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Why3
why3
Commits
6a180e51
Commit
6a180e51
authored
Jul 27, 2012
by
Jean-Christophe Filliâtre
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Plain Diff
proof of algo64
parent
29e42dd4
Changes
3
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3 changed files
with
264 additions
and
11 deletions
+264
-11
.gitignore
.gitignore
+0
-1
examples/programs/algo64.mlw
examples/programs/algo64.mlw
+5
-10
examples/programs/algo64/why3session.xml
examples/programs/algo64/why3session.xml
+259
-0
No files found.
.gitignore
View file @
6a180e51
...
...
@@ -177,7 +177,6 @@ pvsbin/
/examples/programs/vacid_0_red_black_trees_harness/
/examples/programs/next_digit_sum/
/examples/programs/algo63/
/examples/programs/algo64/
/examples/programs/algo65/
/examples/programs/binary_search_c/
/examples/programs/dijkstra/
...
...
examples/programs/algo64.mlw
View file @
6a180e51
...
...
@@ -18,12 +18,7 @@ module Algo64
use import module ref.Ref
use import module array.Array
use import module array.ArrayPermut
predicate sorted_sub (a: array int) (l u: int)
(*
clone import module array.ArraySorted with
type elt = int, predicate le = (<=)
*)
use import module array.ArraySorted
(* Algorithm 63 *)
...
...
@@ -31,7 +26,7 @@ module Algo64
a:array int -> m:int -> n:int -> i:ref int -> j:ref int ->
{ 0 <= m < n < length a }
unit writes a i j
{ m <= !j < !i <= n /\ permut_sub (old a) a m
n
/\
{ m <= !j < !i <= n /\ permut_sub (old a) a m
(n+1)
/\
exists x:int.
(forall r:int. m <= r <= !j -> a[r] <= x) /\
(forall r:int. !j < r < !i -> a[r] = x) /\
...
...
@@ -47,11 +42,11 @@ module Algo64
let j = ref 0 in
partition a m n i j;
'L1: quicksort a m !j;
assert { permut_sub (at a 'L1) a m
n
};
assert { permut_sub (at a 'L1) a m
(n+1)
};
'L2: quicksort a !i n;
assert { permut_sub (at a 'L2) a m
n
}
assert { permut_sub (at a 'L2) a m
(n+1)
}
end
{ permut_sub (old a) a m
n /\ sorted_sub a m n
}
{ permut_sub (old a) a m
(n+1) /\ sorted_sub a m (n+1)
}
end
...
...
examples/programs/algo64/why3session.xml
0 → 100644
View file @
6a180e51
<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session SYSTEM "/home/jc/why3/share/why3session.dtd">
<why3session
name=
"examples/programs/algo64/why3session.xml"
shape_version=
"2"
>
<prover
id=
"0"
name=
"Alt-Ergo"
version=
"0.94"
/>
<prover
id=
"1"
name=
"Z3"
version=
"3.2"
/>
<file
name=
"../algo64.mlw"
verified=
"true"
expanded=
"true"
>
<theory
name=
"Algo64"
locfile=
"examples/programs/algo64/../algo64.mlw"
loclnum=
"15"
loccnumb=
"7"
loccnume=
"13"
verified=
"true"
expanded=
"true"
>
<goal
name=
"WP_parameter quicksort"
locfile=
"examples/programs/algo64/../algo64.mlw"
loclnum=
"37"
loccnumb=
"10"
loccnume=
"19"
expl=
"parameter quicksort"
sum=
"3533c0ea980cde0949f11d81f0039f7d"
proved=
