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HWQueueProphecy.tla
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-------------------------- MODULE HWQueueProphecy --------------------------
(***************************************************************************)
(* *)
(* Queue representation type (REP) from Herlihy & Wing 1990. *)
(* Augmented with a prophecy variable. *)
(* *)
(***************************************************************************)
EXTENDS Naturals, Sequences
CONSTANTS Values, Producers, Consumers, Nmax
null == CHOOSE x : x \notin Values
(*--algorithm Rep
variables
(*********************************************)
(* Public variables *)
(*********************************************)
op = [t \in ProcSet |-> ""];
arg = [t \in ProcSet |-> null];
rval = [t \in ProcSet |-> null];
done = [t \in ProcSet |-> TRUE];
(*********************************************)
(* Internal variables *)
(*********************************************)
q = [back|->1, items|->[n \in 1..Nmax|->null]];
(*********************************************)
(* Prophcey variable *)
(*********************************************)
p = <<>>
(***********************************)
(* Enq(x: Values) *)
(***********************************)
procedure Enq(x)
variable i;
begin
E1: q.back := q.back+1 || i := q.back; (* Allocate a new slot *)
E2: q.items[i] := x; (* Fill it *)
E3: return;
end procedure;
(***********************************)
(* Deq() -> rval[self] : Values *)
(***********************************)
procedure Deq()
variables j, y, range;
begin
D1: while(TRUE) do
D2: range := q.back-1;
D3: j := 1;
D4: while(j<=range) do
D5: await q.items[j] = null \/ q.items[j] = Head(p);
q.items[j] := null || y := q.items[j];
D6: if(y /= null) then
D7: rval[self] := y;
p := Tail(p);
D8: return;
end if;
D9: j:= j+1;
end while;
end while;
end procedure;
process prod \in Producers
begin
enq:
with v \in Values do
p := Append(p, v);
end with;
with item \in Values do
op[self] := "enq";
arg[self] := item;
rval[self] := null;
done[self] := FALSE;
call Enq(item);
end with;
enqdone:
done[self] := TRUE;
end process;
process con \in Consumers
begin
deq:
op[self] := "deq";
arg[self] := null;
rval[self] := null;
done[self] := FALSE;
call Deq();
deqdone:
done[self] := TRUE;
end process;
end algorithm;*)
\* BEGIN TRANSLATION
CONSTANT defaultInitValue
VARIABLES pc, op, arg, rval, done, q, p, stack, x, i, j, y, range
vars == << pc, op, arg, rval, done, q, p, stack, x, i, j, y, range >>
ProcSet == (Producers) \cup (Consumers)
Init == (* Global variables *)
/\ op = [t \in ProcSet |-> ""]
/\ arg = [t \in ProcSet |-> null]
/\ rval = [t \in ProcSet |-> null]
/\ done = [t \in ProcSet |-> TRUE]
/\ q = [back|->1, items|->[n \in 1..Nmax|->null]]
/\ p = <<>>
(* Procedure Enq *)
/\ x = [ self \in ProcSet |-> defaultInitValue]
/\ i = [ self \in ProcSet |-> defaultInitValue]
(* Procedure Deq *)
/\ j = [ self \in ProcSet |-> defaultInitValue]
/\ y = [ self \in ProcSet |-> defaultInitValue]
/\ range = [ self \in ProcSet |-> defaultInitValue]
/\ stack = [self \in ProcSet |-> << >>]
/\ pc = [self \in ProcSet |-> CASE self \in Producers -> "enq"
[] self \in Consumers -> "deq"]
E1(self) == /\ pc[self] = "E1"
/\ /\ i' = [i EXCEPT ![self] = q.back]
/\ q' = [q EXCEPT !.back = q.back+1]
/\ pc' = [pc EXCEPT ![self] = "E2"]
/\ UNCHANGED << op, arg, rval, done, p, stack, x, j, y, range >>
E2(self) == /\ pc[self] = "E2"
/\ q' = [q EXCEPT !.items[i[self]] = x[self]]
/\ pc' = [pc EXCEPT ![self] = "E3"]
/\ UNCHANGED << op, arg, rval, done, p, stack, x, i, j, y, range >>
E3(self) == /\ pc[self] = "E3"
/\ pc' = [pc EXCEPT ![self] = Head(stack[self]).pc]
/\ i' = [i EXCEPT ![self] = Head(stack[self]).i]
/\ x' = [x EXCEPT ![self] = Head(stack[self]).x]
/\ stack' = [stack EXCEPT ![self] = Tail(stack[self])]
/\ UNCHANGED << op, arg, rval, done, q, p, j, y, range >>
Enq(self) == E1(self) \/ E2(self) \/ E3(self)
D1(self) == /\ pc[self] = "D1"
/\ pc' = [pc EXCEPT ![self] = "D2"]
/\ UNCHANGED << op, arg, rval, done, q, p, stack, x, i, j, y,
