def test_bv_zero_ule(self):
x = Symbol("x", BVType(32))
f = BVULE(BVZero(32), x)
self.check_equal_and_valid(f, Bool(True))
def walk_identity_bv(self, formula, args, **kwargs):
#pylint: disable=unused-argument
assert formula is not None
assert len(args) == 0
return BVType(formula.bv_width())
def parse_string(self, strinput):
hts = HTS()
ts = TS()
nodemap = {}
node_covered = set([])
# list of tuples of var and cond_assign_list
# cond_assign_list is tuples of (condition, value)
# where everything is a pysmt FNode
# for btor, the condition is always True
ftrans = []
initlist = []
invarlist = []
invar_props = []
ltl_props = []
prop_count = 0
# clean string input, remove special characters from names
for sc, rep in special_char_replacements.items():
strinput = strinput.replace(sc, rep)
def getnode(nid):
node_covered.add(nid)
if int(nid) < 0:
return Ite(BV2B(nodemap[str(-int(nid))]), BV(0,1), BV(1,1))
return nodemap[nid]
def binary_op(bvop, bop, left, right):
if (get_type(left) == BOOL) and (get_type(right) == BOOL):
return bop(left, right)
return bvop(B2BV(left), B2BV(right))
def unary_op(bvop, bop, left):
if (get_type(left) == BOOL):
return bop(left)
return bvop(left)
for line in strinput.split(NL):
linetok = line.split()
if len(linetok) == 0:
continue
if linetok[0] == COM:
continue
(nid, ntype, *nids) = linetok
if ntype == SORT:
(stype, *attr) = nids
if stype == BITVEC:
nodemap[nid] = BVType(int(attr[0]))
node_covered.add(nid)
if stype == ARRAY:
nodemap[nid] = ArrayType(getnode(attr[0]), getnode(attr[1]))
node_covered.add(nid)
if ntype == WRITE:
nodemap[nid] = Store(*[getnode(n) for n in nids[1:4]])
if ntype == READ:
nodemap[nid] = Select(getnode(nids[1]), getnode(nids[2]))
if ntype == ZERO:
nodemap[nid] = BV(0, getnode(nids[0]).width)
if ntype == ONE:
nodemap[nid] = BV(1, getnode(nids[0]).width)
if ntype == ONES:
width = getnode(nids[0]).width
nodemap[nid] = BV((2**width)-1, width)
if ntype == REDOR:
width = get_type(getnode(nids[1])).width
zeros = BV(0, width)
nodemap[nid] = BVNot(BVComp(getnode(nids[1]), zeros))
if ntype == REDXOR:
width = get_type(getnode(nids[1])).width
nodemap[nid] = BV(0, width)
zeros = BV(0, width)
for yx_i in range(width):
tmp = BV(1 << yx_i, width)
tmp_2 = BVAnd(tmp, B2BV(getnode(nids[1])))
tmp_3 = BVZExt(B2BV(BVComp(tmp_2, zeros)), int(width - 1))
nodemap[nid] = BVAdd(tmp_3, nodemap[nid])
nodemap[nid] = BVComp(BVAnd(BV(1, width), nodemap[nid]), BV(1, width))
if ntype == REDAND:
width = get_type(getnode(nids[1])).width
ones = BV((2**width)-1, width)
nodemap[nid] = BVComp(getnode(nids[1]), ones)
if ntype == CONSTD:
width = getnode(nids[0]).width
nodemap[nid] = BV(int(nids[1]), width)
if ntype == CONST:
width = getnode(nids[0]).width
nodemap[nid] = BV(bin_to_dec(nids[1]), width)
if ntype == STATE:
if len(nids) > 1:
nodemap[nid] = Symbol(nids[1], getnode(nids[0]))
else:
nodemap[nid] = Symbol((SN%nid), getnode(nids[0]))
ts.add_state_var(nodemap[nid])
if ntype == INPUT:
if len(nids) > 1:
nodemap[nid] = Symbol(nids[1], getnode(nids[0]))
else:
nodemap[nid] = Symbol((SN%nid), getnode(nids[0]))
ts.add_input_var(nodemap[nid])
if ntype == OUTPUT:
# unfortunately we need to create an extra symbol just to have the output name
# we could be smarter about this, but then this parser can't be greedy
original_symbol = getnode(nids[0])
output_symbol = Symbol(nids[1], original_symbol.get_type())
nodemap[nid] = EqualsOrIff(output_symbol, original_symbol)
invarlist.append(nodemap[nid])
node_covered.add(nid)
ts.add_output_var(output_symbol)
if ntype == AND:
