Commit ba5e8ca5 authored by MARCHE Claude's avatar MARCHE Claude

fix some broken proofs

parent bd8b6aca
......@@ -2,23 +2,177 @@
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
<why3session shape_version="4">
<prover id="1" name="Alt-Ergo" version="1.30" timelimit="10" steplimit="0" memlimit="1000"/>
<prover id="0" name="Alt-Ergo" version="2.2.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="2" name="CVC4" version="1.6" timelimit="1" steplimit="0" memlimit="1000"/>
<file name="../fenwick.mlw" proved="true">
<theory name="Fenwick" proved="true">
<goal name="VC make" expl="VC for make" proved="true">
<proof prover="1"><result status="valid" time="0.01" steps="39"/></proof>
<proof prover="2"><result status="valid" time="0.06"/></proof>
</goal>
<goal name="VC add" expl="VC for add" proved="true">
<proof prover="1"><result status="valid" time="0.66" steps="721"/></proof>
<transf name="split_vc" proved="true" >
<goal name="VC add.0" expl="precondition" proved="true">
<proof prover="2"><result status="valid" time="0.02"/></proof>
</goal>
<goal name="VC add.1" expl="index in array bounds" proved="true">
<proof prover="2"><result status="valid" time="0.06"/></proof>
</goal>
<goal name="VC add.2" expl="index in array bounds" proved="true">
<proof prover="2"><result status="valid" time="0.05"/></proof>
</goal>
<goal name="VC add.3" expl="loop invariant init" proved="true">
<proof prover="2"><result status="valid" time="0.06"/></proof>
</goal>
<goal name="VC add.4" expl="loop invariant init" proved="true">
<proof prover="0"><result status="valid" time="0.38" steps="493"/></proof>
</goal>
<goal name="VC add.5" expl="loop invariant init" proved="true">
<proof prover="2"><result status="valid" time="0.02"/></proof>
</goal>
<goal name="VC add.6" expl="precondition" proved="true">
<proof prover="2"><result status="valid" time="0.02"/></proof>
</goal>
<goal name="VC add.7" expl="index in array bounds" proved="true">
<proof prover="2"><result status="valid" time="0.05"/></proof>
</goal>
<goal name="VC add.8" expl="index in array bounds" proved="true">
<proof prover="2"><result status="valid" time="0.05"/></proof>
</goal>
<goal name="VC add.9" expl="loop variant decrease" proved="true">
<proof prover="2"><result status="valid" time="0.05"/></proof>
</goal>
<goal name="VC add.10" expl="loop invariant preservation" proved="true">
<proof prover="2"><result status="valid" time="0.05"/></proof>
</goal>
<goal name="VC add.11" expl="loop invariant preservation" proved="true">
<proof prover="0" timelimit="10"><result status="valid" time="1.60" steps="1329"/></proof>
</goal>
<goal name="VC add.12" expl="loop invariant preservation" proved="true">
<proof prover="0"><result status="valid" time="0.11" steps="196"/></proof>
</goal>
<goal name="VC add.13" expl="postcondition" proved="true">
<proof prover="2"><result status="valid" time="0.05"/></proof>
</goal>
<goal name="VC add.14" expl="postcondition" proved="true">
<proof prover="0"><result status="valid" time="0.14" steps="208"/></proof>
</goal>
<goal name="VC add.15" expl="postcondition" proved="true">
<proof prover="0"><result status="valid" time="0.06" steps="112"/></proof>
</goal>
</transf>
</goal>
<goal name="VC sum_dec" expl="VC for sum_dec" proved="true">
<proof prover="1"><result status="valid" time="0.04" steps="37"/></proof>
<proof prover="0"><result status="valid" time="0.31" steps="390"/></proof>
</goal>
<goal name="VC fen_compact" expl="VC for fen_compact" proved="true">
