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class List<T> {
ghost var Repr: set<object>;
ghost var list: seq<T>;
var root: Node<T>;
function Valid_repr(): bool
reads *;
{
this in Repr &&
null !in Repr &&
(root != null ==> root in Repr && root.Repr <= Repr && this !in root.Repr)
}
function Valid_self(): bool
reads *;
{
Valid_repr() &&
(root == null ==> |list| == 0) &&
(root != null ==> list == root.list)
}
function Valid(): bool
reads *;
{
this.Valid_self() &&
(root != null ==> root.Valid())
}
method Double(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 gensym78 := new Node<T>;
gensym78.Double(p, q);
this.list := [p, q];
this.root := gensym78;
// repr stuff
this.Repr := {this} + this.root.Repr;
// assert repr objects are valid (helps verification)
assert gensym78.Valid();
}
method Empty()
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [];
ensures |list| == 0;
{
this.list := [];
this.root := null;
// repr stuff
this.Repr := {this};
}
method Singleton(t: T)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [t];
ensures list[0] == t;
ensures |list| == 1;
{
var gensym77 := new Node<T>;
gensym77.Init(t);
this.list := [t];
this.root := gensym77;
// repr stuff
this.Repr := {this} + this.root.Repr;
// assert repr objects are valid (helps verification)
assert gensym77.Valid();
}
}
class Node<T> {
ghost var Repr: set<object>;
ghost var list: seq<T>;
var data: T;
var next: Node<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 Double(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 gensym87 := new Node<T>;
gensym87.Init(q);
this.data := p;
this.list := [p, q];
this.next := gensym87;
// repr stuff
this.Repr := {this} + this.next.Repr;
// assert repr objects are valid (helps verification)
assert gensym87.Valid();
}
method Find(n: T) returns (ret: bool)
requires Valid();
ensures fresh(Repr - old(Repr));
ensures Valid();
ensures ret == (n in list);
decreases Repr;
{
if (n != this.data && this.next == null) {
ret := n == this.data;
} else {
if (this.next != null) {
var x_6 := this.next.Find(n);
ret := n == this.data || x_6;
} else {
ret := true;
}
}
}
method Get(idx: int) returns (ret: T)
requires Valid();
requires idx >= 0;
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 Init(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 List() 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_8 := this.next.List();
ret := [this.data] + x_8;
}
}
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_9 := this.next.Size();
ret := 1 + x_9;
}
}
method Tail() returns (tail: Node<T>)
requires Valid();
ensures fresh(Repr - old(Repr));
ensures Valid();
ensures |list| == 1 ==> tail == null;
ensures |list| > 1 ==> tail != null && tail.list == list[1..];
ensures tail != null ==> tail.Valid();
{
tail := this.next;
}
}
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