nodemap[nid] = binary_op(BVAnd, And, getnode(nids[1]), getnode(nids[2]))
if ntype == CONCAT:
nodemap[nid] = BVConcat(B2BV(getnode(nids[1])), B2BV(getnode(nids[2])))
if ntype == XOR:
nodemap[nid] = binary_op(BVXor, Xor, getnode(nids[1]), getnode(nids[2]))
if ntype == XNOR:
nodemap[nid] = BVNot(binary_op(BVXor, Xor, getnode(nids[1]), getnode(nids[2])))
if ntype == NAND:
bvop = lambda x,y: BVNot(BVAnd(x, y))
bop = lambda x,y: Not(And(x, y))
nodemap[nid] = binary_op(bvop, bop, getnode(nids[1]), getnode(nids[2]))
if ntype == IMPLIES:
nodemap[nid] = BVOr(BVNot(getnode(nids[1])), getnode(nids[2]))
if ntype == NOT:
nodemap[nid] = unary_op(BVNot, Not, getnode(nids[1]))
if ntype == NEG:
nodemap[nid] = unary_op(BVNeg, Not, getnode(nids[1]))
if ntype == UEXT:
nodemap[nid] = BVZExt(B2BV(getnode(nids[1])), int(nids[2]))
if ntype == SEXT:
nodemap[nid] = BVSExt(B2BV(getnode(nids[1])), int(nids[2]))
if ntype == OR:
nodemap[nid] = binary_op(BVOr, Or, getnode(nids[1]), getnode(nids[2]))
if ntype == ADD:
nodemap[nid] = BVAdd(B2BV(getnode(nids[1])), B2BV(getnode(nids[2])))
if ntype == SUB:
nodemap[nid] = BVSub(B2BV(getnode(nids[1])), B2BV(getnode(nids[2])))
if ntype == UGT:
nodemap[nid] = BVUGT(B2BV(getnode(nids[1])), B2BV(getnode(nids[2])))
if ntype == UGTE:
nodemap[nid] = BVUGE(B2BV(getnode(nids[1])), B2BV(getnode(nids[2])))
if ntype == ULT:
nodemap[nid] = BVULT(B2BV(getnode(nids[1])), B2BV(getnode(nids[2])))
if ntype == ULTE:
nodemap[nid] = BVULE(B2BV(getnode(nids[1])), B2BV(getnode(nids[2])))
if ntype == SGT:
nodemap[nid] = BVSGT(B2BV(getnode(nids[1])), B2BV(getnode(nids[2])))
if ntype == SGTE:
nodemap[nid] = BVSGE(B2BV(getnode(nids[1])), B2BV(getnode(nids[2])))
if ntype == SLT:
nodemap[nid] = BVSLT(B2BV(getnode(nids[1])), B2BV(getnode(nids[2])))
if ntype == SLTE:
nodemap[nid] = BVSLE(B2BV(getnode(nids[1])), B2BV(getnode(nids[2])))
if ntype == EQ:
nodemap[nid] = BVComp(B2BV(getnode(nids[1])), B2BV(getnode(nids[2])))
if ntype == NEQ:
nodemap[nid] = BVNot(BVComp(getnode(nids[1]), getnode(nids[2])))
if ntype == MUL:
nodemap[nid] = BVMul(B2BV(getnode(nids[1])), B2BV(getnode(nids[2])))
if ntype == SLICE:
nodemap[nid] = BVExtract(B2BV(getnode(nids[1])), int(nids[3]), int(nids[2]))
if ntype == SLL:
nodemap[nid] = BVLShl(getnode(nids[1]), getnode(nids[2]))
if ntype == SRA:
nodemap[nid] = BVAShr(getnode(nids[1]), getnode(nids[2]))
if ntype == SRL:
nodemap[nid] = BVLShr(getnode(nids[1]), getnode(nids[2]))
if ntype == ITE:
if (get_type(getnode(nids[2])) == BOOL) or (get_type(getnode(nids[3])) == BOOL):
nodemap[nid] = Ite(BV2B(getnode(nids[1])), B2BV(getnode(nids[2])), B2BV(getnode(nids[3])))
else:
nodemap[nid] = Ite(BV2B(getnode(nids[1])), getnode(nids[2]), getnode(nids[3]))
if ntype == NEXT:
if (get_type(getnode(nids[1])) == BOOL) or (get_type(getnode(nids[2])) == BOOL):
lval = TS.get_prime(getnode(nids[1]))
rval = BV2B(getnode(nids[2]))
else:
lval = TS.get_prime(getnode(nids[1]))
rval = getnode(nids[2])
nodemap[nid] = EqualsOrIff(lval, rval)
ftrans.append(
(lval,
[(TRUE(), rval)])
)
if ntype == INIT:
if (get_type(getnode(nids[1])) == BOOL) or (get_type(getnode(nids[2])) == BOOL):
nodemap[nid] = EqualsOrIff(BV2B(getnode(nids[1])), BV2B(getnode(nids[2])))
else:
nodemap[nid] = EqualsOrIff(getnode(nids[1]), getnode(nids[2]))
initlist.append(getnode(nid))
if ntype == CONSTRAINT:
nodemap[nid] = BV2B(getnode(nids[0]))
invarlist.append(getnode(nid))
if ntype == BAD:
nodemap[nid] = getnode(nids[0])
if ASSERTINFO in line:
filename_lineno = os.path.basename(nids[3])
assert_name = 'embedded_assertion_%s'%filename_lineno
