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|
// RUN: %boogie -noinfer -typeEncoding:m -useArrayTheory "%s" > "%t"
// RUN: %diff "%s.expect" "%t"
type X;
const unique null : int;
const unique nil: X;
const unique done: X;
var {:layer 0} elt : [int]int;
var {:layer 0} valid : [int]bool;
var {:layer 0} lock : [int]X;
var {:layer 0} owner : [int]X;
const max : int;
function {:builtin "MapConst"} MapConstBool(bool) : [X]bool;
function {:inline} {:linear "tid"} TidCollector(x: X) : [X]bool
{
MapConstBool(false)[x := true]
}
axiom (max > 0);
procedure {:yields} {:layer 0} acquire(i : int, {:linear "tid"} tid: X);
ensures {:right} |{ A:
assert 0 <= i && i < max;
assert tid != nil && tid != done;
assume lock[i] == nil;
lock[i] := tid;
return true;
}|;
procedure {:yields} {:layer 0} release(i : int, {:linear "tid"} tid: X);
ensures {:left} |{ A:
assert 0 <= i && i < max;
assert lock[i] == tid;
assert tid != nil && tid != done;
lock[i] := nil;
return true;
}|;
procedure {:yields} {:layer 0,1} getElt(j : int, {:linear "tid"} tid: X) returns (elt_j:int);
ensures {:both} |{ A:
assert 0 <= j && j < max;
assert lock[j] == tid;
assert tid != nil && tid != done;
elt_j := elt[j];
return true;
}|;
procedure {:yields} {:layer 0,1} setElt(j : int, x : int, {:linear "tid"} tid: X);
ensures {:both} |{ A:
assert x != null;
assert owner[j] == nil;
assert 0 <= j && j < max;
assert lock[j] == tid;
assert tid != nil && tid != done;
elt[j] := x;
owner[j] := tid;
return true;
}|;
procedure {:yields} {:layer 0,2} setEltToNull(j : int, {:linear "tid"} tid: X);
ensures {:left} |{ A:
assert owner[j] == tid;
assert 0 <= j && j < max;
assert lock[j] == tid;
assert !valid[j];
assert tid != nil && tid != done;
elt[j] := null;
owner[j] := nil;
return true;
}|;
procedure {:yields} {:layer 0,2} setValid(j : int, {:linear "tid"} tid: X);
ensures {:both} |{ A:
assert 0 <= j && j < max;
assert lock[j] == tid;
assert tid != nil && tid != done;
assert owner[j] == tid;
valid[j] := true;
owner[j] := done;
return true;
}|;
procedure {:yields} {:layer 0,2} isEltThereAndValid(j : int, x : int, {:linear "tid"} tid: X) returns (fnd:bool);
ensures {:both} |{ A:
assert 0 <= j && j < max;
assert lock[j] == tid;
assert tid != nil && tid != done;
fnd := (elt[j] == x) && valid[j];
return true;
}|;
procedure {:yields} {:layer 1,2} FindSlot(x : int, {:linear "tid"} tid: X) returns (r : int)
requires {:layer 1} Inv(valid, elt, owner) && x != null && tid != nil && tid != done;
ensures {:layer 1} Inv(valid, elt, owner);
ensures {:right} |{ A: assert tid != nil && tid != done;
assert x != null;
goto B, C;
B: assume (0 <= r && r < max);
assume elt[r] == null;
assume owner[r] == nil;
assume !valid[r];
elt[r] := x;
owner[r] := tid;
return true;
C: assume (r == -1); return true;
}|;
{
var j : int;
var elt_j : int;
par Yield1();
j := 0;
while(j < max)
invariant {:layer 1} Inv(valid, elt, owner);
invariant {:layer 1} 0 <= j;
{
call acquire(j, tid);
call elt_j := getElt(j, tid);
if(elt_j == null)
{
call setElt(j, x, tid);
call release(j, tid);
r := j;
par Yield1();
return;
}
call release(j,tid);
par Yield1();
j := j + 1;
}
r := -1;
par Yield1();
return;
}
procedure {:yields} {:layer 2} Insert(x : int, {:linear "tid"} tid: X) returns (result : bool)
requires {:layer 1} Inv(valid, elt, owner) && x != null && tid != nil && tid != done;
ensures {:layer 1} Inv(valid, elt, owner);
requires {:layer 2} Inv(valid, elt, owner) && x != null && tid != nil && tid != done;
ensures {:layer 2} Inv(valid, elt, owner);
ensures {:atomic} |{ var r:int;
A: goto B, C;
B: assume (0 <= r && r < max);
assume valid[r] == false;
assume elt[r] == null;
assume owner[r] == nil;
elt[r] := x; valid[r] := true; owner[r] := done;
result := true; return true;
C: result := false; return true;
}|;
{
var i: int;
par Yield12();
call i := FindSlot(x, tid);
if(i == -1)
{
result := false;
par Yield12();
return;
}
par Yield1();
assert {:layer 1} i != -1;
assert {:layer 2} i != -1;
call acquire(i, tid);
assert {:layer 2} elt[i] == x;
assert {:layer 2} valid[i] == false;
