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Why3
why3
Commits
7c2f228f
Commit
7c2f228f
authored
Feb 18, 2019
by
François Bobot
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[Tagset] Don't require a maximal size, add remove
parent
df5f2b28
Changes
2
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2 changed files
with
59 additions
and
39 deletions
+59
-39
examples/stdlib/tagset/why3session.xml
examples/stdlib/tagset/why3session.xml
+7
-7
stdlib/mach/tagset.mlw
stdlib/mach/tagset.mlw
+52
-32
No files found.
examples/stdlib/tagset/why3session.xml
View file @
7c2f228f
...
...
@@ -4,7 +4,6 @@
<why3session
shape_version=
"5"
>
<prover
id=
"0"
name=
"Alt-Ergo"
version=
"2.2.0"
timelimit=
"1"
steplimit=
"0"
memlimit=
"1000"
/>
<prover
id=
"1"
name=
"CVC4"
version=
"1.6"
timelimit=
"1"
steplimit=
"0"
memlimit=
"1000"
/>
<prover
id=
"2"
name=
"Z3"
version=
"4.4.1"
timelimit=
"1"
steplimit=
"0"
memlimit=
"1000"
/>
<file
proved=
"true"
>
<path
name=
".."
/>
<path
name=
".."
/>
...
...
@@ -13,13 +12,8 @@
<path
name=
"mach"
/>
<path
name=
"tagset.mlw"
/>
<theory
name=
"TagSetIntf"
proved=
"true"
>
<goal
name=
"VC t"
expl=
"VC for t"
proved=
"true"
>
<proof
prover=
"1"
><result
status=
"valid"
time=
"0.08"
/></proof>
</goal>
<goal
name=
"VC iterator"
expl=
"VC for iterator"
proved=
"true"
>
<proof
prover=
"0"
obsolete=
"true"
><result
status=
"unknown"
time=
"0.01"
/></proof>
<proof
prover=
"1"
><result
status=
"valid"
time=
"0.05"
/></proof>
<proof
prover=
"2"
obsolete=
"true"
><result
status=
"timeout"
time=
"1.00"
/></proof>
</goal>
</theory>
<theory
name=
"TagSet"
proved=
"true"
>
...
...
@@ -38,9 +32,15 @@
<goal
name=
"VC max_tags"
expl=
"VC for max_tags"
proved=
"true"
>
<proof
prover=
"1"
><result
status=
"valid"
time=
"0.06"
/></proof>
</goal>
<goal
name=
"VC resize"
expl=
"VC for resize"
proved=
"true"
>
<proof
prover=
"1"
><result
status=
"valid"
time=
"0.54"
/></proof>
</goal>
<goal
name=
"VC add"
expl=
"VC for add"
proved=
"true"
>
<proof
prover=
"1"
><result
status=
"valid"
time=
"0.28"
/></proof>
</goal>
<goal
name=
"VC remove"
expl=
"VC for remove"
proved=
"true"
>
<proof
prover=
"1"
><result
status=
"valid"
time=
"0.92"
/></proof>
</goal>
<goal
name=
"VC iterator"
expl=
"VC for iterator"
proved=
"true"
>
<proof
prover=
"1"
><result
status=
"valid"
time=
"0.10"
/></proof>
</goal>
...
...
@@ -53,7 +53,7 @@
<goal
name=
"Iterator.VC next"
expl=
"VC for next"
proved=
"true"
>
<transf
name=
"split_vc"
proved=
"true"
>
<goal
name=
"VC next.0"
expl=
"assertion"
proved=
"true"
>
<proof
prover=
"0"
><result
status=
"valid"
time=
"0.02"
steps=
"1
22
"
/></proof>
<proof
prover=
"0"
><result
status=
"valid"
time=
"0.02"
steps=
"1
07
"
/></proof>
</goal>
<goal
name=
"VC next.1"
expl=
"index in array bounds"
proved=
"true"
>
<proof
prover=
"1"
><result
status=
"valid"
time=
"0.06"
/></proof>
...
...
stdlib/mach/tagset.mlw
View file @
7c2f228f
...
...
@@ -6,7 +6,7 @@ module S
type key
val function tag (k:key): Int63.int63
ensures { 0 <= result }
ensures { 0 <= result
< Int63.max_int63
}
axiom tag_correct: forall x y. tag x = tag y -> x = y
...
...
@@ -34,32 +34,30 @@ module TagSetIntf
type t = abstract {
mutable elts: S.set key;
max_tags_: int;
mutable iterated: iteration_state;
}
invariant { forall v. S.mem v elts -> tag v <= max_tags_ }
by {
elts = S.empty;
max_tags_ = 0;
iterated = any iteration_state;
}
val create (s:Int63.int63) (def:key) : t
requires { -1 <= s < Int63.max_int63 }
val create (default:key) : t
ensures { result.elts = S.empty }
ensures { result.max_tags_ = s }
val function mem (k: key) (h: t) : bool
ensures { result = S.mem k h.elts }
val function max_tags (h: t) : Int63.int63
ensures {
result = h.max_tags_
}
ensures {
forall v. S.mem v h.elts -> tag v <= result
}
val add (h: t) (k: key): unit
requires { tag k <= h.max_tags }
ensures { h.elts = S.add k (old h.elts) }
writes { h.elts, h.iterated }
val remove (h: t) (k: key): unit
ensures { h.elts = S.remove k (old h.elts) }
writes { h.elts, h.iterated }
type iterator = abstract {
iterating: iteration_state;
mutable seen: S.set key;
...
