Skip to content
GitLab
Projects
Groups
Snippets
Help
Loading...
Help
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in
Toggle navigation
why3
Project overview
Project overview
Details
Activity
Releases
Repository
Repository
Files
Commits
Branches
Tags
Contributors
Graph
Compare
Issues
125
Issues
125
List
Boards
Labels
Service Desk
Milestones
Merge Requests
15
Merge Requests
15
Operations
Operations
Incidents
Packages & Registries
Packages & Registries
Container Registry
Analytics
Analytics
Repository
Value Stream
Wiki
Wiki
Snippets
Snippets
Members
Members
Collapse sidebar
Close sidebar
Activity
Graph
Create a new issue
Commits
Issue Boards
Open sidebar
Why3
why3
Commits
312f137e
Commit
312f137e
authored
Apr 11, 2015
by
Jean-Christophe Filliâtre
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
gallery: some experiments in vstte10_queens to count solutions
parent
20cdf859
Changes
3
Hide whitespace changes
Inline
Side-by-side
Showing
3 changed files
with
245 additions
and
22 deletions
+245
-22
examples/vstte10_queens.mlw
examples/vstte10_queens.mlw
+117
-0
examples/vstte10_queens/why3session.xml
examples/vstte10_queens/why3session.xml
+128
-22
examples/vstte10_queens/why3shapes.gz
examples/vstte10_queens/why3shapes.gz
+0
-0
No files found.
examples/vstte10_queens.mlw
View file @
312f137e
...
...
@@ -111,4 +111,121 @@ module NQueens
with Solution -> a
end
(** variant: counting solutions (not part of the competition)
TODO: prove soundness i.e. we indeed count the number of solutions *)
use import ref.Refint
let rec count_bt_queens (board: array int) (n: int) (pos: int) : int
variant { n - pos }
requires { length board = n /\ 0 <= pos <= n /\ solution board pos }
ensures { eq_board board (old board) pos }
= 'Init:
if pos = n then
1
else begin
let s = ref 0 in
for i = 0 to n - 1 do
invariant { eq_board board (at board 'Init) pos }
board[pos] <- i;
if check_is_consistent board pos then
s += count_bt_queens board n (pos+1)
done;
!s
end
let count_queens (board: array int) (n: int) : int
requires { length board = n }
ensures { true }
= count_bt_queens board n 0
let test_count_8 () =
let a = Array.make 8 0 in
count_queens a 8
end
(** counting solutions with machine integers *)
module MachineArithmetic
use import ref.Refint
use import mach.array.Array63
use import mach.int.Int63
predicate is_board (board: array int63) (pos: int) =
forall q: int. 0 <= q < pos ->
0 <= to_int board[q] < to_int (length board)
exception MInconsistent int63
let mcheck_is_consistent (board: array int63) (pos: int63)
requires { 0 <= to_int pos < to_int (length board) }
requires { is_board board (to_int pos + 1) }
= try
let rec forloop q (* for q = 0 to pos-1 do *) =
requires { 0 <= to_int q <= to_int pos }
requires { is_board board (to_int pos + 1) }
variant { to_int pos - to_int q }
raises { MInconsistent -> true }
if q < pos then begin
let bq = board[q] in
let bpos = board[pos] in
if bq = bpos then raise (MInconsistent q);
if bq - bpos = pos - q then raise (MInconsistent q);
if bpos - bq = pos - q then raise (MInconsistent q);
forloop (q + of_int 1)
end in
forloop (of_int 0);
True
with MInconsistent _ ->
False
end
use mach.onetime.OneTime as O
(***
let rec mcount_bt_queens (board: array int63) (n: int63) (pos: int63) : O.t
requires { to_int (length board) = to_int n }
requires { 0 <= to_int pos <= to_int n }
requires { is_board board (to_int pos) }
variant { to_int n - to_int pos }
ensures { is_board board (to_int pos) }
=
if eq pos n then
O.succ (O.zero ())
else begin
let s = ref (O.zero ()) in
let rec forloop (i: int63) = (* for i = 0 to n-1 do *)
requires { 0 <= to_int i <= to_int n }
requires { is_board board (to_int pos) }
variant { to_int n - to_int i }
ensures { is_board board (to_int pos) }
if i < n then begin
board[pos] <- i;
if mcheck_is_consistent board pos then
s := O.add !s (mcount_bt_queens board n (pos + of_int 1));
(* let _ = O.add !s (mcount_bt_queens board n (pos + of_int 1))
in (); *)
forloop (i + of_int 1)
end in
forloop (of_int 0);
!s
end
let mcount_queens (board: array int63) (n: int63) : O.t
requires { to_int (length board) = to_int n }
ensures { true }
= mcount_bt_queens board n (of_int 0)
let test_mcount_8 () =
let n = of_int 8 in
let a = Array63.make n (of_int 0) in
mcount_queens a n
***)
end
examples/vstte10_queens/why3session.xml
View file @
312f137e
...