call setValid(i, tid);
call release(i, tid);
result := true;
par Yield12();
return;
}
procedure {:yields} {:layer 2} InsertPair(x : int, y : int, {:linear "tid"} tid: X) returns (result : bool)
requires {:layer 1} Inv(valid, elt, owner) && x != null && y != null && tid != nil && tid != done;
ensures {:layer 1} Inv(valid, elt, owner);
requires {:layer 2} Inv(valid, elt, owner) && x != null && y != null && tid != nil && tid != done;
ensures {:layer 2} Inv(valid, elt, owner);
ensures {:atomic} |{ var rx:int;
var ry:int;
A: goto B, C;
B: assume (0 <= rx && rx < max && 0 <= ry && ry < max && rx != ry);
assume valid[rx] == false;
assume valid[ry] == false;
assume elt[rx] == null;
assume elt[rx] == null;
elt[rx] := x;
elt[ry] := y;
valid[rx] := true;
valid[ry] := true;
owner[rx] := done;
owner[ry] := done;
result := true; return true;
C: result := false; return true;
}|;
{
var i : int;
var j : int;
par Yield12();
call i := FindSlot(x, tid);
if (i == -1)
{
result := false;
par Yield12();
return;
}
par Yield1();
call j := FindSlot(y, tid);
if(j == -1)
{
par Yield1();
call acquire(i,tid);
call setEltToNull(i, tid);
call release(i,tid);
result := false;
par Yield12();
return;
}
par Yield1();
assert {:layer 2} i != -1 && j != -1;
call acquire(i, tid);
call acquire(j, tid);
assert {:layer 2} elt[i] == x;
assert {:layer 2} elt[j] == y;
assert {:layer 2} valid[i] == false;
assert {:layer 2} valid[j] == false;
call setValid(i, tid);
call setValid(j, tid);
call release(j, tid);
call release(i, tid);
result := true;
par Yield12();
return;
}
procedure {:yields} {:layer 2} LookUp(x : int, {:linear "tid"} tid: X, old_valid:[int]bool, old_elt:[int]int) returns (found : bool)
requires {:layer 1} {:layer 2} old_valid == valid && old_elt == elt;
requires {:layer 1} {:layer 2} Inv(valid, elt, owner);
requires {:layer 1} {:layer 2} (tid != nil && tid != done);
ensures {:layer 1} {:layer 2} Inv(valid, elt, owner);
ensures {:atomic} |{ A: assert tid != nil && tid != done;
assert x != null;
assume found ==> (exists ii:int :: 0 <= ii && ii < max && valid[ii] && elt[ii] == x);
assume !found ==> (forall ii:int :: 0 <= ii && ii < max ==> !(old_valid[ii] && old_elt[ii] == x));
return true;
}|;
{
var j : int;
var isThere : bool;
par Yield12() | YieldLookUp(old_valid, old_elt);
j := 0;
while(j < max)
invariant {:layer 1} {:layer 2} Inv(valid, elt, owner);
invariant {:layer 1} {:layer 2} (forall ii:int :: 0 <= ii && ii < j ==> !(old_valid[ii] && old_elt[ii] == x));
invariant {:layer 1} {:layer 2} (forall ii:int :: 0 <= ii && ii < max && old_valid[ii] ==> valid[ii] && old_elt[ii] == elt[ii]);
invariant {:layer 1} {:layer 2} 0 <= j;
{
call acquire(j, tid);
call isThere := isEltThereAndValid(j, x, tid);
if(isThere)
{
call release(j, tid);
found := true;
par Yield12() | YieldLookUp(old_valid, old_elt);
return;
}
call release(j,tid);
par Yield12() | YieldLookUp(old_valid, old_elt);
j := j + 1;
}
found := false;
par Yield12() | YieldLookUp(old_valid, old_elt);
return;
}
procedure {:yields} {:layer 1} Yield1()
requires {:layer 1} Inv(valid, elt, owner);
ensures {:layer 1} Inv(valid, elt, owner);
{
yield;
assert {:layer 1} Inv(valid, elt, owner);
}
procedure {:yields} {:layer 2} Yield12()
requires {:layer 1} {:layer 2} Inv(valid, elt, owner);
ensures {:layer 1} {:layer 2} Inv(valid, elt, owner);
{
yield;
assert {:layer 1} {:layer 2} Inv(valid, elt, owner);
}
function {:inline} Inv(valid: [int]bool, elt: [int]int, owner: [int]X): (bool)
{
(forall i:int :: 0 <= i && i < max ==> (elt[i] == null <==> (!valid[i] && owner[i] == nil)))
}
procedure {:yields} {:layer 2} YieldLookUp(old_valid: [int]bool, old_elt: [int]int)
requires {:layer 1} {:layer 2} (forall ii:int :: 0 <= ii && ii < max && old_valid[ii] ==> valid[ii] && old_elt[ii] == elt[ii]);
ensures {:layer 1} {:layer 2} (forall ii:int :: 0 <= ii && ii < max && old_valid[ii] ==> valid[ii] && old_elt[ii] == elt[ii]);
{
yield;
assert {:layer 1} {:layer 2} (forall ii:int :: 0 <= ii && ii < max && old_valid[ii] ==> valid[ii] && old_elt[ii] == elt[ii]);
}
|
