Time_true
Time, correct version
function ora(self: Ref) : Int
function volume_totale(self: Ref) : Int
define return(x) {
assert !returned
returned := true
res := x
}
function sgn(i: Int) : Int
ensures i > 0 ==> result == 1
ensures i == 0 ==> result == 0
ensures i < 0 ==> result == -1
method Int_compare(o1: Int, o2: Int) returns (res: Int)
ensures (rel(o1, 0) == rel(o2, 1) && rel(o2, 0) == rel(o1, 1)) ==> (sgn(rel(res, 0)) == -sgn(rel(res, 1))) // P1
ensures (rel(o1, 0) == rel(o2, 2) && rel(o2, 0) == rel(o1, 2)) ==> (sgn(rel(res, 0)) == -sgn(rel(res, 2))) // P1
ensures (rel(o1, 2) == rel(o2, 1) && rel(o2, 2) == rel(o1, 1)) ==> (sgn(rel(res, 2)) == -sgn(rel(res, 1))) // P1
ensures (rel(o1, 0) == rel(o1, 1) && rel(o2, 0) == rel(o2, 1)) ==> (rel(res, 0) == rel(res, 1)) // deterministic
ensures (rel(o1, 0) == rel(o1, 2) && rel(o2, 0) == rel(o2, 2)) ==> (rel(res, 0) == rel(res, 2)) // deterministic
ensures (rel(o1, 2) == rel(o1, 1) && rel(o2, 2) == rel(o2, 1)) ==> (rel(res, 2) == rel(res, 1)) // deterministic
ensures ((rel(res, 0) > 0) && rel(res, 1) > 0 && rel(o2, 0) == rel(o1, 1) && rel(o1, 2) == rel(o1, 0) && rel(o2, 2) == rel(o2, 1)) ==> (rel(res, 2) > 0) // P2
ensures (rel(o2, 0) == rel(o1, 1) && rel(o1, 2) == rel(o1, 0) && rel(o2, 2) == rel(o2, 1) && rel(res, 0) == 0) ==> (sgn(rel(res, 1)) == sgn(rel(res, 2)))
ensures (rel(o2, 0) == rel(o1, 1) && rel(o1, 2) == rel(o1, 0) && rel(o2, 2) == rel(o2, 1) && rel(res, 1) == 0) ==> (sgn(rel(res, 0)) == sgn(rel(res, 2)))
ensures (rel(o2, 0) == rel(o1, 1) && rel(o1, 2) == rel(o1, 0) && rel(o2, 2) == rel(o2, 1) && rel(res, 2) == 0) ==> (sgn(rel(res, 1)) == sgn(rel(res, 0)))
method compare(o1: Ref, o2: Ref) returns (res: Int)
requires rel(o2, 0) == rel(o1, 1) && rel(o1, 2) == rel(o1, 0) && rel(o2, 2) == rel(o2, 1)
ensures ((rel(res, 0) > 0) && rel(res, 1) > 0) ==> (rel(res, 2) > 0) // P2
{
var returned : Bool
returned := false
var time1 : Int
var time2 : Int
time1 := ora(o1);
time2 := ora(o2);
var cmp : Int
cmp := Int_compare(time1, time2);
if (cmp == 0){
cmp := Int_compare(volume_totale(o1), volume_totale(o2));
}
return(cmp)
assert returned
}