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module A {
class X { }
class T {
method M(x: int) returns (y: int)
requires 0 <= x;
ensures 0 <= y;
{
y := 2 * x;
}
method Q() returns (q: int, r: int, s: int)
ensures 0 <= q && 0 <= r && 0 <= s;
{ // error: failure to establish postcondition about q
r, s := 100, 200;
}
}
}
module B refines A {
class C { }
datatype Dt = Ax | Bx;
class T {
method P() returns (p: int)
{
p := 18;
}
method M(x: int) returns (y: int)
ensures y % 2 == 0; // add a postcondition
method Q ...
ensures 12 <= r;
ensures 1200 <= s; // error: postcondition is not established by
// inherited method body
}
}
// ------------------------------------------------
module A_AnonymousClass {
var x: int;
method Increment(d: int)
modifies this;
{
x := x + d;
}
}
module B_AnonymousClass refines A_AnonymousClass {
method Increment...
ensures x <= old(x) + d;
}
module C_AnonymousClass refines B_AnonymousClass {
method Increment(d: int)
ensures old(x) + d <= x;
method Main()
modifies this;
{
x := 25;
Increment(30);
assert x == 55;
Increment(12);
assert x == 66; // error: it's 67
}
}
// ------------------------------------------------
module BodyFree {
function F(x: int): int
ensures 0 <= F(x);
method TestF() {
assert F(6) == F(7); // error: no information about F so far
}
method M() returns (a: int, b: int)
ensures a == b;
}
module SomeBody refines BodyFree {
function F(x: int): int
{ if x < 0 then 2 else 3 }
method TestFAgain() {
assert F(6) == F(7);
}
method M() returns (a: int, b: int)
{
a := b; // good
}
}
module FullBodied refines BodyFree {
function F(x: int): int
{ x } // error: does not meet the inherited postcondition
method M() returns (a: int, b: int)
{ // error: does not establish postcondition
a := b + 1;
}
}
// ------------------------------------------------
module Abstract {
class MyNumber {
ghost var N: int;
ghost var Repr: set<object>;
predicate Valid
reads this, Repr;
{
this in Repr && null !in Repr
}
constructor Init()
modifies this;
ensures N == 0;
ensures Valid && fresh(Repr - {this});
{
N, Repr := 0, {this};
}
method Inc()
requires Valid;
modifies Repr;
ensures N == old(N) + 1;
ensures Valid && fresh(Repr - old(Repr));
{
N := N + 1;
}
method Get() returns (n: int)
requires Valid;
ensures n == N;
{
var k; assume k == N;
n := k;
}
}
}
module Concrete refines Abstract {
class MyNumber {
var a: int;
var b: int;
predicate Valid
{
N == a - b
}
constructor Init()
{
a := b;
}
method Inc()
{
if (*) { a := a + 1; } else { b := b - 1; }
}
method Get() returns (n: int)
{
var k := a - b;
assert ...;
}
}
}
module Client imports Concrete {
class TheClient {
method Main() {
var n := new MyNumber.Init();
n.Inc();
n.Inc();
var k := n.Get();
assert k == 2;
}
}
}
module IncorrectConcrete refines Abstract {
class MyNumber {
var a: int;
var b: int;
predicate Valid
{
N == 2*a - b
}
constructor Init()
{ // error: postcondition violation
a := b;
}
method Inc()
{ // error: postcondition violation
if (*) { a := a + 1; } else { b := b - 1; }
}
method Get() returns (n: int)
{
var k := a - b;
assert ...; // error: assertion violation
}
}
}
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