"true"
expanded=
"true"
shape=
"iainfix <V1V2asorted_subV8V1ainfix +V2c1Aapermut_subV3V8V1ainfix +V2c1Aapermut_subV7V8V1ainfix +V2c1Iasorted_subV8V5ainfix +V2c1Aapermut_subV7V8V5ainfix +V2c1FAainfix <V2V0Aainfix <=V5V2Aainfix <=c0V5Aainfix <ainfix -V2V5ainfix -V2V1Aainfix <=c0ainfix -V2V1Aapermut_subV6V7V1ainfix +V2c1Iasorted_subV7V1ainfix +V4c1Aapermut_subV6V7V1ainfix +V4c1FAainfix <V4V0Aainfix <=V1V4Aainfix <=c0V1Aainfix <ainfix -V4V1ainfix -V2V1Aainfix <=c0ainfix -V2V1Iainfix >=agetV6V10V9Iainfix <=V10V2Aainfix <=V5V10FAainfix =agetV6V11V9Iainfix <V11V5Aainfix <V4V11FAainfix <=agetV6V12V9Iainfix <=V12V4Aainfix <=V1V12FEAapermut_subV3V6V1ainfix +V2c1Aainfix <=V5V2Aainfix <V4V5Aainfix <=V1V4FAainfix <V2V0Aainfix <V1V2Aainfix <=c0V1asorted_subV3V1ainfix +V2c1Aapermut_subV3V3V1ainfix +V2c1Iainfix <V2V0Aainfix <=V1V2Aainfix <=c0V1FF"
>
<label
name=
"expl:parameter quicksort"
/>
<transf
name=
"split_goal"
proved=
"true"
expanded=
"true"
>
<goal
name=
"WP_parameter quicksort.1"
locfile=
"examples/programs/algo64/../algo64.mlw"
loclnum=
"37"
loccnumb=
"10"
loccnume=
"19"
expl=
"precondition"
sum=
"1937b51a248d0b81e263cfda90830a31"
proved=
"true"
expanded=
"false"
shape=
"ainfix <V2V0Aainfix <V1V2Aainfix <=c0V1Iainfix <V1V2Iainfix <V2V0Aainfix <=V1V2Aainfix <=c0V1FF"
>
<label
name=
"expl:parameter quicksort"
/>
<proof
prover=
"0"
timelimit=
"5"
memlimit=
"1000"
obsolete=
"false"
archived=
"false"
>
<result
status=
"valid"
time=
"0.02"
/>
</proof>
</goal>
<goal
name=
"WP_parameter quicksort.2"
locfile=
"examples/programs/algo64/../algo64.mlw"
loclnum=
"37"
loccnumb=
"10"
loccnume=
"19"
expl=
"variant decreases"
sum=
"194b5831756da65b29d0a1aea48225f1"
proved=
"true"
expanded=
"false"
shape=
"ainfix <ainfix -V4V1ainfix -V2V1Aainfix <=c0ainfix -V2V1Iainfix >=agetV6V8V7Iainfix <=V8V2Aainfix <=V5V8FAainfix =agetV6V9V7Iainfix <V9V5Aainfix <V4V9FAainfix <=agetV6V10V7Iainfix <=V10V4Aainfix <=V1V10FEAapermut_subV3V6V1ainfix +V2c1Aainfix <=V5V2Aainfix <V4V5Aainfix <=V1V4FIainfix <V2V0Aainfix <V1V2Aainfix <=c0V1Iainfix <V1V2Iainfix <V2V0Aainfix <=V1V2Aainfix <=c0V1FF"
>
<label
name=
"expl:parameter quicksort"
/>
<proof
prover=
"0"
timelimit=
"5"
memlimit=
"1000"
obsolete=
"false"
archived=
"false"
>
<result
status=
"valid"
time=
"0.03"
/>
</proof>
</goal>
<goal
name=
"WP_parameter quicksort.3"
locfile=
"examples/programs/algo64/../algo64.mlw"
loclnum=
"37"
loccnumb=
"10"
loccnume=
"19"
expl=
"precondition"
sum=
"034928eff8a6ffb4a2a09d9cef39ca33"
proved=
"true"
expanded=
"false"
shape=
"ainfix <V4V0Aainfix <=V1V4Aainfix <=c0V1Iainfix >=agetV6V8V7Iainfix <=V8V2Aainfix <=V5V8FAainfix =agetV6V9V7Iainfix <V9V5Aainfix <V4V9FAainfix <=agetV6V10V7Iainfix <=V10V4Aainfix <=V1V10FEAapermut_subV3V6V1ainfix +V2c1Aainfix <=V5V2Aainfix <V4V5Aainfix <=V1V4FIainfix <V2V0Aainfix <V1V2Aainfix <=c0V1Iainfix <V1V2Iainfix <V2V0Aainfix <=V1V2Aainfix <=c0V1FF"