description = "Embedded assertion at line {1} in {0}".format(*filename_lineno.split(COLON_REP))
else:
assert_name = 'embedded_assertion_%i'%prop_count
description = 'Embedded assertion number %i'%prop_count
prop_count += 1
# Following problem format (name, description, strformula)
invar_props.append((assert_name, description, Not(BV2B(getnode(nid)))))
if nid not in nodemap:
Logger.error("Unknown node type \"%s\""%ntype)
# get wirename if it exists
if ntype not in {STATE, INPUT, OUTPUT, BAD}:
# check for wirename, if it's an integer, then it's a node ref
try:
a = int(nids[-1])
except:
try:
wire = Symbol(str(nids[-1]), getnode(nids[0]))
invarlist.append(EqualsOrIff(wire, B2BV(nodemap[nid])))
ts.add_var(wire)
except:
pass
if Logger.level(1):
name = lambda x: str(nodemap[x]) if nodemap[x].is_symbol() else x
uncovered = [name(x) for x in nodemap if x not in node_covered]
uncovered.sort()
if len(uncovered) > 0:
Logger.warning("Unlinked nodes \"%s\""%",".join(uncovered))
if not self.symbolic_init:
init = simplify(And(initlist))
else:
init = TRUE()
invar = simplify(And(invarlist))
# instead of trans, we're using the ftrans format -- see below
ts.set_behavior(init, TRUE(), invar)
# add ftrans
for var, cond_assign_list in ftrans:
ts.add_func_trans(var, cond_assign_list)
hts.add_ts(ts)
return (hts, invar_props, ltl_props)
def parse_string(self, strinput):
hts = HTS()
ts = TS()
nodemap = {}
node_covered = set([])
# list of tuples of var and cond_assign_list
# cond_assign_list is tuples of (condition, value)
# where everything is a pysmt FNode
# for btor, the condition is always True
ftrans = []
initlist = []
invarlist = []
invar_props = []
ltl_props = []
prop_count = 0
# clean string input, remove special characters from names
for sc, rep in special_char_replacements.items():
strinput = strinput.replace(sc, rep)
def getnode(nid):
node_covered.add(nid)
if int(nid) < 0:
return Ite(BV2B(nodemap[str(-int(nid))]), BV(0, 1), BV(1, 1))
return nodemap[nid]
def binary_op(bvop, bop, left, right):
if (get_type(left) == BOOL) and (get_type(right) == BOOL):
return bop(left, right)
return bvop(B2BV(left), B2BV(right))
def unary_op(bvop, bop, left):
if (get_type(left) == BOOL):
return bop(left)
return bvop(left)
for line in strinput.split(NL):
linetok = line.split()
if len(linetok) == 0:
continue
if linetok[0] == COM:
continue
(nid, ntype, *nids) = linetok
if ntype == SORT:
(stype, *attr) = nids
if stype == BITVEC:
nodemap[nid] = BVType(int(attr[0]))
node_covered.add(nid)
if stype == ARRAY:
nodemap[nid] = ArrayType(getnode(attr[0]),
getnode(attr[1]))
node_covered.add(nid)
if ntype == WRITE:
nodemap[nid] = Store(*[getnode(n) for n in nids[1:4]])
if ntype == READ:
nodemap[nid] = Select(getnode(nids[1]), getnode(nids[2]))
if ntype == ZERO:
nodemap[nid] = BV(0, getnode(nids[0]).width)
if ntype == ONE:
nodemap[nid] = BV(1, getnode(nids[0]).width)
if ntype == ONES:
width = getnode(nids[0]).width
nodemap[nid] = BV((2**width) - 1, width)
if ntype == REDOR:
width = get_type(getnode(nids[1])).width
zeros = BV(0, width)
nodemap[nid] = BVNot(BVComp(getnode(nids[1]), zeros))
if ntype == REDAND:
width = get_type(getnode(nids[1])).width
ones = BV((2**width) - 1, width)
nodemap[nid] = BVComp(getnode(nids[1]), ones)
if ntype == CONSTD:
width = getnode(nids[0]).width
nodemap[nid] = BV(int(nids[1]), width)
if ntype == CONST:
width = getnode(nids[0]).width
try:
nodemap[nid] = BV(bin_to_dec(nids[1]), width)
except ValueError:
if not all([i == 'x' or i == 'z' for i in nids[1]]):
raise RuntimeError(
"If not a valid number, only support "
"all don't cares or high-impedance but got {}".