...
@@ -2,43 +2,149 @@
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
<why3session
shape_version=
"4"
>
<prover
id=
"0"
name=
"C
oq"
version=
"8.4pl4"
timelimit=
"20"
memlimit=
"
0"
/>
<prover
id=
"0"
name=
"C
VC4"
version=
"1.4"
timelimit=
"6"
memlimit=
"100
0"
/>
<prover
id=
"1"
name=
"CVC3"
version=
"2.4.1"
timelimit=
"20"
memlimit=
"0"
/>
<prover
id=
"2"
name=
"Alt-Ergo"
version=
"0.95.1"
timelimit=
"20"
memlimit=
"0"
/>
<prover
id=
"3"
name=
"Z3"
version=
"3.2"
timelimit=
"8"
memlimit=
"1000"
/>
<prover
id=
"4"
name=
"Alt-Ergo"
version=
"0.95.2"
timelimit=
"5"
memlimit=
"0"
/>
<prover
id=
"4"
name=
"Alt-Ergo"
version=
"0.95.2"
timelimit=
"6"
memlimit=
"0"
/>
<prover
id=
"5"
name=
"Z3"
version=
"4.3.1"
timelimit=
"6"
memlimit=
"1000"
/>
<file
name=
"../vstte10_queens.mlw"
expanded=
"true"
>
<theory
name=
"NQueens"
sum=
"
762623aaf4b051407a7a7e388df720fc"
expanded=
"tru
e"
>
<goal
name=
"eq_board_set"
expanded=
"true"
>
<proof
prover=
"4"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.00
"
/></proof>
<theory
name=
"NQueens"
sum=
"
05ca6b285c56c769408f7ad47741cff
e"
>
<goal
name=
"eq_board_set"
>
<proof
prover=
"4"
timelimit=
"5"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.00"
steps=
"7
"
/></proof>
</goal>
<goal
name=
"eq_board_sym"
expanded=
"true"
>
<proof
prover=
"2"
><result
status=
"valid"
time=
"0.01"
/></proof>
<goal
name=
"eq_board_sym"
>
<proof
prover=
"2"
><result
status=
"valid"
time=
"0.01"
steps=
"7"
/></proof>
</goal>
<goal
name=
"eq_board_trans"
expanded=
"true"
>
<proof
prover=
"2"
><result
status=
"valid"
time=
"0.01"
/></proof>
<goal
name=
"eq_board_trans"
>
<proof
prover=
"2"
><result
status=
"valid"
time=
"0.01"
steps=
"10"
/></proof>
</goal>
<goal
name=
"eq_board_extension"
expanded=
"true"
>
<proof
prover=
"2"
><result
status=
"valid"
time=
"0.01"
/></proof>
<goal
name=
"eq_board_extension"
>
<proof
prover=
"2"
><result
status=
"valid"
time=
"0.01"
steps=
"9"
/></proof>
</goal>
<goal
name=
"consistent_row_eq"
expanded=
"true"
>
<proof
prover=
"2"
><result
status=
"valid"
time=
"0.06"
/></proof>
<goal
name=
"consistent_row_eq"
>
<proof
prover=
"2"
><result
status=
"valid"
time=
"0.06"
steps=
"37"
/></proof>
</goal>
<goal
name=
"WP_parameter check_is_consistent"
expl=
"VC for check_is_consistent"
expanded=
"true"
>
<goal
name=
"WP_parameter check_is_consistent"
expl=
"VC for check_is_consistent"
>
<proof
prover=
"1"
><result
status=
"valid"
time=
"0.02"
/></proof>
</goal>
<goal
name=
"solution_eq_board"
expanded=
"true"
>
<proof
prover=
"0"
edited=
"vstte10_queens_NQueens_solution_eq_board_1.v"
><result
status=
"valid"
time=
"1.31"
/></proof>
<goal
name=
"solution_eq_board"
>
<proof
prover=
"3"
><result
status=
"valid"
time=
"0.06"
/></proof>
</goal>
<goal
name=
"WP_parameter bt_queens"
expl=
"VC for bt_queens"
expanded=
"true"
>
<proof
prover=
"1"
><result
status=
"valid"
time=
"1.