>
<label
name=
"expl:parameter quicksort"
/>
<proof
prover=
"0"
timelimit=
"5"
memlimit=
"1000"
obsolete=
"false"
archived=
"false"
>
<result
status=
"valid"
time=
"0.03"
/>
</proof>
</goal>
<goal
name=
"WP_parameter quicksort.4"
locfile=
"examples/programs/algo64/../algo64.mlw"
loclnum=
"37"
loccnumb=
"10"
loccnume=
"19"
expl=
"assertion"
sum=
"c02cf84424f0d3f80a18bbd62f4f9d7f"
proved=
"true"
expanded=
"false"
shape=
"apermut_subV6V7V1ainfix +V2c1Iasorted_subV7V1ainfix +V4c1Aapermut_subV6V7V1ainfix +V4c1FIainfix <V4V0Aainfix <=V1V4Aainfix <=c0V1Aainfix <ainfix -V4V1ainfix -V2V1Aainfix <=c0ainfix -V2V1Iainfix >=agetV6V9V8Iainfix <=V9V2Aainfix <=V5V9FAainfix =agetV6V10V8Iainfix <V10V5Aainfix <V4V10FAainfix <=agetV6V11V8Iainfix <=V11V4Aainfix <=V1V11FEAapermut_subV3V6V1ainfix +V2c1Aainfix <=V5V2Aainfix <V4V5Aainfix <=V1V4FIainfix <V2V0Aainfix <V1V2Aainfix <=c0V1Iainfix <V1V2Iainfix <V2V0Aainfix <=V1V2Aainfix <=c0V1FF"
>
<label
name=
"expl:parameter quicksort"
/>
<proof
prover=
"0"
timelimit=
"5"
memlimit=
"1000"
obsolete=
"false"
archived=
"false"
>
<result
status=
"valid"
time=
"0.04"
/>
</proof>
</goal>
<goal
name=
"WP_parameter quicksort.5"
locfile=
"examples/programs/algo64/../algo64.mlw"
loclnum=
"37"
loccnumb=
"10"
loccnume=
"19"
expl=
"variant decreases"
sum=
"2acdc20b13b77e830b11f6b0ff7915bc"
proved=
"true"
expanded=
"false"
shape=
"ainfix <ainfix -V2V5ainfix -V2V1Aainfix <=c0ainfix -V2V1Iapermut_subV6V7V1ainfix +V2c1Iasorted_subV7V1ainfix +V4c1Aapermut_subV6V7V1ainfix +V4c1FIainfix <V4V0Aainfix <=V1V4Aainfix <=c0V1Aainfix <ainfix -V4V1ainfix -V2V1Aainfix <=c0ainfix -V2V1Iainfix >=agetV6V9V8Iainfix <=V9V2Aainfix <=V5V9FAainfix =agetV6V10V8Iainfix <V10V5Aainfix <V4V10FAainfix <=agetV6V11V8Iainfix <=V11V4Aainfix <=V1V11FEAapermut_subV3V6V1ainfix +V2c1Aainfix <=V5V2Aainfix <V4V5Aainfix <=V1V4FIainfix <V2V0Aainfix <V1V2Aainfix <=c0V1Iainfix <V1V2Iainfix <V2V0Aainfix <=V1V2Aainfix <=c0V1FF"
>
<label
name=
"expl:parameter quicksort"
/>
<proof
prover=
"0"
timelimit=
"5"
memlimit=
"1000"
obsolete=
"false"
archived=
"false"
>
<result
status=
"valid"
time=
"0.03"
/>
</proof>
</goal>
<goal
name=
"WP_parameter quicksort.6"
locfile=
"examples/programs/algo64/../algo64.mlw"
loclnum=
"37"
loccnumb=
"10"
loccnume=
"19"
expl=
"precondition"
sum=
"2e6be7b6dba972c3888cf2d815f92588"
proved=
"true"
expanded=
"false"
shape=
"ainfix <V2V0Aainfix <=V5V2Aainfix <=c0V5Iapermut_subV6V7V1ainfix +V2c1Iasorted_subV7V1ainfix +V4c1Aapermut_subV6V7V1ainfix +V4c1FIainfix <V4V0Aainfix <=V1V4Aainfix <=c0V1Aainfix <ainfix -V4V1ainfix -V2V1Aainfix <=c0ainfix -V2V1Iainfix >=agetV6V9V8Iainfix <=V9V2Aainfix <=V5V9FAainfix =agetV6V10V8Iainfix <V10V5Aainfix <V4V10FAainfix <=agetV6V11V8Iainfix <=V11V4Aainfix <=V1V11FEAapermut_subV3V6V1ainfix +V2c1Aainfix <=V5V2Aainfix <V4V5Aainfix <=V1V4FIainfix <V2V0Aainfix <V1V2Aainfix <=c0V1Iainfix <V1V2Iainfix <V2V0Aainfix <=V1V2Aainfix <=c0V1FF"
