</goal>
|
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<goal name="WP_parameter search_rec.4" expl="precondition" sum="1aa5fc2b9d9f2274df86f567e8367758" proved="true" expanded="true">
|
||||
<goal name="WP_parameter search_rec.8" expl="normal postcondition" sum="23b6323ce32882d20cbec4416c19c5fc" proved="true" expanded="false">
|
||||
<proof prover="alt-ergo" timelimit="10" edited="" obsolete="false">
|
||||
<result status="valid" time="0.02"/>
|
||||
</proof>
|
||||
<proof prover="z3" timelimit="10" edited="" obsolete="false">
|
||||
<result status="valid" time="0.02"/>
|
||||
</proof>
|
||||
</goal>
|
||||
<goal name="WP_parameter search_rec.5" expl="precondition" sum="df4ce06ace5afed63c8806a0409bc373" proved="true" expanded="true">
|
||||
<proof prover="alt-ergo" timelimit="10" edited="" obsolete="false">
|
||||
<result status="valid" time="0.02"/>
|
||||
</proof>
|
||||
<proof prover="z3" timelimit="10" edited="" obsolete="false">
|
||||
<result status="valid" time="0.03"/>
|
||||
</proof>
|
||||
</goal>
|
||||
<goal name="WP_parameter search_rec.6" expl="normal postcondition" sum="66a382fecdcc926c2651f0df8b934922" proved="true" expanded="true">
|
||||
<proof prover="z3" timelimit="10" edited="" obsolete="false">
|
||||
<result status="valid" time="0.24"/>
|
||||
</proof>
|
||||
</goal>
|
||||
<goal name="WP_parameter search_rec.7" expl="precondition" sum="3cd087502acbddf93bedd2e7ae41368f" proved="true" expanded="true">
|
||||
<proof prover="alt-ergo" timelimit="10" edited="" obsolete="false">
|
||||
<result status="valid" time="0.02"/>
|
||||
</proof>
|
||||
<proof prover="z3" timelimit="10" edited="" obsolete="false">
|
||||
<result status="valid" time="0.03"/>
|
||||
</proof>
|
||||
</goal>
|
||||
<goal name="WP_parameter search_rec.8" expl="normal postcondition" sum="aa8066ccccfb75f3b09a443bfcc18824" proved="true" expanded="true">
|
||||
<proof prover="alt-ergo" timelimit="10" edited="" obsolete="false">
|
||||
<result status="valid" time="0.06"/>
|
||||
</proof>
|
||||
<proof prover="z3" timelimit="10" edited="" obsolete="false">
|
||||
<result status="valid" time="0.04"/>
|
||||
</proof>
|
||||
</goal>
|
||||
<goal name="WP_parameter search_rec.9" expl="normal postcondition" sum="43a3bb410f2b3ac8d455124eb75c46bc" proved="true" expanded="true">
|
||||
<goal name="WP_parameter search_rec.9" expl="normal postcondition" sum="a6ad2af03185d4f9110d519f3155f374" proved="true" expanded="false">
|
||||
<proof prover="alt-ergo" timelimit="10" edited="" obsolete="false">
|
||||
<result status="valid" time="0.02"/>
|
||||
</proof>
|
||||
|
||||
Reference in New Issue
Block a user