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/*
COST Verification Competition. vladimir@cost-ic0701.org
Challenge 1: Maximum in an array
Given: A non-empty integer array a.
Verify that the index returned by the method max() given below points to
an element maximal in the array.
*/
/*@ axiomatic integer_max {
@ logic integer max(integer x, integer y);
@ axiom max_is_ge : \forall integer x y; max(x,y) >= x && max(x,y) >= y;
@ axiom max_is_some : \forall integer x y; max(x,y) == x || max(x,y) == y;
@ }
@*/
public class ArrayMax {
/*@ requires a.length > 0;
@ ensures 0 <= \result < a.length &&
@ \forall integer i; 0 <= i < a.length ==> a[i] <= a[\result];
@*/
public static int max(int[] a) {
int x = 0;
int y = a.length-1;
/*@ loop_invariant 0 <= x <= y < a.length &&
@ \forall integer i;
@ 0 <= i < x || y < i < a.length ==>
@ a[i] <= max(a[x],a[y]);
@ loop_variant y - x;
@*/
while (x != y) {
if (a[x] <= a[y]) x++;
else y--;
}
return x;
}
}
/*
Local Variables:
compile-command: "make ArrayMax.why3ml"
End:
*/
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