46
"
/></proof>
<goal
name=
"WP_parameter bt_queens"
expl=
"VC for bt_queens"
>
<proof
prover=
"1"
><result
status=
"valid"
time=
"1.
21
"
/></proof>
</goal>
<goal
name=
"WP_parameter queens"
expl=
"VC for queens"
expanded=
"true"
>
<proof
prover=
"4"
timelimit=
"20"
><result
status=
"valid"
time=
"0.02"
/></proof>
<goal
name=
"WP_parameter queens"
expl=
"VC for queens"
>
<proof
prover=
"4"
timelimit=
"20"
><result
status=
"valid"
time=
"0.02"
steps=
"21"
/></proof>
</goal>
<goal
name=
"WP_parameter test8"
expl=
"VC for test8"
expanded=
"true"
>
<proof
prover=
"4"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.01"
/></proof>
<goal
name=
"WP_parameter test8"
expl=
"VC for test8"
>
<proof
prover=
"4"
timelimit=
"5"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.01"
steps=
"0"
/></proof>
</goal>
<goal
name=
"WP_parameter count_bt_queens"
expl=
"VC for count_bt_queens"
>
<proof
prover=
"5"
><result
status=
"valid"
time=
"0.06"
/></proof>
</goal>
<goal
name=
"WP_parameter count_queens"
expl=
"VC for count_queens"
>
<proof
prover=
"4"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.01"
steps=
"8"
/></proof>
</goal>
<goal
name=
"WP_parameter test_count_8"
expl=
"VC for test_count_8"
>
<proof
prover=
"4"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.01"
steps=
"0"
/></proof>
</goal>
</theory>
<theory
name=
"MachineArithmetic"
sum=
"0500018a9f9265efb1b389c414cb9813"
expanded=
"true"
>
<goal
name=
"WP_parameter mcheck_is_consistent"
expl=
"VC for mcheck_is_consistent"
expanded=
"true"
>
<proof
prover=
"0"
><result
status=
"valid"
time=
"0.27"
/></proof>
</goal>
<goal
name=
"WP_parameter mcount_bt_queens"
expl=
"VC for mcount_bt_queens"
>
<transf
name=
"split_goal_wp"
>
<goal
name=
"WP_parameter mcount_bt_queens.1"
expl=
"1. postcondition"
>
<proof
prover=
"4"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.02"
steps=
"10"
/></proof>
</goal>
<goal
name=
"WP_parameter mcount_bt_queens.2"
expl=
"2. index in array bounds"
>
<proof
prover=
"4"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.02"
steps=
"15"
/></proof>
</goal>
<goal
name=
"WP_parameter mcount_bt_queens.3"
expl=
"3. precondition"
>
<proof
prover=
"4"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.02"
steps=
"17"
/></proof>
</goal>
<goal
name=
"WP_parameter mcount_bt_queens.4"
expl=
"4. precondition"
>
<proof
prover=
"0"
><result
status=
"valid"
time=
"0.05"
/></proof>
</goal>
<goal
name=
"WP_parameter mcount_bt_queens.5"
expl=
"5. integer overflow"
>
<proof
prover=
"4"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.02"
steps=
"20"
/></proof>
</goal>
<goal
name=
"WP_parameter mcount_bt_queens.6"
expl=
"6. integer overflow"
>
<proof
prover=
"4"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.04"
steps=
"47"
/></proof>
</goal>
<goal
name=
"WP_parameter mcount_bt_queens.7"
expl=
"7. variant decrease"
>
<proof
prover=
"4"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.02"
steps=
"23"
/></proof>
</goal>
<goal
name=
"WP_parameter mcount_bt_queens.8"
expl=
"8. precondition"
>
<proof
prover=
"4"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.02"
steps=
"23"
/></proof>
</goal>
<goal
name=
"WP_parameter mcount_bt_queens.9"
expl=
"9. precondition"
>
<proof
prover=
"4"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.02"
steps=
"23"
/></proof>
</goal>
<goal
name=
"WP_parameter mcount_bt_queens.10"
expl=
"10. precondition"
>
<proof
prover=
"4"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.01"
steps=
"23"
/></proof>
</goal>
<goal
name=
"WP_parameter mcount_bt_queens.11"
expl=
"11. integer overflow"
>
<proof
prover=
"4"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.02"