...
@@ -101,6 +99,7 @@ end
module TagSet
use int.Int
use mach.int.MinMax63
use import mach.int.Int63 as Int63
use set.Fset as S
use import mach.array.Array63 as Array
...
...
@@ -113,19 +112,16 @@ module TagSet
clone import S as S with axiom tag_correct
type iteration_state = mutable {
ghost max_tags_': int;
ghost mutable elts': S.set key;
present: array bool;
value: array key;
mutable
present: array bool;
mutable
value: array key;
}
invariant { forall v. S.mem v elts' -> tag v <
= max_tags_'
}
invariant { forall v. S.mem v elts' -> tag v <
present.length
}
invariant { forall v. S.mem v elts' -> present[tag v] }
invariant { forall i. 0 <= i <= max_tags_' -> present[i] -> tag (value[i]) = i }
invariant { forall i. 0 <= i <= max_tags_' -> present[i] -> forall v. tag v = i -> S.mem v elts' }
invariant { present.length = max_tags_' + 1 }
invariant { value.length = max_tags_' + 1 }
invariant { forall i. 0 <= i < present.length -> present[i] -> tag (value[i]) = i }
invariant { forall i. 0 <= i < present.length -> present[i] -> forall v. tag v = i -> S.mem v elts' }
invariant { value.length = present.length }
by {
max_tags_' = -1;
elts' = S.empty;
present = Array.make 0 false;
value = Array.make 0 (any key);
...
...
@@ -133,26 +129,21 @@ module TagSet
type t = {
ghost mutable elts: S.set key;
ghost max_tags_: int;
mutable iterated: iteration_state;
}
invariant { max_tags_ = iterated.max_tags_' }
invariant { elts = iterated.elts' }
let create (s:Int63.int63) (def:key) : t
requires { -1 <= s < Int63.max_int63 }
let create (def:key) : t
ensures { result.elts = S.empty }
ensures { result.max_tags_ = s }
=
=
let iterated = {
elts' = S.empty;
max_tags_' = Int63.to_int s;
present = Array.make (s+1) false;
value = Array.make (s+1) def;
present = Array.make 8 false;
value = Array.make 8 def;
}
in
{
elts = S.empty;
max_tags_ = Int63.to_int s;
iterated = iterated;
}
...
...
@@ -161,25 +152,55 @@ module TagSet
tag k < Array.length h.iterated.present && Array.(h.iterated.present[tag k])
let function max_tags (h: t) : Int63.int63
ensures {
result = h.max_tags_
} =
ensures {
forall v. S.mem v h.elts -> tag v <= result
} =
Array.(length h.iterated.present) - 1
let resize (h:t) (k:key) : unit
ensures { tag k < Array.(length h.iterated.present) }
=
let len = tag k + 1 in
let n = Array.length h.iterated.value in
if len > n then begin
let nlen = (max len (2 * (min n (Int63.max_int / 2)))) in
let a = Array.(make nlen k) in
Array.blit h.iterated.value 0 a 0 n;
h.iterated.value <- a;
let b = Array.make nlen false in
Array.blit h.iterated.present 0 b 0 n;
h.iterated.present <- b
end
let add (h: t) (k: key): unit
requires { tag k <= h.max_tags }
ensures { h.elts = S.add k (old h.elts) }
writes { h.elts , h.iterated, h.iterated.present, h.iterated.value(*, h.iterated.elts'*) } =
writes { h.elts , h.iterated } =
resize h k;
h.elts <- S.add k h.elts;
h.iterated.elts' <- S.add k h.iterated.elts';
h.iterated.present[tag k] <- true;
h.iterated.value[tag k] <- k ;
if false then
h.iterated <- {
max_tags_' = h.iterated.max_tags_';
elts' = h.iterated.elts';
present = h.iterated.present;
value = h.iterated.value;
}
let remove (k: key) (h: t) : unit
ensures { h.elts = S.remove k h.elts } =
if tag k < Array.length h.iterated.present then begin
h.elts <- S.remove k h.elts;
h.iterated.elts' <- S.remove k h.iterated.elts';
Array.(h.iterated.present[tag k] <- false);
end;
if false then
h.iterated <- {
elts' = h.iterated.elts';
present = h.iterated.present;
value = h.iterated.value;
}
type iterator = {
iterating: iteration_state;
ghost mutable seen: S.set key;
...
...
@@ -199,7 +220,6 @@ module TagSet
all = S.empty;
offset = 0;
iterating = {
max_tags_' = -1;
elts' = S.empty;
present = Array.make 0 false;
value = Array.make 0 (any key);
...
...
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