<proof prover="1"><result status="valid" time="0.82" steps="850"/></proof>
<proof prover="2"><result status="valid" time="0.13"/></proof>
</goal>
<goal name="VC query" expl="VC for query" proved="true">
<proof prover="1"><result status="valid" time="2.57" steps="2527"/></proof>
<transf name="split_vc" proved="true" >
<goal name="VC query.0" expl="precondition" proved="true">
<proof prover="2"><result status="valid" time="0.02"/></proof>
</goal>
<goal name="VC query.1" expl="precondition" proved="true">
<proof prover="2"><result status="valid" time="0.04"/></proof>
</goal>
<goal name="VC query.2" expl="loop invariant init" proved="true">
<proof prover="2"><result status="valid" time="0.05"/></proof>
</goal>
<goal name="VC query.3" expl="loop invariant init" proved="true">
<transf name="inline_goal" proved="true" >
<goal name="VC query.3.0" expl="loop invariant init" proved="true">
<proof prover="0"><result status="valid" time="0.38" steps="846"/></proof>
</goal>
</transf>
</goal>
<goal name="VC query.4" expl="precondition" proved="true">
<proof prover="2"><result status="valid" time="0.03"/></proof>
</goal>
<goal name="VC query.5" expl="index in array bounds" proved="true">
<proof prover="2"><result status="valid" time="0.03"/></proof>
</goal>
<goal name="VC query.6" expl="precondition" proved="true">
<proof prover="2"><result status="valid" time="0.03"/></proof>
</goal>
<goal name="VC query.7" expl="precondition" proved="true">
<proof prover="2"><result status="valid" time="0.03"/></proof>
</goal>
<goal name="VC query.8" expl="index in array bounds" proved="true">
<proof prover="2"><result status="valid" time="0.04"/></proof>
</goal>
<goal name="VC query.9" expl="precondition" proved="true">
<proof prover="2"><result status="valid" time="0.03"/></proof>
</goal>
<goal name="VC query.10" expl="precondition" proved="true">
<proof prover="2"><result status="valid" time="0.07"/></proof>
</goal>
<goal name="VC query.11" expl="loop variant decrease" proved="true">
<proof prover="2"><result status="valid" time="0.06"/></proof>
</goal>
<goal name="VC query.12" expl="loop invariant preservation" proved="true">
<proof prover="2"><result status="valid" time="0.09"/></proof>
</goal>
<goal name="VC query.13" expl="loop invariant preservation" proved="true">
<proof prover="0"><result status="valid" time="0.04" steps="42"/></proof>
</goal>
<goal name="VC query.14" expl="precondition" proved="true">
<proof prover="2"><result status="valid" time="0.03"/></proof>
</goal>
<goal name="VC query.15" expl="precondition" proved="true">
<proof prover="2"><result status="valid" time="0.09"/></proof>
</goal>
<goal name="VC query.16" expl="loop variant decrease" proved="true">
<proof prover="2"><result status="valid" time="0.05"/></proof>
</goal>
<goal name="VC query.17" expl="loop invariant preservation" proved="true">
<proof prover="2"><result status="valid" time="0.06"/></proof>
</goal>
<goal name="VC query.18" expl="loop invariant preservation" proved="true">
<proof prover="0"><result status="valid" time="0.03" steps="40"/></proof>
</goal>
<goal name="VC query.19" expl="precondition" proved="true">
<proof prover="2"><result status="valid" time="0.03"/></proof>
</goal>
<goal name="VC query.20" expl="precondition" proved="true">
<proof prover="2"><result status="valid" time="0.04"/></proof>
</goal>
<goal name="VC query.21" expl="index in array bounds" proved="true">
<proof prover="2"><result status="valid" time="0.05"/></proof>
</goal>
<goal name="VC query.22" expl="precondition" proved="true">
