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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;
}
/** Interesting issues */
/* We can expose representation here */
method magic1() returns (c: Cell)
requires acc(x)
ensures acc(c.n) && x == old(x);
{
var c [acc(c.n)];
}
/* This should prevent us from exposing representation */
method magic2() returns (c: Cell)
requires acc(x);
ensures acc(x) && x == old(x) && acc(c.n);
{
var c [acc(c.n)];
}
}
class Counter1 refines Counter0 {
var y: int;
var z: int;
replaces x by acc(y) && acc(z) && x == y - z && y >= 0 && z >= 0;
transforms init()
{
replaces * by {this.y := 0; this.z := 0;}
}
transforms inc()
{
replaces * by {this.y := this.y + 1;}
}
transforms dec()
{
replaces * by {this.z := this.z + 1;}
}
/** This violates abstraction of x -- we must hold all permissions to x to update it */
method magic3()
requires acc(y);
{
y := y + 1;
}
/** This does also -- but it also prohibits us from reading part of the state across refinement */
method magic4() returns (i)
requires acc(y);
{
i := y;
}
}
class Cell {var n: int}
/*
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;
transforms init()
{
replaces * by {
this.a := new Cell {n := 0};
this.b := new Cell {n := 0};
}
}
transforms inc()
{
replaces * by {this.a.n := this.a.n + 1;}
}
transforms dec()
{
replaces * by {this.b.n := this.b.n + 1;}
}
transforms magic1() returns (c: Cell)
{
replaces * by {c := this.a;}
}
transforms magic2() returns (c: Cell)
{
replaces * by {c := this.a;}
}
transforms magic3()
{
replaces * by {this.a.n := this.a.n + 1;}
}
transforms magic4() returns (i)
{
replaces * by {i := this.a.n;}
}
}
*/
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