range >>
D2(self) == /\ pc[self] = "D2"
/\ range' = [range EXCEPT ![self] = q.back-1]
/\ pc' = [pc EXCEPT ![self] = "D3"]
/\ UNCHANGED << op, arg, rval, done, q, p, stack, x, i, j, y >>
D3(self) == /\ pc[self] = "D3"
/\ j' = [j EXCEPT ![self] = 1]
/\ pc' = [pc EXCEPT ![self] = "D4"]
/\ UNCHANGED << op, arg, rval, done, q, p, stack, x, i, y, range >>
D4(self) == /\ pc[self] = "D4"
/\ IF (j[self]<=range[self])
THEN /\ pc' = [pc EXCEPT ![self] = "D5"]
ELSE /\ pc' = [pc EXCEPT ![self] = "D1"]
/\ UNCHANGED << op, arg, rval, done, q, p, stack, x, i, j, y,
range >>
D5(self) == /\ pc[self] = "D5"
/\ q.items[j[self]]=null \/ q.items[j[self]] = Head(p)
/\ /\ q' = [q EXCEPT !.items[j[self]] = null]
/\ y' = [y EXCEPT ![self] = q.items[j[self]]]
/\ pc' = [pc EXCEPT ![self] = "D6"]
/\ UNCHANGED << op, arg, rval, done, p, stack, x, i, j, range >>
D6(self) == /\ pc[self] = "D6"
/\ IF (y[self] /= null)
THEN /\ pc' = [pc EXCEPT ![self] = "D7"]
ELSE /\ pc' = [pc EXCEPT ![self] = "D9"]
/\ UNCHANGED << op, arg, rval, done, q, p, stack, x, i, j, y,
range >>
D7(self) == /\ pc[self] = "D7"
/\ rval' = [rval EXCEPT ![self] = y[self]]
/\ pc' = [pc EXCEPT ![self] = "D8"]
/\ UNCHANGED << op, arg, done, q, p, stack, x, i, j, y, range >>
D8(self) == /\ pc[self] = "D8"
/\ pc' = [pc EXCEPT ![self] = Head(stack[self]).pc]
/\ j' = [j EXCEPT ![self] = Head(stack[self]).j]
/\ y' = [y EXCEPT ![self] = Head(stack[self]).y]
/\ range' = [range EXCEPT ![self] = Head(stack[self]).range]
/\ stack' = [stack EXCEPT ![self] = Tail(stack[self])]
/\ UNCHANGED << op, arg, rval, done, q, p, x, i >>
D9(self) == /\ pc[self] = "D9"
/\ j' = [j EXCEPT ![self] = j[self]+1]
/\ pc' = [pc EXCEPT ![self] = "D4"]
/\ UNCHANGED << op, arg, rval, done, q, p, stack, x, i, y, range >>
Deq(self) == D1(self) \/ D2(self) \/ D3(self) \/ D4(self) \/ D5(self)
\/ D6(self) \/ D7(self) \/ D8(self) \/ D9(self)
enq(self) == /\ pc[self] = "enq"
/\ \E v \in Values:
p' = Append(p, v)
/\ \E item \in Values:
/\ op' = [op EXCEPT ![self] = "enq"]
/\ arg' = [arg EXCEPT ![self] = item]
/\ rval' = [rval EXCEPT ![self] = null]
/\ done' = [done EXCEPT ![self] = FALSE]
/\ /\ stack' = [stack EXCEPT ![self] = << [ procedure |-> "Enq",
pc |-> "enqdone",
i |-> i[self],
x |-> x[self] ] >>
\o stack[self]]
/\ x' = [x EXCEPT ![self] = item]
/\ i' = [i EXCEPT ![self] = defaultInitValue]
/\ pc' = [pc EXCEPT ![self] = "E1"]
/\ UNCHANGED << q, j, y, range >>
enqdone(self) == /\ pc[self] = "enqdone"
/\ done' = [done EXCEPT ![self] = TRUE]
/\ pc' = [pc EXCEPT ![self] = "Done"]
/\ UNCHANGED << op, arg, rval, q, p, stack, x, i, j, y, range >>
prod(self) == enq(self) \/ enqdone(self)
deq(self) == /\ pc[self] = "deq"
/\ op' = [op EXCEPT ![self] = "deq"]
/\ arg' = [arg EXCEPT ![self] = null]
/\ rval' = [rval EXCEPT ![self] = null]
/\ done' = [done EXCEPT ![self] = FALSE]
/\ stack' = [stack EXCEPT ![self] = << [ procedure |-> "Deq",
pc |-> "deqdone",
j |-> j[self],
y |-> y[self],
range |-> range[self] ] >>
\o stack[self]]
/\ j' = [j EXCEPT ![self] = defaultInitValue]
/\ y' = [y EXCEPT ![self] = defaultInitValue]
/\ range' = [range EXCEPT ![self] = defaultInitValue]
/\ pc' = [pc EXCEPT ![self] = "D1"]
/\ UNCHANGED << q, p, x, i >>
deqdone(self) == /\ pc[self] = "deqdone"
/\ done' = [done EXCEPT ![self] = TRUE]
/\ pc' = [pc EXCEPT ![self] = "Done"]
/\ UNCHANGED << op, arg, rval, q, p, stack, x, i, j, y, range >>
con(self) == deq(self) \/ deqdone(self)
(* Allow infinite stuttering to prevent deadlock on termination. *)
Terminating == /\ \A self \in ProcSet: pc[self] = "Done"
/\ UNCHANGED vars
Next == (\E self \in ProcSet: Enq(self) \/ Deq(self))
\/ (\E self \in Producers: prod(self))
\/ (\E self \in Consumers: con(self))
\/ Terminating
Spec == Init /\ [][Next]_vars
Termination == <>(\A self \in ProcSet: pc[self] = "Done")
\* END TRANSLATION
=============================================================================
\* Modification History
\* Last modified Thu Nov 08 17:28:50 PST 2018 by lhochstein
\* Created Wed Oct 24 18:53:25 PDT 2018 by lhochstein