format(nids[1]))
# create a fresh variable for this non-deterministic constant
nodemap[nid] = Symbol('const_' + nids[1], BVType(width))
ts.add_state_var(nodemap[nid])
Logger.warning(
"Creating a fresh symbol for unsupported X/Z constant %s"
% nids[1])
if ntype == STATE:
if len(nids) > 1:
nodemap[nid] = Symbol(nids[1], getnode(nids[0]))
else:
nodemap[nid] = Symbol((SN % nid), getnode(nids[0]))
ts.add_state_var(nodemap[nid])
if ntype == INPUT:
if len(nids) > 1:
nodemap[nid] = Symbol(nids[1], getnode(nids[0]))
else:
nodemap[nid] = Symbol((SN % nid), getnode(nids[0]))
ts.add_input_var(nodemap[nid])
if ntype == OUTPUT:
# unfortunately we need to create an extra symbol just to have the output name
# we could be smarter about this, but then this parser can't be greedy
original_symbol = B2BV(getnode(nids[0]))
output_symbol = Symbol(nids[1], original_symbol.get_type())
nodemap[nid] = EqualsOrIff(output_symbol, original_symbol)
invarlist.append(nodemap[nid])
node_covered.add(nid)
ts.add_output_var(output_symbol)
if ntype == AND:
nodemap[nid] = binary_op(BVAnd, And, getnode(nids[1]),
getnode(nids[2]))
if ntype == CONCAT:
nodemap[nid] = BVConcat(B2BV(getnode(nids[1])),
B2BV(getnode(nids[2])))
if ntype == XOR:
nodemap[nid] = binary_op(BVXor, Xor, getnode(nids[1]),
getnode(nids[2]))
if ntype == XNOR:
nodemap[nid] = BVNot(
binary_op(BVXor, Xor, getnode(nids[1]), getnode(nids[2])))
if ntype == NAND:
bvop = lambda x, y: BVNot(BVAnd(x, y))
bop = lambda x, y: Not(And(x, y))
nodemap[nid] = binary_op(bvop, bop, getnode(nids[1]),
getnode(nids[2]))
if ntype == IMPLIES:
nodemap[nid] = BVOr(BVNot(getnode(nids[1])), getnode(nids[2]))
if ntype == NOT:
nodemap[nid] = unary_op(BVNot, Not, getnode(nids[1]))
if ntype == NEG:
nodemap[nid] = unary_op(BVNeg, Not, getnode(nids[1]))
if ntype == UEXT:
nodemap[nid] = BVZExt(B2BV(getnode(nids[1])), int(nids[2]))
if ntype == SEXT:
nodemap[nid] = BVSExt(B2BV(getnode(nids[1])), int(nids[2]))
if ntype == OR:
nodemap[nid] = binary_op(BVOr, Or, getnode(nids[1]),
getnode(nids[2]))
if ntype == ADD:
nodemap[nid] = BVAdd(B2BV(getnode(nids[1])),
B2BV(getnode(nids[2])))
if ntype == SUB:
nodemap[nid] = BVSub(B2BV(getnode(nids[1])),
B2BV(getnode(nids[2])))
if ntype == UGT:
nodemap[nid] = BVUGT(B2BV(getnode(nids[1])),
B2BV(getnode(nids[2])))
if ntype == UGTE:
nodemap[nid] = BVUGE(B2BV(getnode(nids[1])),
B2BV(getnode(nids[2])))
if ntype == ULT:
nodemap[nid] = BVULT(B2BV(getnode(nids[1])),
B2BV(getnode(nids[2])))
if ntype == ULTE:
nodemap[nid] = BVULE(B2BV(getnode(nids[1])),
B2BV(getnode(nids[2])))
if ntype == SGT:
nodemap[nid] = BVSGT(B2BV(getnode(nids[1])),
B2BV(getnode(nids[2])))
if ntype == SGTE:
nodemap[nid] = BVSGE(B2BV(getnode(nids[1])),
B2BV(getnode(nids[2])))
if ntype == SLT:
nodemap[nid] = BVSLT(B2BV(getnode(nids[1])),
B2BV(getnode(nids[2])))
if ntype == SLTE:
nodemap[nid] = BVSLE(B2BV(getnode(nids[1])),
B2BV(getnode(nids[2])))
if ntype == EQ:
nodemap[nid] = BVComp(B2BV(getnode(nids[1])),
B2BV(getnode(nids[2])))
if ntype == NEQ:
nodemap[nid] = BVNot(BVComp(getnode(nids[1]),
getnode(nids[2])))
if ntype == MUL:
nodemap[nid] = BVMul(B2BV(getnode(nids[1])),
B2BV(getnode(nids[2])))
if ntype == SLICE:
nodemap[nid] = BVExtract(B2BV(getnode(nids[1])), int(nids[3]),
int(nids[2]))
if ntype == SLL:
nodemap[nid] = BVLShl(getnode(nids[1]), getnode(nids[2]))
if ntype == SRA:
nodemap[nid] = BVAShr(getnode(nids[1]), getnode(nids[2]))
if ntype == SRL:
nodemap[nid] = BVLShr(getnode(nids[1]), getnode(nids[2]))
if ntype == ITE:
if (get_type(getnode(nids[2])) == BOOL) or (get_type(
getnode(nids[3])) == BOOL):
nodemap[nid] = Ite(BV2B(getnode(nids[1])),
B2BV(getnode(nids[2])),
B2BV(getnode(nids[3])))
else:
nodemap[nid] = Ite(BV2B(getnode(nids[1])),
getnode(nids[2]), getnode(nids[3]))
if ntype == NEXT:
if (get_type(getnode(nids[1])) == BOOL) or (get_type(
getnode(nids[2])) == BOOL):
lval = TS.get_prime(getnode(nids[1]))
rval = B2BV(getnode(nids[2]))
else:
lval = TS.get_prime(getnode(nids[1]))
rval = getnode(nids[2])
nodemap[nid] = EqualsOrIff(lval, rval)
ftrans.append((lval, [(TRUE(), rval)]))
if ntype == INIT:
if (get_type(getnode(nids[1])) == BOOL) or (get_type(
getnode(nids[2])) == BOOL):
nodemap[nid] = EqualsOrIff(BV2B(getnode(nids[1])),
BV2B(getnode(nids[2])))
elif get_type(getnode(nids[1])).is_array_type():
_type = get_type(getnode(nids[1]))
nodemap[nid] = EqualsOrIff(
getnode(nids[1]),
Array(_type.index_type, default=getnode(nids[2])))
else:
nodemap[nid] = EqualsOrIff(getnode(nids[1]),
getnode(nids[2]))
initlist.append(getnode(nid))
if ntype == CONSTRAINT:
nodemap[nid] = BV2B(getnode(nids[0]))
invarlist.append(getnode(nid))
if ntype == BAD:
nodemap[nid] = getnode(nids[0])
if len(nids) > 1:
assert_name = nids[1]
description = "Embedded assertion: {}".format(assert_name)
else:
assert_name = 'embedded_assertion_%i' % prop_count
description = 'Embedded assertion number %i' % prop_count
prop_count += 1
# Following problem format (name, description, strformula)
invar_props.append(
(assert_name, description, Not(BV2B(getnode(nid)))))
if nid not in nodemap:
Logger.error("Unknown node type \"%s\"" % ntype)
# get wirename if it exists
if ntype not in {STATE, INPUT, OUTPUT, BAD}:
# disregard comments at the end of the line
try:
symbol_idx = nids.index(';')
symbol_idx -= 1 # the symbol should be before the comment
except:
# the symbol is just the end
symbol_idx = -1
# check for wirename, if it's an integer, then it's a node ref
try:
a = int(nids[symbol_idx])
except:
try:
name = str(nids[symbol_idx])
# use the exact name, unless it has already been used
wire = Symbol(name, getnode(nids[0]))
if wire in ts.vars:
wire = FreshSymbol(getnode(nids[0]),
template=name + "%d")
invarlist.append(EqualsOrIff(wire, B2BV(nodemap[nid])))
ts.add_var(wire)
except:
pass
if Logger.level(1):
name = lambda x: str(nodemap[x]) if nodemap[x].is_symbol() else x
uncovered = [name(x) for x in nodemap if x not in node_covered]
uncovered.sort()
if len(uncovered) > 0:
Logger.warning("Unlinked nodes \"%s\"" % ",".join(uncovered))
if not self.symbolic_init:
init = simplify(And(initlist))
else:
init = TRUE()
invar = simplify(And(invarlist))
# instead of trans, we're using the ftrans format -- see below
ts.set_behavior(init, TRUE(), invar)
# add ftrans
for var, cond_assign_list in ftrans:
ts.add_func_trans(var, cond_assign_list)
hts.add_ts(ts)
return (hts, invar_props, ltl_props)
def walk_bv_comp(self, formula, args, **kwargs):
# We check that all children are BV and the same size
a, b = args
if a != b or (not a.is_bv_type()):
return None
return BVType(1)
def compile_sts(self, name, params):
sparser = StringParser()
in_port, max_val, c_push, c_pop = list(params)
max_val = int(max_val)
if type(c_push) == str:
c_push = sparser.parse_formula(c_push)
if type(c_pop) == str:
c_pop = sparser.parse_formula(c_pop)
tracking = Symbol("%s.tracking" % name, BOOL)
end = Symbol("%s.end" % name, BOOL)
done = Symbol("%s.done" % name, BOOL)
packet = Symbol("%s.packet" % name,
BVType(in_port.symbol_type().width))
max_width = math.ceil(math.log(max_val) / math.log(2))
max_bvval = BV(max_val, max_width)
zero = BV(0, max_width)
one = BV(1, max_width)
count = Symbol("%s.count" % name, BVType(max_width))
size = Symbol("%s.size" % name, BVType(max_width))
pos_c_push = BV2B(c_push)
neg_c_push = Not(BV2B(c_push))
pos_c_pop = BV2B(c_pop)
neg_c_pop = Not(BV2B(c_pop))
init = []
trans = []
invar = []
# INIT DEFINITION #
# count = 0
init.append(EqualsOrIff(count, BV(0, max_width)))
# tracking = False
init.append(EqualsOrIff(tracking, FALSE()))
# size = 0
init.append(EqualsOrIff(size, BV(0, max_width)))
# end = false
init.append(EqualsOrIff(end, FALSE()))
# INVAR DEFINITION #
# !done -> (end = (tracking & (size = count)))
invar.append(
Implies(Not(done),
EqualsOrIff(end, And(tracking, EqualsOrIff(size, count)))))
# count <= size
invar.append(BVULE(count, size))
# count <= maxval
invar.append(BVULE(count, max_bvval))
# size <= maxval
invar.append(BVULE(size, max_bvval))
# done -> (end <-> False);
invar.append(Implies(done, EqualsOrIff(end, FALSE())))
# done -> (count = 0_8);
invar.append(Implies(done, EqualsOrIff(count, BV(0, max_width))))
# done -> (size = 0_8);
invar.append(Implies(done, EqualsOrIff(size, BV(0, max_width))))
# done -> (packet = 0_8);
invar.append(
Implies(done,
EqualsOrIff(packet, BV(0,
in_port.symbol_type().width))))
# TRANS DEFINITION #
# (!end & !done) -> next(!done);
trans.append(Implies(And(Not(end), Not(done)), TS.to_next(Not(done))))
# end -> next(done);
trans.append(Implies(end, TS.to_next(done)))
# done -> next(done);
trans.append(Implies(done, TS.to_next(done)))
# tracking -> next(tracking);
trans.append(
Implies(Not(done), Implies(tracking, TS.to_next(tracking))))
# tracking -> (next(packet) = packet);
trans.append(
Implies(Not(done),
Implies(tracking, EqualsOrIff(TS.to_next(packet),
packet))))
# !tracking & next(tracking) -> c_push;
trans.append(
Implies(
Not(done),
Implies(And(Not(tracking), TS.to_next(tracking)), pos_c_push)))
# (c_push & next(tracking)) -> ((packet = in) & (next(packet) = in);
trans.append(
Implies(
Not(done),
Implies(
And(pos_c_push, TS.to_next(tracking)),
And(EqualsOrIff(packet, in_port),
EqualsOrIff(TS.to_next(packet), in_port)))))
# (c_push & !c_pop & tracking) -> (next(count) = (count + 1_8));
trans.append(
Implies(
Not(done),
Implies(
And(pos_c_push, neg_c_pop, tracking),
EqualsOrIff(TS.to_next(count),
BVAdd(count, BV(1, max_width))))))
# (c_push & size < maxval) -> (next(size) = (size + 1_8));
trans.append(
Implies(
Not(done),
Implies(
And(pos_c_push, BVULT(size, max_bvval)),
EqualsOrIff(TS.to_next(size),
BVAdd(size, BV(1, max_width))))))
