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class Number {
ghost var Repr: set<object>;
ghost var num: int;
function Valid_repr(): bool
reads *;
{
this in Repr &&
null !in Repr
}
function Valid_self(): bool
reads *;
{
Valid_repr() &&
true
}
function Valid(): bool
reads *;
{
this.Valid_self() &&
true
}
method Abs(a: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures num in {a, -a};
ensures num >= 0;
{
if (a >= 0) {
this.Init(a);
} else {
this.Init(-a);
}
}
method Double(p: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures num == 2 * p;
{
this.Init(2 * p);
}
method Init(p: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures num == p;
{
this.num := p;
// repr stuff
this.Repr := {this};
}
method Min2(a: int, b: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures a < b ==> num == a;
ensures a >= b ==> num == b;
{
if (a < b) {
this.Init(a);
} else {
this.Init(b);
}
}
method Min22(a: int, b: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures num in {a, b};
ensures num <= a;
ensures num <= b;
{
if (a <= b) {
this.Init(a);
} else {
this.Init(b);
}
}
method Min3(a: int, b: int, c: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures num in {a, b, c};
ensures num <= a;
ensures num <= b;
ensures num <= c;
{
this.Min32(a, b, c);
}
method Min32(a: int, b: int, c: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures num in {a, b, c};
ensures num <= a;
ensures num <= b;
ensures num <= c;
{
if (a <= b && a <= c) {
this.Init(a);
} else {
if (c <= a && c <= b) {
this.Init(c);
} else {
this.Init(b);
}
}
}
method Min4(a: int, b: int, c: int, d: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures num in {a, b, c, d};
ensures num <= a;
ensures num <= b;
ensures num <= c;
ensures num <= d;
{
if ((a <= b && a <= c) && a <= d) {
this.Init(a);
} else {
if ((d <= a && d <= b) && d <= c) {
this.Init(d);
} else {
if ((c <= a && c <= b) && c <= d) {
this.Init(c);
} else {
this.Init(b);
}
}
}
}
method MinSum(a: int, b: int, c: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures num in {a + b, a + c, b + c};
ensures num <= a + b;
ensures num <= b + c;
ensures num <= a + c;
{
this.Min3(a + b, b + c, a + c);
}
method Sum(a: int, b: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures num == a + b;
{
this.Init(a + b);
}
}
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