--- layout: fc_discuss_archives title: Message 8 from Frama-C-discuss on February 2015 ---
Dear All, verifying an implementation of partition I have something like /*@ axiomatic List { @ type listInt; @ logic listInt nil; @ logic listInt cons(integer x, listInt xs); @ logic listInt append(listInt xs, listInt ys); @ logic listInt arrayToList{L}(int *arr, integer length); @ logic boolean member(integer elem, listInt xs); @ axiom appendNil: @ \forall listInt ys; append(nil, ys) == ys; @ axiom appendCons: @ \forall listInt xs, ys; \forall integer x; append(cons(x, xs), ys) == cons(x, append(xs, ys)); @ axiom arrayToListNull{L}: @ \forall int *arr; \forall integer i; i == 0 ==> arrayToList{L}(arr, i) == nil; @ axiom arrayToListN{L}: @ \forall int *arr; \forall integer length, newLength; length > 0 && newLength == length-1 @ ==> arrayToList{L}(arr, length) == cons(\at(arr[0], L), arrayToList{L}(arr+1, newLength)); @ axiom memberNil: @ \forall integer elem; !member(elem, nil); @ axiom memberConsHead: @ \forall integer elem; \forall listInt xs; member(elem, cons(elem, xs)); @ axiom memberConsTail: @ \forall integer elem, x; \forall listInt xs; member(elem, xs) ==> member(elem, cons(x, xs)); @ predicate permutationLists(listInt a, listInt b); @ axiom permutationListsNil: @ permutationLists(nil, nil); @ axiom permutationListsCons: @ \forall listInt a1, a2, a3, ta, b1, b2, b3, tb; ta == append(a1, append(a2, a3)) @ && tb == append(b1, append(b2, b3)) && a2 != nil && a2 == b2 @ && permutationLists(append(a1, a3), append(b1, b3)) @ ==> permutationLists(ta, b1); @} @*/ /*@ @predicate permutation{L1, L2}(int *a, int *b, integer count) = @ permutationLists(arrayToList{L1}(a, count), arrayToList{L2}(b, count)); @ @predicate property(integer x); @*/ /*@ assigns \nothing; @ ensures \result == \true <==> property(x); @*/ int property(int x); /*@ requires length >= 0 && \valid(arr+(0..length-1)) && \valid(ind+(0..length-1)); @ ensures 0 <= \result < length; @ ensures \forall int i; 0 <= i <= \result ==> property(arr[ind[i]]); @ ensures \forall int i; \result + 1 <= i < length ==> !property(arr[ind[i]]); @ assigns ind[0..length-1]; @*/ int partition(int *arr, int *ind, int length) { int gr = 0, j = length-1; /*@ loop invariant 0 <= gr <= j+1 <= length ; @ loop invariant \forall integer i; 0 <= i < gr ==> property(arr[ind[i]]); @ loop invariant \forall integer i; j+1 <= i < length ==> !property(arr[ind[i]]); @ loop invariant permutationLists(append(arrayToList{Here}(ind, gr), arrayToList{Here}(ind+j+1, length-j)), arrayToList{Here}(arr, gr + length - j)); @ loop variant j - gr; @*/ while (gr <= j) { if (property(arr[gr + length - 1 - j])) { ind[gr] = gr + length - 1 - j; //@ assert ind[gr] == gr + length - 1 - j && property(arr[gr + length - 1 - j]) && property(arr[ind[gr]]); gr++; } else { ind[j] = gr + length - 1 - j; j--; } } return gr-1; } Frama-C Neon/WP failed to discharge the second part of the invariant, so I started experimenting with some assertions. When I write the assertion as above the PO is not discharged. When I turn on 'split' the first of the three generated POs is discharged. When I write the three assertions as separate assertions: //@ assert ind[gr] == gr + length - 1 - j; //@ assert property(arr[gr + length - 1 - j]); //@ assert property(arr[ind[gr]]); then the first and the last are discharged. Any hints on how I should deal with this and how I could get the invariant proved? Thanks and best regards, Marko -------------- next part -------------- A non-text attachment was scrubbed... Name: not available Type: application/pgp-signature Size: 181 bytes Desc: OpenPGP Digital Signature URL: <http://lists.gforge.inria.fr/pipermail/frama-c-discuss/attachments/20150212/c3ae5274/attachment.sig>