# (c_pop & size > 0) -> (next(size) = (size - 1_8));
trans.append(
Implies(
Not(done),
Implies(
And(pos_c_pop, BVUGT(size, zero)),
EqualsOrIff(TS.to_next(size),
BVSub(size, BV(1, max_width))))))
# (!(c_push | c_pop)) -> (next(count) = count);
trans.append(
Implies(
Not(done),
Implies(Not(Or(pos_c_push, pos_c_pop)),
EqualsOrIff(count, TS.to_next(count)))))
# ((c_push | c_pop) & !tracking) -> (next(count) = count);
trans.append(
Implies(
Not(done),
Implies(And(Or(pos_c_push, pos_c_pop), Not(tracking)),
EqualsOrIff(count, TS.to_next(count)))))
# (c_push & size = maxval) -> (next(size) = size);
trans.append(
Implies(
Not(done),
Implies(And(pos_c_push, EqualsOrIff(size, max_bvval)),
EqualsOrIff(TS.to_next(size), size))))
# (!(c_push | c_pop)) -> (next(size) = size);
trans.append(
Implies(
Not(done),
Implies(Not(Or(pos_c_push, pos_c_pop)),
EqualsOrIff(size, TS.to_next(size)))))
# (!(c_push | c_pop)) -> (next(count) = count);
trans.append(
Implies(
Not(done),
Implies(Not(Or(pos_c_push, pos_c_pop)),
EqualsOrIff(count, TS.to_next(count)))))
# (c_pop & size = 0) -> (next(size) = 0);
trans.append(
Implies(
Not(done),
Implies(And(pos_c_pop, EqualsOrIff(size, zero)),
EqualsOrIff(TS.to_next(size), zero))))
# (!c_push) -> (next(count) = count);
trans.append(
Implies(Not(done),
Implies(neg_c_push, EqualsOrIff(TS.to_next(count),
count))))
init = And(init)
invar = And(invar)
trans = And(trans)
ts = TS()
ts.vars, ts.init, ts.invar, ts.trans = set(
[tracking, end, packet, count, size]), init, invar, trans
return ts
VECT_WIDTH = 5
class Cell(Enum):
s = BV(0, VECT_WIDTH) # space
x = BV(1, VECT_WIDTH) # x - human player goes first
o = BV(2, VECT_WIDTH) # o - cpu player
x_turns = 0
o_turns = 0
x_val = Cell.x.value.constant_value()
o_val = Cell.o.value.constant_value()
board = [[FreshSymbol(BVType(VECT_WIDTH)) for _ in range(3)] for _ in range(3)]
solver = Solver()
# initialise board cells, each one has to be blank, x or o
for row in board:
for cell in row:
solver.add_assertion(Or([Equals(cell, i.value) for i in Cell]))
# load board
test = 'tests/blank.txt'
with open(test) as fh:
for row, line in enumerate(fh.readlines()):
for col, cell in enumerate(line.strip().split(' ')):
if cell == Cell.x.name:
solver.add_assertion(Equals(board[row][col], Cell.x.value))
def test_bv_zero_lshr(self):
x = Symbol("x", BVType(32))
f = BVLShr(BVZero(32), x)
self.check_equal_and_valid(f, BVZero(32))
def test_bv_lshr_underflow(self):
x = Symbol("x", BVType(32))
f = BVLShr(x, BV(33, 32))
self.check_equal_and_valid(f, BVZero(32))
def test_bv_sub_eq(self):
x, y = (Symbol(name, BVType(32)) for name in "xy")
f = BVSub(BVMul(x, y), BVMul(x, y))
self.check_equal_and_valid(f, BVZero(32))
def test_bv_lshl_zero(self):
x = Symbol("x", BVType(32))
f = BVLShl(x, BVZero(32))
self.check_equal_and_valid(f, x)
def test_bv_sub_zero(self):
x = Symbol("x", BVType(32))
f = BVSub(x, BVZero(32))
self.check_equal_and_valid(f, x)
def test_bv_all_ones_or(self):
x = Symbol("x", BVType(32))
f = BVOr(BV(2**32 - 1, 32), x)
self.check_equal_and_valid(f, BV(2**32 - 1, 32))
def test_bv_and_all_ones(self):
x = Symbol("x", BVType(32))
f = BVAnd(x, BV(2**32 - 1, 32))
self.check_equal_and_valid(f, x)