steps=
"28"
/></proof>
</goal>
<goal
name=
"WP_parameter mcount_bt_queens.12"
expl=
"12. integer overflow"
>
<proof
prover=
"4"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.15"
steps=
"62"
/></proof>
</goal>
<goal
name=
"WP_parameter mcount_bt_queens.13"
expl=
"13. variant decrease"
>
<proof
prover=
"4"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.02"
steps=
"31"
/></proof>
</goal>
<goal
name=
"WP_parameter mcount_bt_queens.14"
expl=
"14. precondition"
>
<proof
prover=
"4"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.02"
steps=
"31"
/></proof>
</goal>
<goal
name=
"WP_parameter mcount_bt_queens.15"
expl=
"15. precondition"
>
<proof
prover=
"4"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.48"
steps=
"81"
/></proof>
</goal>
<goal
name=
"WP_parameter mcount_bt_queens.16"
expl=
"16. postcondition"
>
<proof
prover=
"4"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.02"
steps=
"35"
/></proof>
</goal>
<goal
name=
"WP_parameter mcount_bt_queens.17"
expl=
"17. integer overflow"
>
<proof
prover=
"4"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.01"
steps=
"20"
/></proof>
</goal>
<goal
name=
"WP_parameter mcount_bt_queens.18"
expl=
"18. integer overflow"
>
<proof
prover=
"4"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.08"
steps=
"47"
/></proof>
</goal>
<goal
name=
"WP_parameter mcount_bt_queens.19"
expl=
"19. variant decrease"
>
<proof
prover=
"4"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.02"
steps=
"23"
/></proof>
</goal>
<goal
name=
"WP_parameter mcount_bt_queens.20"
expl=
"20. precondition"
>
<proof
prover=
"4"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.02"
steps=
"23"
/></proof>
</goal>
<goal
name=
"WP_parameter mcount_bt_queens.21"
expl=
"21. precondition"
>
<proof
prover=
"4"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.23"
steps=
"65"
/></proof>
</goal>
<goal
name=
"WP_parameter mcount_bt_queens.22"
expl=
"22. postcondition"
>
<proof
prover=
"4"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.02"
steps=
"27"
/></proof>
</goal>
<goal
name=
"WP_parameter mcount_bt_queens.23"
expl=
"23. postcondition"
>
<proof
prover=
"4"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.01"
steps=
"15"
/></proof>
</goal>
<goal
name=
"WP_parameter mcount_bt_queens.24"
expl=
"24. integer overflow"
>
<proof
prover=
"4"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.02"
steps=
"11"
/></proof>
</goal>
<goal
name=
"WP_parameter mcount_bt_queens.25"
expl=
"25. precondition"
>
<proof
prover=
"4"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.02"
steps=
"12"
/></proof>
</goal>
<goal
name=
"WP_parameter mcount_bt_queens.26"
expl=
"26. precondition"
>
<proof
prover=
"4"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.02"
steps=
"12"
/></proof>
</goal>
<goal
name=
"WP_parameter mcount_bt_queens.27"
expl=
"27. postcondition"
>
<proof
prover=
"4"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.02"
steps=
"15"
/></proof>
</goal>
</transf>
</goal>
<goal
name=
"WP_parameter mcount_queens"
expl=
"VC for mcount_queens"
>
<proof
prover=
"4"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.02"
steps=
"14"
/></proof>
</goal>
<goal
name=
"WP_parameter test_mcount_8"
expl=
"VC for test_mcount_8"
>
<proof
prover=
"4"
memlimit=
"1000"
><result
status=
"valid"
time=
"0.02"
steps=
"10"
/></proof>
<proof
prover=
"5"
><result
status=
"valid"
time=
"0.01"
/></proof>
</goal>
</theory>
</file>
...
...
examples/vstte10_queens/why3shapes.gz
View file @
312f137e
No preview for this file type
Write
Preview
Markdown
is supported
0%
Try again
or
attach a new file
.
Attach a file
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment