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|
// RUN: %boogie -noinfer -useArrayTheory "%s" > "%t"
// RUN: %diff "%s.expect" "%t"
function {:builtin "MapConst"} MapConstBool(bool) : [int]bool;
type lmap;
function {:linear "mem"} dom(lmap): [int]bool;
function map(lmap): [int]int;
function cons([int]bool, [int]int) : lmap;
axiom (forall x: [int]bool, y: [int]int :: {cons(x,y)} dom(cons(x, y)) == x && map(cons(x,y)) == y);
function EmptyLmap(): (lmap);
axiom (dom(EmptyLmap()) == MapConstBool(false));
function Add(x: lmap, i: int): (lmap);
axiom (forall x: lmap, i: int :: dom(Add(x, i)) == dom(x)[i:=true] && map(Add(x, i)) == map(x));
function Remove(x: lmap, i: int): (lmap);
axiom (forall x: lmap, i: int :: dom(Remove(x, i)) == dom(x)[i:=false] && map(Remove(x, i)) == map(x));
function {:inline} PoolInv(unallocated:[int]bool, pool: lmap) : (bool)
{
(forall x: int :: unallocated[x] ==> dom(pool)[x])
}
procedure {:yields} {:layer 2} Main()
requires {:layer 1} PoolInv(unallocated, pool);
ensures {:layer 1} PoolInv(unallocated, pool);
{
var {:layer 1} {:linear "mem"} l: lmap;
var i: int;
par Yield() | Dummy();
while (*)
invariant {:layer 1} PoolInv(unallocated, pool);
{
call l, i := Alloc();
async call Thread(l, i);
par Yield() | Dummy();
}
par Yield() | Dummy();
}
procedure {:yields} {:layer 2} Thread({:layer 1} {:linear_in "mem"} local_in: lmap, i: int)
requires {:layer 1} PoolInv(unallocated, pool);
ensures {:layer 1} PoolInv(unallocated, pool);
requires {:layer 1} dom(local_in)[i] && map(local_in)[i] == mem[i];
requires {:layer 2} dom(local_in)[i];
{
var y, o: int;
var {:layer 1} {:linear "mem"} local: lmap;
var {:layer 1} {:linear "mem"} l: lmap;
par YieldMem(local_in, i) | Dummy();
call local := Copy(local_in);
call local := Write(local, i, 42);
call o := Read(local, i);
assert {:layer 2} o == 42;
while (*)
invariant {:layer 1} PoolInv(unallocated, pool);
{
call l, y := Alloc();
call l := Write(l, y, 42);
call o := Read(l, y);
assert {:layer 2} o == 42;
call Free(l, y);
par Yield() | Dummy();
}
par Yield() | Dummy();
}
procedure {:pure} {:inline 1} Copy({:linear_in "mem"} l: lmap) returns ({:linear "mem"} l': lmap)
{
l' := l;
}
procedure {:yields} {:layer 1,2} Alloc() returns ({:layer 1} {:linear "mem"} l: lmap, i: int)
requires {:layer 1} PoolInv(unallocated, pool);
ensures {:layer 1} PoolInv(unallocated, pool);
ensures {:layer 1} dom(l)[i] && map(l)[i] == mem[i];
ensures {:right} |{ A: assume dom(l)[i]; return true; }|;
{
call Yield();
call i := PickAddr();
call l := AllocLinear(i);
call YieldMem(l, i);
}
procedure {:yields} {:layer 1,2} Free({:layer 1} {:linear_in "mem"} l: lmap, i: int)
requires {:layer 1} PoolInv(unallocated, pool);
ensures {:layer 1} PoolInv(unallocated, pool);
requires {:layer 1} dom(l)[i];
ensures {:both} |{ A: return true; }|;
{
call Yield();
call FreeLinear(l, i);
call ReturnAddr(i);
call Yield();
}
procedure {:yields} {:layer 1,2} Read({:layer 1} {:linear "mem"} l: lmap, i: int) returns (o: int)
requires {:layer 1} PoolInv(unallocated, pool);
ensures {:layer 1} PoolInv(unallocated, pool);
requires {:layer 1} dom(l)[i] && map(l)[i] == mem[i];
ensures {:both} |{ A: assert dom(l)[i]; o := map(l)[i]; return true; }|;
{
call YieldMem(l, i);
call o := ReadLow(i);
call YieldMem(l, i);
}
procedure {:yields} {:layer 1,2} Write({:layer 1} {:linear_in "mem"} l: lmap, i: int, o: int) returns ({:layer 1} {:linear "mem"} l': lmap)
requires {:layer 1} PoolInv(unallocated, pool);
ensures {:layer 1} PoolInv(unallocated, pool);
requires {:layer 1} dom(l)[i] && map(l)[i] == mem[i];
ensures {:layer 1} dom(l')[i] && map(l')[i] == mem[i];
ensures {:both} |{ A: assert dom(l)[i]; l' := cons(dom(l), map(l)[i := o]); return true; }|;
{
call YieldMem(l, i);
call WriteLow(i, o);
call l' := WriteLinear(l, i, o);
call YieldMem(l', i);
}
procedure {:layer 1} AllocLinear(i: int) returns ({:linear "mem"} l: lmap);
modifies pool;
requires dom(pool)[i];
ensures pool == Remove(old(pool), i) && dom(l)[i] && map(l)[i] == mem[i];
procedure {:layer 1} FreeLinear({:linear_in "mem"} l: lmap, i: int);
modifies pool;
requires !dom(pool)[i];
ensures pool == Add(old(pool), i);
procedure {:layer 1} WriteLinear({:layer 1} {:linear_in "mem"} l: lmap, i: int, o: int) returns ({:layer 1} {:linear "mem"} l': lmap);
requires dom(l)[i];
ensures l' == cons(dom(l), map(l)[i := o]);
procedure {:yields} {:layer 1} Yield()
requires {:layer 1} PoolInv(unallocated, pool);
ensures {:layer 1} PoolInv(unallocated, pool);
{
yield;
assert {:layer 1} PoolInv(unallocated, pool);
}
procedure {:yields} {:layer 1} YieldMem({:layer 1} {:linear "mem"} l: lmap, i: int)
requires {:layer 1} PoolInv(unallocated, pool);
ensures {:layer 1} PoolInv(unallocated, pool);
requires {:layer 1} dom(l)[i] && map(l)[i] == mem[i];
ensures {:layer 1} dom(l)[i] && map(l)[i] == mem[i];
{
yield;
assert {:layer 1} PoolInv(unallocated, pool);
assert {:layer 1} dom(l)[i] && map(l)[i] == mem[i];
}
procedure {:yields} {:layer 2} Dummy()
{
yield;
}
var {:layer 1, 1} {:linear "mem"} pool: lmap;
var {:layer 0, 1} mem:[int]int;
var {:layer 0, 1} unallocated:[int]bool;
procedure {:yields} {:layer 0, 1} ReadLow(i: int) returns (o: int);
ensures {:atomic} |{ A: o := mem[i]; return true; }|;
procedure {:yields} {:layer 0, 1} WriteLow(i: int, o: int);
ensures {:atomic} |{ A: mem[i] := o; return true; }|;
procedure {:yields} {:layer 0, 1} PickAddr() returns (i: int);
ensures {:atomic} |{ A: assume unallocated[i]; unallocated[i] := false; return true; }|;
procedure {:yields} {:layer 0, 1} ReturnAddr(i: int);
ensures {:atomic} |{ A: unallocated[i] := true; return true; }|;
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