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// Edited B6 to include GetChar and PutChar
//This is the Queue from Benchmark 3.
//restriction:we assume streams are finite
//what else can we specify?
class Queue<T> {
var contents: seq<T>;
method Init()
modifies this;
ensures |contents| == 0;
method Enqueue(x: T)
modifies this;
ensures contents == old(contents) + [x];
method Dequeue() returns (x: T)
requires 0 < |contents|;
modifies this;
ensures contents == old(contents)[1..] && x == old(contents)[0];
function Head(): T
requires 0 < |contents|;
reads this;
{ contents[0] }
function Get(i: int): T
requires 0 <= i && i < |contents|;
reads this;
{ contents[i] }
}
class Stream {
ghost var footprint:set<object>;
var stream:seq<int>;
var isOpen:bool;
function Valid():bool
reads this, footprint;
{
null !in footprint && this in footprint && isOpen
}
method GetCount() returns (c:int)
requires Valid();
ensures 0 <= c;
{
c := |stream|;
}
method Create() //writing
modifies this;
ensures Valid() && fresh(footprint - {this});
ensures stream == [];
{
stream := [];
footprint := {this};
isOpen := true;
}
method Open() //reading
modifies this;
ensures Valid() && fresh(footprint - {this});
{
footprint := {this};
isOpen := true;
}
method PutChar(x:int )
requires Valid();
modifies footprint;
ensures Valid() && fresh(footprint - old(footprint));
ensures stream == old(stream) + [x];
{
stream:= stream + [x];
}
method GetChar()returns(x:int)
requires Valid() && 0 < |stream|;
modifies footprint;
ensures Valid() && fresh(footprint - old(footprint));
ensures x ==old(stream)[0];
ensures stream == old(stream)[1..];
{
x := stream[0];
stream := stream[1..];
}
method AtEndOfStream() returns(eos:bool)
requires Valid();
ensures eos <==> |stream| == 0;
{
eos := |stream| == 0;
}
method Close()
requires Valid();
modifies footprint;
{
isOpen := false;
}
}
class Client {
method Sort(q: Queue<int>) returns (r: Queue<int>, perm:seq<int>)
requires q != null;
modifies q;
ensures r != null && fresh(r);
ensures |r.contents| == |old(q.contents)|;
ensures (forall i, j :: 0 <= i && i < j && j < |r.contents| ==>
r.Get(i) <= r.Get(j));
//perm is a permutation
ensures |perm| == |r.contents|; // ==|pperm|
ensures (forall i: int :: 0 <= i && i < |perm|==> 0 <= perm[i] && perm[i] < |perm| );
ensures (forall i, j: int :: 0 <= i && i < j && j < |perm| ==> perm[i] != perm[j]);
// the final Queue is a permutation of the input Queue
ensures (forall i: int :: 0 <= i && i < |perm| ==> r.contents[i] == old(q.contents)[perm[i]]);
method Main()
{
var rd := new Stream;
rd.Open();
var q := new Queue<int>;
while (true)
invariant rd.Valid() && fresh(rd.footprint) && fresh(q);
decreases |rd.stream|;
{
var eos := rd.AtEndOfStream();
if (eos) {
break;
}
var ch := rd.GetChar();
q.Enqueue(ch);
}
rd.Close();
var perm;
q,perm := Sort(q);
var wr := new Stream;
wr.Create();
while (0 < |q.contents|)
invariant wr.Valid() && fresh(wr.footprint) && fresh(q) && q !in wr.footprint;
{
var ch := q.Dequeue();
wr.PutChar(ch);
}
wr.Close();
}
}
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