>
<label
name=
"expl:parameter quicksort"
/>
<proof
prover=
"0"
timelimit=
"5"
memlimit=
"1000"
obsolete=
"false"
archived=
"false"
>
<result
status=
"valid"
time=
"0.03"
/>
</proof>
</goal>
<goal
name=
"WP_parameter quicksort.7"
locfile=
"examples/programs/algo64/../algo64.mlw"
loclnum=
"37"
loccnumb=
"10"
loccnume=
"19"
expl=
"assertion"
sum=
"4cb0e10c07f7d1266dcbca3b21e61000"
proved=
"true"
expanded=
"false"
shape=
"apermut_subV7V8V1ainfix +V2c1Iasorted_subV8V5ainfix +V2c1Aapermut_subV7V8V5ainfix +V2c1FIainfix <V2V0Aainfix <=V5V2Aainfix <=c0V5Aainfix <ainfix -V2V5ainfix -V2V1Aainfix <=c0ainfix -V2V1Iapermut_subV6V7V1ainfix +V2c1Iasorted_subV7V1ainfix +V4c1Aapermut_subV6V7V1ainfix +V4c1FIainfix <V4V0Aainfix <=V1V4Aainfix <=c0V1Aainfix <ainfix -V4V1ainfix -V2V1Aainfix <=c0ainfix -V2V1Iainfix >=agetV6V10V9Iainfix <=V10V2Aainfix <=V5V10FAainfix =agetV6V11V9Iainfix <V11V5Aainfix <V4V11FAainfix <=agetV6V12V9Iainfix <=V12V4Aainfix <=V1V12FEAapermut_subV3V6V1ainfix +V2c1Aainfix <=V5V2Aainfix <V4V5Aainfix <=V1V4FIainfix <V2V0Aainfix <V1V2Aainfix <=c0V1Iainfix <V1V2Iainfix <V2V0Aainfix <=V1V2Aainfix <=c0V1FF"
>
<label
name=
"expl:parameter quicksort"
/>
<proof
prover=
"0"
timelimit=
"5"
memlimit=
"1000"
obsolete=
"false"
archived=
"false"
>
<result
status=
"valid"
time=
"0.04"
/>
</proof>
</goal>
<goal
name=
"WP_parameter quicksort.8"
locfile=
"examples/programs/algo64/../algo64.mlw"
loclnum=
"37"
loccnumb=
"10"
loccnume=
"19"
expl=
"normal postcondition"
sum=
"73b08ee7a978f24b740f747e96186b06"
proved=
"true"
expanded=
"true"
shape=
"asorted_subV8V1ainfix +V2c1Aapermut_subV3V8V1ainfix +V2c1Iapermut_subV7V8V1ainfix +V2c1Iasorted_subV8V5ainfix +V2c1Aapermut_subV7V8V5ainfix +V2c1FIainfix <V2V0Aainfix <=V5V2Aainfix <=c0V5Aainfix <ainfix -V2V5ainfix -V2V1Aainfix <=c0ainfix -V2V1Iapermut_subV6V7V1ainfix +V2c1Iasorted_subV7V1ainfix +V4c1Aapermut_subV6V7V1ainfix +V4c1FIainfix <V4V0Aainfix <=V1V4Aainfix <=c0V1Aainfix <ainfix -V4V1ainfix -V2V1Aainfix <=c0ainfix -V2V1Iainfix >=agetV6V10V9Iainfix <=V10V2Aainfix <=V5V10FAainfix =agetV6V11V9Iainfix <V11V5Aainfix <V4V11FAainfix <=agetV6V12V9Iainfix <=V12V4Aainfix <=V1V12FEAapermut_subV3V6V1ainfix +V2c1Aainfix <=V5V2Aainfix <V4V5Aainfix <=V1V4FIainfix <V2V0Aainfix <V1V2Aainfix <=c0V1Iainfix <V1V2Iainfix <V2V0Aainfix <=V1V2Aainfix <=c0V1FF"
>
<label
name=
"expl:parameter quicksort"
/>
<transf
name=
"split_goal"
proved=
"true"
expanded=
"true"
>
<goal
name=
"WP_parameter quicksort.8.1"
locfile=
"examples/programs/algo64/../algo64.mlw"
loclnum=
"37"
loccnumb=
"10"
loccnume=
"19"
expl=
"parameter quicksort"
sum=
"ad5ce69bb20a3c62372c864f4a9a6cdc"