<proof prover="2"><result status="valid" time="0.03"/></proof>
</goal>
<goal name="VC query.23" expl="precondition" proved="true">
<proof prover="2"><result status="valid" time="0.07"/></proof>
</goal>
<goal name="VC query.24" expl="loop variant decrease" proved="true">
<proof prover="2"><result status="valid" time="0.08"/></proof>
</goal>
<goal name="VC query.25" expl="loop invariant preservation" proved="true">
<proof prover="2"><result status="valid" time="0.09"/></proof>
</goal>
<goal name="VC query.26" expl="loop invariant preservation" proved="true">
<proof prover="0"><result status="valid" time="0.04" steps="40"/></proof>
</goal>
<goal name="VC query.27" expl="precondition" proved="true">
<proof prover="2"><result status="valid" time="0.03"/></proof>
</goal>
<goal name="VC query.28" expl="precondition" proved="true">
<proof prover="2"><result status="valid" time="0.07"/></proof>
</goal>
<goal name="VC query.29" expl="loop variant decrease" proved="true">
<proof prover="2"><result status="valid" time="0.08"/></proof>
</goal>
<goal name="VC query.30" expl="loop invariant preservation" proved="true">
<proof prover="2"><result status="valid" time="0.06"/></proof>
</goal>
<goal name="VC query.31" expl="loop invariant preservation" proved="true">
<proof prover="0"><result status="valid" time="0.04" steps="38"/></proof>
</goal>
<goal name="VC query.32" expl="postcondition" proved="true">
<proof prover="2"><result status="valid" time="0.04"/></proof>
</goal>
</transf>
</goal>
</theory>
</file>
......
......@@ -30,7 +30,7 @@ module TreeOfArray
else
let mid = lo + div (hi - lo) 2 in
let left = tree_of_array_aux a lo mid in
let right = tree_of_array_aux a (mid + 1) hi in
let right = tree_of_array_aux a (mid+1) hi in
Node left a[mid] right
let tree_of_array (a: array 'a) : tree 'a
......
......@@ -2,14 +2,109 @@
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
<why3session shape_version="4">
<prover id="0" name="Alt-Ergo" version="1.30" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="1" name="Eprover" version="2.0" timelimit="5" steplimit="0" memlimit="2000"/>
<prover id="2" name="Alt-Ergo" version="2.2.0" timelimit="5" steplimit="0" memlimit="2000"/>
<prover id="3" name="CVC4" version="1.6" timelimit="1" steplimit="0" memlimit="1000"/>
<file name="../tree_of_array.mlw" proved="true">
<theory name="TreeOfArray" proved="true">
<goal name="VC tree_of_array_aux" expl="VC for tree_of_array_aux" proved="true">
<proof prover="0"><result status="valid" time="1.17" steps="1293"/></proof>
<transf name="split_vc" proved="true" >
<goal name="VC tree_of_array_aux.0" expl="precondition" proved="true">
<proof prover="3"><result status="valid" time="0.03"/></proof>
</goal>
<goal name="VC tree_of_array_aux.1" expl="variant decrease" proved="true">
<proof prover="3"><result status="valid" time="0.07"/></proof>
</goal>
<goal name="VC tree_of_array_aux.2" expl="precondition" proved="true">
<proof prover="3"><result status="valid" time="0.06"/></proof>
</goal>
<goal name="VC tree_of_array_aux.3" expl="variant decrease" proved="true">
<proof prover="3"><result status="valid" time="0.04"/></proof>
</goal>
<goal name="VC tree_of_array_aux.4" expl="precondition" proved="true">
<proof prover="3"><result status="valid" time="0.10"/></proof>
</goal>
<goal name="VC tree_of_array_aux.5" expl="index in array bounds" proved="true">
<proof prover="3"><result status="valid" time="0.07"/></proof>
</goal>
<goal name="VC tree_of_array_aux.6" expl="postcondition" proved="true">
