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// VSComp 2010, problem 1, compute the sum and max of the elements of an array and prove
// that 'sum <= N * max'.
// Rustan Leino, 18 August 2010.
//
// The problem statement gave the pseudo-code for the method, but did not ask to prove
// that 'sum' or 'max' return as the sum and max, respectively, of the array. The
// given assumption that the array's elements are non-negative is not needed to establish
// the requested postcondition.
method M(N: int, a: array<int>) returns (sum: int, max: int)
requires 0 <= N && a != null && a.Length == N && (forall k :: 0 <= k && k < N ==> 0 <= a[k]);
ensures sum <= N * max;
{
sum := 0;
max := 0;
var i := 0;
while (i < N)
invariant i <= N && sum <= i * max;
{
if (max < a[i]) {
max := a[i];
}
sum := sum + a[i];
i := i + 1;
}
}
method Main()
{
var a := new int[10];
a[0] := 9;
a[1] := 5;
a[2] := 0;
a[3] := 2;
a[4] := 7;
a[5] := 3;
a[6] := 2;
a[7] := 1;
a[8] := 10;
a[9] := 6;
var s, m := M(10, a);
print "N = ", a.Length, " sum = ", s, " max = ", m, "\n";
}
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