documentation: solution for VSTTE'10 problem 4

examples/programs/vstte10_queens.mlw

@@ -49,7 +49,7 @@ module NQueens
 
   exception Inconsistent int
 
-  let check_is_consistent (board: array int) pos =
+  let check_is_consistent (board: array int) (pos: int) =
     { 0 <= pos < length board }
     try
       for q = 0 to pos - 1 do
@@ -80,28 +80,27 @@ module NQueens
 
   exception Solution
 
-  let rec bt_queens (board: array int) n pos variant { n - pos } =
+  let rec bt_queens (board: array int) (n: int) (pos: int) variant { n - pos } =
     { length board = n and 0 <= pos <= n and solution board pos }
     label Init:
     if pos = n then raise Solution;
     for i = 0 to n - 1 do
       invariant {
-        length board = n and eq_board board (at board Init) pos and
+        eq_board board (at board Init) pos and
         forall b:array int. length b = n -> is_board b n ->
           eq_board board b pos -> 0 <= b[pos] < i -> not (solution b n) }
       board[pos] <- i;
-      assert { eq_board board (at board Init) pos };
       if check_is_consistent board pos then bt_queens board n (pos+1)
     done
     { (* no solution *)
-      length board = n and eq_board board (old board) pos and
+      eq_board board (old board) pos and
       forall b:array int. length b = n -> is_board b n ->
         eq_board board b pos -> not (solution b n) }
     | Solution ->
     { (* a solution *)
       solution board n }
 
-  let queens (board: array int) n =
+  let queens (board: array int) (n: int) =
     { 0 <= length board = n }
     bt_queens board n 0
     { forall b:array int. length b = n -> is_board b n -> not (solution b n) }

examples/programs/vstte10_queens/why3session.xml

@@ -43,14 +43,14 @@
      <result status="valid" time="0.60"/>
     </proof>
    </goal>
-   <goal name="WP_parameter bt_queens" expl="correctness of parameter bt_queens" sum="b59f9ab1ac42b3755b8e06f7dc04fc2a" proved="true" expanded="true">
+   <goal name="WP_parameter bt_queens" expl="correctness of parameter bt_queens" sum="90c2b563e0abbc3b4a70fec2410b7f1b" proved="true" expanded="true">
     <proof prover="cvc3" timelimit="20" edited="" obsolete="false">
-     <result status="valid" time="0.96"/>
+     <result status="valid" time="0.36"/>
     </proof>
    </goal>
-   <goal name="WP_parameter queens" expl="correctness of parameter queens" sum="fa29a0090876c2c2eae4d8423017ff3c" proved="true" expanded="true">
+   <goal name="WP_parameter queens" expl="correctness of parameter queens" sum="67746ab73fbf4bab85d11e7011676a38" proved="true" expanded="true">
     <proof prover="alt-ergo" timelimit="20" edited="" obsolete="false">
-     <result status="valid" time="0.03"/>
+     <result status="valid" time="0.05"/>
     </proof>
    </goal>
   </theory>