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// Note: There is a bug in the well-formedness of functions. In particular,
// it doesn't look at the requires clause (in the proper way). Fixed!
// Note:Implemented arrays as Dafny does not provide them
class Benchmark2 {
method BinarySearch(a: Array, key: int) returns (result: int)
requires a != null;
requires (forall i, j ::
0 <= i && i < j && j < a.Length() ==> a.Get(i) <= a.Get(j));
ensures -1 <= result && result < a.Length();
ensures 0 <= result ==> a.Get(result) == key;
ensures result == -1 ==>
(forall i :: 0 <= i && i < a.Length() ==> a.Get(i) != key);
{
var low := 0;
var high := a.Length();
while (low < high)
invariant 0 <= low && high <= a.Length();
invariant (forall i :: 0 <= i && i < low ==> a.Get(i) < key);
invariant (forall i :: high <= i && i < a.Length() ==> key < a.Get(i));
decreases high - low;
{
var mid := low + (high - low) / 2;
var midVal := a.Get(mid);
if (midVal < key) {
low := mid + 1;
} else if (key < midVal) {
high := mid;
} else {
result := mid; // key found
return;
}
}
result := -1; // key not present
}
}
class Array {
var contents: seq<int>;
method Init(n: int);
requires 0 <= n;
modifies this;
ensures |contents| == n;
function method Length(): int
reads this;
{ |contents| }
function method Get(i: int): int
requires 0 <= i && i < |contents|;
reads this;
{ contents[i] }
method Set(i: int, x: int);
requires 0 <= i && i < |contents|;
modifies this;
ensures |contents| == |old(contents)|;
ensures contents[..i] == old(contents[..i]);
ensures contents[i] == x;
ensures contents[i+1..] == old(contents[i+1..]);
}
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