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class Counter0 {
var x: int;
method init()
requires acc(x);
ensures acc(x) && x == 0;
{
x := 0;
}
method inc()
requires acc(x);
ensures acc(x) && x == old(x) + 1;
{
x := x + 1;
}
method dec()
requires acc(x);
ensures acc(x) && x == old(x) - 1;
{
x := x - 1;
}
}
class Counter1 refines Counter0 {
var y: int;
var z: int;
replaces x by acc(y) && acc(z) && x == y - z && y >= 0 && z >= 0;
refines init()
{
this.y := 0;
this.z := 0;
}
refines inc()
{
this.y := this.y + 1;
}
refines dec()
{
this.z := this.z + 1;
}
}
class Cell {var n: int}
/** TODO:
Two-step data refinement doesn't work for the following reason:
the spec of Counter1 uses the abstract field x which disappears at the concrete method body level.
I'm not sure what a good solution to this problem...
*/
class Counter2 refines Counter1 {
var a: Cell;
var b: Cell;
replaces y, z by acc(a) && acc(b) && acc(a.n) && acc(b.n) && y == a.n && z == b.n;
refines init()
{
this.a := new Cell {n := 0};
this.b := new Cell {n := 0};
}
refines inc()
{
this.a.n := this.a.n + 1;
}
refines dec()
{
this.b.n := this.b.n + 1;
}
}
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