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class Global {
static function G(x: int): int { x+x }
static method N(ghost x: int) returns (ghost r: int)
ensures r == Global.G(x);
{
if {
case true => r := G(x+0);
case true =>
var g: Global;
r := g.G(x);
case true =>
var g: Global := null;
r := g.G(x);
case true =>
r := Global.G(x);
}
}
}
method TestCalls(k: nat) {
var g: Global, h: Global;
assume g != h;
ghost var r: int;
ghost var s := Global.G(k);
r := Global.N(k);
assert r == s;
r := g.N(k);
assert r == s;
r := h.N(k);
assert r == s;
g := null;
r := g.N(k);
assert r == s;
r := Global.N(r);
if (k == 0) {
assert r == s;
} else {
assert r == s; // error: G(k) and G(k+k) are different
}
}
// ---------- chaining operators ------------------------------------
function UpTruth(j: int, k: int): bool
requires 10 <= j < 180 < 220 <= k;
{
0 < 2 <= 2 < j != 200 < k < k + 1
}
function DownTruth(j: int, k: int): bool
requires k >= 220 > 180 > j >= 10;
{
k + 1 > k > 200 != j > 2 >= 2 > 0
}
method ChallengeTruth(j: int, k: int)
requires 80 <= j < 150 && 250 <= k < 1000;
{
assert UpTruth(j, k);
assert DownTruth(j, k);
// but this is not equally true:
assert j <= j + k != k + j + 1 < k+k+j <=/*this is the error*/ j+j+k < k+k+j+j == 2*k + 2*j == 2*(k+j);
}
// --------- multi assignments --------------------------------
class Multi {
var x: int;
var y: int;
var next: Multi;
method Mutate(z: int) returns (m: Multi)
requires 0 <= z;
modifies this;
ensures y == old(y);
{
x := x + z;
}
method IncX() returns (oldX: int)
modifies this;
ensures x == old(x) + 1 && oldX == old(x);
{
x, oldX := x + 1, x;
}
}
method TestMulti(m: Multi, p: Multi)
requires m != null && p != null;
modifies m, p;
{
m.x := 10;
m.y := 12;
p.x := 20;
p.y := 22;
if (*) {
assert p.x == 20;
assert m.x == 10; // error: m and p may be the same
}
var t, u;
u, m.x, t := 100, u + t + m.x, 200;
m.x := 0;
u, m.x, t := 200, u + t + m.x, 400;
assert m.x == 300;
if (p.x != 300) {
p.x, m.x := m.x, p.x;
}
assert p.x == 300;
if (*) {
p.x, m.y := 10, 10;
p.x, m.x := 8, 8; // error: duplicate assignment (since m and p may be the same)
}
var a, b := new int[20], new int[30];
a[4], b[10], a[0], a[3], b[18] := 0, 1, 2, 3, 4;
a[4], b[b[18]] := 271, 272;
a[4], a[b[18]] := 273, 274; // error: duplicate assignment (since b[18] is 4)
}
class MyBoxyClass<T> {
var f: T;
}
method TestBoxAssignment<T>(x: MyBoxyClass<int>, y: MyBoxyClass<T>, t: T)
requires x != null && y != null;
modifies x, y;
{
y.f := t;
x.f := 15;
// all together now:
y.f, x.f := t, 15; // error: duplicate assignment (if T==int and x==y)
var k: int := x.f;
}
method TestCallsWithFancyLhss(m: Multi)
requires m != null && m.next != null;
modifies m, m.next;
{
m.x := 10;
var p := m.next;
m.next.next := m.Mutate(m.x); // fine
if (*) {
assert m.next == old(m.next); // error: the call to Mutate may have changed m.next
}
m.next.next := m.Mutate(20); // error: LHS may not be well defined (m.next may be null)
m.x, m.next := 12, p;
m.x, m.y := SwapEm(m.x, m.y);
assert m.y == 12;
if (*) {
m.x, m.x := SwapEm(m.x, m.y); // error: duplicate among LHSs
}
m.x := 30;
var xx := m.IncX();
assert xx == 30;
m.y := m.IncX();
assert m.y == 31 && m.x == 32;
m.x := m.IncX();
assert m.x == 32;
xx := m.IncX();
if (*) {
assert xx == 33; // error: xx will in fact be 32
} else {
assert xx == 32; // see!
}
}
method SwapEm(a: int, b: int) returns (x: int, y: int)
ensures x == b && y == a;
{
x, y := b, a;
}
function method abs(a:int): int
{
if a <= 0 then -a else a
}
// test of verifier using euclidean division.
method EuclideanTest(a: int, b: int)
requires b != 0;
{
var q, r := a / b, a % b;
assert 0 <= r < abs(b);
assert a == b * q + r;
assert (a/b) * b + a % b == a;
}
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