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|
// RUN: %boogie -noinfer -typeEncoding:m -useArrayTheory "%s" > "%t"
// RUN: %diff "%s.expect" "%t"
var {:layer 0,2} a:[int]int;
var {:layer 0,1} count: int;
var {:layer 1,1} {:linear "tid"} allocated:[int]bool;
procedure {:yields} {:layer 2} main()
requires {:layer 1} allocated == MapConstBool(false);
{
var {:layer 1} {:linear "tid"} tid:int;
var i: int;
yield;
assert {:layer 1} AllocInv(count, allocated);
while (true)
invariant {:layer 1} AllocInv(count, allocated);
{
call tid, i := Allocate();
async call P(tid, i);
yield;
assert {:layer 1} AllocInv(count, allocated);
}
yield;
}
procedure {:yields} {:layer 2} P({:layer 1} {:linear "tid"} tid: int, i: int)
requires {:layer 1} tid == i;
requires {:layer 1} AllocInv(count, allocated);
ensures {:layer 1} AllocInv(count, allocated);
ensures {:layer 2} a[tid] == old(a)[tid] + 1;
{
var t:int;
yield;
assert {:layer 1} AllocInv(count, allocated);
assert {:layer 2} a[tid] == old(a)[tid];
call t := Read(tid, i);
yield;
assert {:layer 1} AllocInv(count, allocated);
assert {:layer 2} a[tid] == t;
call Write(tid, i, t + 1);
yield;
assert {:layer 1} AllocInv(count, allocated);
assert {:layer 2} a[tid] == t + 1;
}
procedure {:yields} {:layer 1,2} Allocate() returns ({:layer 1} {:linear "tid"} tid: int, i: int)
requires {:layer 1} AllocInv(count, allocated);
ensures {:layer 1} AllocInv(count, allocated);
ensures {:layer 1} tid == i;
ensures {:atomic}
|{A:
return true;
}|;
{
yield;
assert {:layer 1} AllocInv(count, allocated);
call i := AllocateLow();
call tid := MakeLinear(i);
yield;
assert {:layer 1} AllocInv(count, allocated);
}
procedure {:yields} {:layer 1,2} Read({:layer 1} {:linear "tid"} tid: int, i: int) returns (val: int)
requires {:layer 1} tid == i;
requires {:layer 1} AllocInv(count, allocated);
ensures {:layer 1} AllocInv(count, allocated);
ensures {:atomic}
|{A:
val := a[tid]; return true;
}|;
{
yield;
assert {:layer 1} AllocInv(count, allocated);
call val := ReadLow(i);
yield;
assert {:layer 1} AllocInv(count, allocated);
}
procedure {:yields} {:layer 1,2} Write({:layer 1} {:linear "tid"} tid: int, i: int, val: int)
requires {:layer 1} tid == i;
requires {:layer 1} AllocInv(count, allocated);
ensures {:layer 1} AllocInv(count, allocated);
ensures {:atomic}
|{A:
a[tid] := val; return true;
}|;
{
yield;
assert {:layer 1} AllocInv(count, allocated);
call WriteLow(i, val);
yield;
assert {:layer 1} AllocInv(count, allocated);
}
function {:inline} AllocInv(count: int, allocated:[int]bool): (bool)
{
(forall x: int :: allocated[x] ==> x < count)
}
procedure {:yields} {:layer 0,1} ReadLow(i: int) returns (val: int);
ensures {:atomic}
|{A:
val := a[i]; return true;
}|;
procedure {:yields} {:layer 0,1} WriteLow(i: int, val: int);
ensures {:atomic}
|{A:
a[i] := val; return true;
}|;
procedure {:yields} {:layer 0,1} AllocateLow() returns (i: int);
ensures {:atomic}
|{A:
i := count;
count := i + 1;
return true;
}|;
// We can prove that this primitive procedure preserves the permission invariant locally.
// We only need to using its specification and the definitions of TidCollector and TidSetCollector.
procedure {:layer 1} MakeLinear(i: int) returns ({:linear "tid"} tid: int);
requires !allocated[i];
modifies allocated;
ensures tid == i && allocated == old(allocated)[i := true];
function {:builtin "MapConst"} MapConstBool(bool): [int]bool;
function {:builtin "MapOr"} MapOr([int]bool, [int]bool) : [int]bool;
function {:inline} {:linear "tid"} TidCollector(x: int) : [int]bool
{
MapConstBool(false)[x := true]
}
function {:inline} {:linear "tid"} TidSetCollector(x: [int]bool) : [int]bool
{
x
}
|
