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+// program inspired by "Proving Copyless Message Passing" (Villard, Lozes and Calcagno, APLAS 2009)
+
+// msg tag indicates what the type of the message
+// channel is freed by Getter when it completes
+// ack-channel instead of single channel with ack message channel
+// using Owicki-Gries ghostfields can be used to remove the "assume false;" statements
+
+// Conjecture: it is ok to send debit credit(d, -x) over a channel c as long as
+// a) d.mu << c.mu
+// b) leaking positive or negative debit is not allowed
+
+channel AckChannel(ch: C) where ch != null && credit(ch, -1); // ack
+
+channel C(msg: int, n: Node, ackC: AckChannel) where
+ (msg == 0 || msg == 1) &&
+ (msg == 0 ==> acc(this.mu, 50) && acc(ackC.mu, 50)) &&
+ (msg == 1 ==> n != null && acc(n.next) && acc(n.mu) && credit(ackC, -1)); // cell
+
+class Node {
+ var next: Node;
+
+ function length(): int
+ requires this.list;
+ {
+ unfolding this.list in 1 + (next == null ? 0 : next.length())
+ }
+
+ predicate list {
+ acc(next) && acc(mu) && (next != null ==> next.list)
+ }
+}
+
+class Program {
+ method Putter(e: C, x0: Node, ackC: AckChannel)
+ requires e!= null && acc(e.mu, 50) && e.mu == maxlock && acc(ackC.mu, 50) && e.mu << ackC.mu && (x0 != null ==> x0.list) && (x0 != null ==> credit(e, - 1));
+ {
+ var x: Node := x0;
+ var t: Node;
+
+ while(x != null)
+ invariant (x != null ==> x.list) && acc(e.mu, 50) && acc(ackC.mu, 50) && e.mu << ackC.mu && credit(e, - 1);
+ {
+ unfold x.list;
+ t := x.next;
+ send e(1, x, ackC);
+ x := t;
+ var ack;
+ assume maxlock << ackC.mu; // Chalice should be able to figure this out itself?
+ var ctmp: C;
+ receive ctmp := ackC;
+ if(ctmp != e) { assume false; /* abort */ }
+ }
+ send e(0, null, ackC);
+ }
+
+ method Getter(f: C, ackC: AckChannel)
+ requires f!= null && credit(f, 1) && acc(f.mu, 50) && maxlock << f.mu && ackC != null && acc(ackC.mu, 50) && f.mu << ackC.mu;
+ {
+ var x: Node := null;
+ var msg := 1;
+ while(msg != 0)
+ invariant acc(f.mu, 50) && maxlock << f.mu && (msg == 1 ==> credit(f, 1)) && (msg == 0 ==> acc(f.mu, 50) && acc(ackC.mu, 50));
+ {
+ var ackC2: AckChannel;
+ receive msg, x, ackC2 := f;
+ if(ackC2 != ackC) { assume false; /* abort */ }
+ if(msg == 0) {
+ }
+ if(msg == 1) {
+ free x;
+ send ackC(f);
+ }
+ }
+ free f; // close the channel
+ }
+
+ method Main(x: Node)
+ requires x.list;
+ {
+ var e := new C;
+ var ackC := new AckChannel above e;
+ fork Putter(e, x, ackC);
+ fork Getter(e, ackC);
+ }
+}
+
+
+