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class List<T> {
ghost var Repr: set<object>;
ghost var list: seq<T>;
var data: T;
var next: List<T>;
function Valid_repr(): bool
reads *;
{
this in Repr &&
null !in Repr &&
(next != null ==> next in Repr && next.Repr <= Repr && this !in next.Repr)
}
function Valid_self(): bool
reads *;
{
Valid_repr() &&
(next == null ==> (list == [data] && list[0] == data) && |list| == 1) &&
(next != null ==> list == [data] + next.list) &&
(|list| > 0)
}
function Valid(): bool
reads *;
decreases Repr;
{
this.Valid_self() &&
(next != null ==> next.Valid()) &&
(next != null ==> next.Valid_self()) &&
(next != null && next.next != null ==> next.next.Valid_self())
}
method Dupleton(p: T, q: T)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [p, q];
ensures list[0] == p;
ensures list[1] == q;
ensures |list| == 2;
{
var gensym71 := new List<T>;
gensym71.Singleton(q);
this.data := p;
this.list := [p, q];
this.next := gensym71;
// repr stuff
this.Repr := {this} + this.next.Repr;
// assert repr objects are valid (helps verification)
assert gensym71.Valid();
}
method Elems() returns (ret: seq<T>)
requires Valid();
ensures fresh(Repr - old(Repr));
ensures Valid();
ensures ret == list;
decreases Repr;
{
if (this.next == null) {
ret := [this.data];
} else {
var x_5 := this.next.Elems();
ret := [this.data] + x_5;
}
}
method Find(n: T) returns (ret: bool)
requires Valid();
ensures fresh(Repr - old(Repr));
ensures Valid();
ensures ret == (n in list);
decreases Repr;
{
if (this.next == null) {
ret := n == this.data;
} else {
var x_6 := this.next.Find(n);
ret := n == this.data || x_6;
}
}
method Get(idx: int) returns (ret: T)
requires Valid();
requires 0 <= idx;
requires idx < |list|;
ensures fresh(Repr - old(Repr));
ensures Valid();
ensures ret == list[idx];
decreases Repr;
{
if (this.next == null) {
ret := this.data;
} else {
if (idx == 0) {
ret := this.data;
} else {
var x_7 := this.next.Get(idx - 1);
ret := x_7;
}
}
}
method Singleton(t: T)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [t];
ensures list[0] == t;
ensures |list| == 1;
{
this.data := t;
this.list := [t];
this.next := null;
// repr stuff
this.Repr := {this};
}
method Size() returns (ret: int)
requires Valid();
ensures fresh(Repr - old(Repr));
ensures Valid();
ensures ret == |list|;
decreases Repr;
{
if (this.next == null) {
ret := 1;
} else {
var x_8 := this.next.Size();
ret := 1 + x_8;
}
}
}
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