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class NumberMethods {
ghost var Repr: set<object>;
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) returns (ret: int)
requires Valid();
ensures fresh(Repr - old(Repr));
ensures Valid();
ensures ret in {a, -a};
ensures ret >= 0;
{
if (-a >= 0) {
ret := -a;
} else {
ret := a;
}
}
method Double(p: int) returns (ret: int)
requires Valid();
ensures fresh(Repr - old(Repr));
ensures Valid();
ensures ret == 2 * p;
{
ret := 2 * p;
}
method Min2(a: int, b: int) returns (ret: int)
requires Valid();
ensures fresh(Repr - old(Repr));
ensures Valid();
ensures a < b ==> ret == a;
ensures a >= b ==> ret == b;
{
if (a < b) {
ret := a;
} else {
ret := b;
}
}
method Min22(a: int, b: int) returns (ret: int)
requires Valid();
ensures fresh(Repr - old(Repr));
ensures Valid();
ensures ret in {a, b};
ensures ret <= a;
ensures ret <= b;
{
if (a <= b) {
ret := a;
} else {
ret := b;
}
}
method Min3(a: int, b: int, c: int) returns (ret: int)
requires Valid();
ensures fresh(Repr - old(Repr));
ensures Valid();
ensures ret in {a, b, c};
ensures ret <= a;
ensures ret <= b;
ensures ret <= c;
{
ret := this.Min32(a, b, c);
}
method Min32(a: int, b: int, c: int) returns (ret: int)
requires Valid();
ensures fresh(Repr - old(Repr));
ensures Valid();
ensures ret in {a, b, c};
ensures ret <= a;
ensures ret <= b;
ensures ret <= c;
{
if (a <= b && a <= c) {
ret := a;
} else {
if (c <= a && c <= b) {
ret := c;
} else {
ret := b;
}
}
}
method Min4(a: int, b: int, c: int, d: int) returns (ret: int)
requires Valid();
ensures fresh(Repr - old(Repr));
ensures Valid();
ensures ret in {a, b, c, d};
ensures ret <= a;
ensures ret <= b;
ensures ret <= c;
ensures ret <= d;
{
if ((a <= b && a <= c) && a <= d) {
ret := a;
} else {
if ((d <= a && d <= b) && d <= c) {
ret := d;
} else {
if ((c <= a && c <= b) && c <= d) {
ret := c;
} else {
ret := b;
}
}
}
}
method MinSum(a: int, b: int, c: int) returns (ret: int)
requires Valid();
ensures fresh(Repr - old(Repr));
ensures Valid();
ensures ret in {a + b, a + c, b + c};
ensures ret <= a + b;
ensures ret <= b + c;
ensures ret <= a + c;
{
ret := this.Min3(a + b, b + c, a + c);
}
method Sum(a: int, b: int) returns (ret: int)
requires Valid();
ensures fresh(Repr - old(Repr));
ensures Valid();
ensures ret == a + b;
{
ret := a + b;
}
}
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