proved=
"true"
expanded=
"false"
shape=
"apermut_subV3V8V1ainfix +V2c1Iapermut_subV7V8V1ainfix +V2c1Iasorted_subV8V5ainfix +V2c1Aapermut_subV7V8V5ainfix +V2c1FIainfix <V2V0Aainfix <=V5V2Aainfix <=c0V5Aainfix <ainfix -V2V5ainfix -V2V1Aainfix <=c0ainfix -V2V1Iapermut_subV6V7V1ainfix +V2c1Iasorted_subV7V1ainfix +V4c1Aapermut_subV6V7V1ainfix +V4c1FIainfix <V4V0Aainfix <=V1V4Aainfix <=c0V1Aainfix <ainfix -V4V1ainfix -V2V1Aainfix <=c0ainfix -V2V1Iainfix >=agetV6V10V9Iainfix <=V10V2Aainfix <=V5V10FAainfix =agetV6V11V9Iainfix <V11V5Aainfix <V4V11FAainfix <=agetV6V12V9Iainfix <=V12V4Aainfix <=V1V12FEAapermut_subV3V6V1ainfix +V2c1Aainfix <=V5V2Aainfix <V4V5Aainfix <=V1V4FIainfix <V2V0Aainfix <V1V2Aainfix <=c0V1Iainfix <V1V2Iainfix <V2V0Aainfix <=V1V2Aainfix <=c0V1FF"
>
<label
name=
"expl:parameter quicksort"
/>
<proof
prover=
"0"
timelimit=
"5"
memlimit=
"1000"
obsolete=
"false"
archived=
"false"
>
<result
status=
"valid"
time=
"0.10"
/>
</proof>
</goal>
<goal
name=
"WP_parameter quicksort.8.2"
locfile=
"examples/programs/algo64/../algo64.mlw"
loclnum=
"37"
loccnumb=
"10"
loccnume=
"19"
expl=
"parameter quicksort"
sum=
"af0bb134c03b7b81b0ec6db2673c6e7c"
proved=
"true"
expanded=
"true"
shape=
"asorted_subV8V1ainfix +V2c1Iapermut_subV7V8V1ainfix +V2c1Iasorted_subV8V5ainfix +V2c1Aapermut_subV7V8V5ainfix +V2c1FIainfix <V2V0Aainfix <=V5V2Aainfix <=c0V5Aainfix <ainfix -V2V5ainfix -V2V1Aainfix <=c0ainfix -V2V1Iapermut_subV6V7V1ainfix +V2c1Iasorted_subV7V1ainfix +V4c1Aapermut_subV6V7V1ainfix +V4c1FIainfix <V4V0Aainfix <=V1V4Aainfix <=c0V1Aainfix <ainfix -V4V1ainfix -V2V1Aainfix <=c0ainfix -V2V1Iainfix >=agetV6V10V9Iainfix <=V10V2Aainfix <=V5V10FAainfix =agetV6V11V9Iainfix <V11V5Aainfix <V4V11FAainfix <=agetV6V12V9Iainfix <=V12V4Aainfix <=V1V12FEAapermut_subV3V6V1ainfix +V2c1Aainfix <=V5V2Aainfix <V4V5Aainfix <=V1V4FIainfix <V2V0Aainfix <V1V2Aainfix <=c0V1Iainfix <V1V2Iainfix <V2V0Aainfix <=V1V2Aainfix <=c0V1FF"
>
<label
name=
"expl:parameter quicksort"
/>
<proof
prover=
"1"
timelimit=
"19"
memlimit=
"1000"
obsolete=
"false"
archived=
"false"
>
<result
status=
"valid"
time=
"14.69"
/>
</proof>
</goal>
</transf>
</goal>
<goal
name=
"WP_parameter quicksort.9"
locfile=
"examples/programs/algo64/../algo64.mlw"
loclnum=
"37"
loccnumb=
"10"
loccnume=
"19"
expl=
"normal postcondition"
sum=
"07812c408c2ef8ba959a4c34a2b3e06e"
proved=
"true"
expanded=
"false"
shape=
"asorted_subV3V1ainfix +V2c1Aapermut_subV3V3V1ainfix +V2c1Iainfix <V1V2NIainfix <V2V0Aainfix <=V1V2Aainfix <=c0V1FF"
>
<label
name=
"expl:parameter quicksort"
/>
<proof
prover=
"0"
timelimit=
"5"
memlimit=
"1000"
obsolete=
"false"
archived=
"false"
>
<result
status=
"valid"
time=
"0.04"
/>
</proof>
</goal>
</transf>
</goal>
</theory>
</file>
</why3session>
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