<transf name="split_all_full" proved="true" >
<goal name="VC tree_of_array_aux.6.0" expl="VC for tree_of_array_aux" proved="true">
<proof prover="2" timelimit="1" memlimit="1000"><result status="valid" time="0.02" steps="35"/></proof>
</goal>
<goal name="VC tree_of_array_aux.6.1" expl="VC for tree_of_array_aux" proved="true">
<transf name="split_all_full" proved="true" >
<goal name="VC tree_of_array_aux.6.1.0" expl="VC for tree_of_array_aux" proved="true">
<proof prover="2"><result status="valid" time="1.27" steps="1803"/></proof>
</goal>
</transf>
</goal>
<goal name="VC tree_of_array_aux.6.2" expl="VC for tree_of_array_aux" proved="true">
<transf name="case" proved="true" arg1="hi=lo">
<goal name="VC tree_of_array_aux.6.2.0" expl="true case" proved="true">
<proof prover="3"><result status="valid" time="0.04"/></proof>
</goal>
<goal name="VC tree_of_array_aux.6.2.1" expl="false case" proved="true">
<transf name="case" proved="true" arg1="hi=lo+1">
<goal name="VC tree_of_array_aux.6.2.1.0" expl="false case (true case)" proved="true">
<transf name="split_all_full" proved="true" >
<goal name="VC tree_of_array_aux.6.2.1.0.0" expl="false case (true case)" proved="true">
<proof prover="1"><result status="valid" time="2.42"/></proof>
</goal>
</transf>
</goal>
<goal name="VC tree_of_array_aux.6.2.1.1" expl="false case" proved="true">
<transf name="split_all_full" proved="true" >
<goal name="VC tree_of_array_aux.6.2.1.1.0" expl="false case" proved="true">
<proof prover="2"><result status="valid" time="1.09" steps="1079"/></proof>
</goal>
</transf>
</goal>
</transf>
</goal>
</transf>
</goal>
<goal name="VC tree_of_array_aux.6.3" expl="VC for tree_of_array_aux" proved="true">
<transf name="case" proved="true" arg1="hi=lo">
<goal name="VC tree_of_array_aux.6.3.0" expl="true case" proved="true">
<proof prover="3"><result status="valid" time="0.04"/></proof>
</goal>
<goal name="VC tree_of_array_aux.6.3.1" expl="false case" proved="true">
<transf name="case" proved="true" arg1="hi=lo+1">
<goal name="VC tree_of_array_aux.6.3.1.0" expl="false case (true case)" proved="true">
<transf name="assert" proved="true" arg1="left=Empty">
<goal name="VC tree_of_array_aux.6.3.1.0.0" proved="true">
<proof prover="3"><result status="valid" time="0.08"/></proof>
</goal>
<goal name="VC tree_of_array_aux.6.3.1.0.1" expl="false case (true case)" proved="true">
<transf name="assert" proved="true" arg1="right=Empty">
<goal name="VC tree_of_array_aux.6.3.1.0.1.0" proved="true">
<proof prover="3"><result status="valid" time="0.06"/></proof>
</goal>
<goal name="VC tree_of_array_aux.6.3.1.0.1.1" expl="false case (true case)" proved="true">
<proof prover="2" timelimit="1" memlimit="1000"><result status="valid" time="0.03" steps="93"/></proof>
</goal>
</transf>
</goal>
</transf>
</goal>
<goal name="VC tree_of_array_aux.6.3.1.1" expl="false case" proved="true">
<transf name="split_all_full" proved="true" >
<goal name="VC tree_of_array_aux.6.3.1.1.0" expl="false case" proved="true">
<proof prover="2"><result status="valid" time="1.83" steps="1121"/></proof>
</goal>
</transf>
</goal>
</transf>
</goal>
</transf>
</goal>
</transf>
</goal>
</transf>
</goal>
<goal name="VC tree_of_array" expl="VC for tree_of_array" proved="true">
<proof prover="0"><result status="valid" time="0.01" steps="7"/></proof>
<proof prover="3"><result status="valid" time="0.04"/></proof>
</goal>
</theory>
</file>
......
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