def generate_STS(self, lines):
ts = TS("Additional system")
init = TRUE()
trans = TRUE()
invar = TRUE()
states = {}
assigns = set([])
varsmap = {}
def def_var(name, vtype):
if name in varsmap:
return varsmap[name]
var = Symbol(name, vtype)
ts.add_state_var(var)
return var
for line in lines:
if line.comment:
continue
if line.init:
if T_I not in states:
states[T_I] = TRUE()
if line.init.varname != "":
(value, typev) = self.__get_value(line.init.value)
ivar = def_var(line.init.varname, typev)
state = EqualsOrIff(ivar, value)
else:
state = TRUE() if line.init.value == T_TRUE else FALSE()
states[T_I] = And(states[T_I], state)
# Optimization for the initial state assignment
init = And(init, state)
state = TRUE()
if line.state:
sname = T_S + line.state.id
if (line.state.varname != ""):
(value, typev) = self.__get_value(line.state.value)
ivar = def_var(line.state.varname, typev)
state = EqualsOrIff(ivar, value)
assval = (sname, line.state.varname)
if assval not in assigns:
assigns.add(assval)
else:
Logger.error(
"Double assignment for variable \"%s\" at state \"%s\""
% (line.state.varname, sname))
else:
state = TRUE() if line.state.value == T_TRUE else FALSE()
if sname not in states:
states[sname] = TRUE()
states[sname] = And(states[sname], state)
stateid_width = math.ceil(math.log(len(states)) / math.log(2))
stateid_var = Symbol(self.new_state_id(), BVType(stateid_width))
init = And(init, EqualsOrIff(stateid_var, BV(0, stateid_width)))
invar = And(
invar,
Implies(EqualsOrIff(stateid_var, BV(0, stateid_width)),
states[T_I]))
states[T_I] = EqualsOrIff(stateid_var, BV(0, stateid_width))
count = 1
state_items = list(states.keys())
state_items.sort()
for state in state_items:
if state == T_I:
continue
invar = And(
invar,
Implies(EqualsOrIff(stateid_var, BV(count, stateid_width)),
states[state]))
states[state] = EqualsOrIff(stateid_var, BV(count, stateid_width))
count += 1
transdic = {}
for line in lines:
if line.comment:
continue
if line.trans:
if states[line.trans.start] not in transdic:
transdic[states[line.trans.start]] = []
transdic[states[line.trans.start]].append(
states[line.trans.end])
for transition in transdic:
(start, end) = (transition, transdic[transition])
trans = And(trans, Implies(start, TS.to_next(Or(end))))
vars_ = [v for v in get_free_variables(trans) if not TS.is_prime(v)]
vars_ += get_free_variables(init)
vars_ += get_free_variables(invar)
invar = And(invar, BVULE(stateid_var, BV(count - 1, stateid_width)))
ts.set_behavior(init, trans, invar)
ts.add_state_var(stateid_var)
hts = HTS("ETS")
hts.add_ts(ts)
invar_props = []
ltl_props = []
return (hts, invar_props, ltl_props)
def test_bv_sle_eq(self):
x, y = (Symbol(name, BVType(32)) for name in "xy")
f = BVSLE(BVMul(x, y), BVMul(x, y))
self.check_equal_and_valid(f, Bool(True))
def get_full_example_formulae(environment=None):
"""Return a list of Examples using the given environment."""
if environment is None:
environment = get_env()
with environment:
x = Symbol("x", BOOL)
y = Symbol("y", BOOL)
p = Symbol("p", INT)
q = Symbol("q", INT)
r = Symbol("r", REAL)
s = Symbol("s", REAL)
aii = Symbol("aii", ARRAY_INT_INT)
ari = Symbol("ari", ArrayType(REAL, INT))
arb = Symbol("arb", ArrayType(REAL, BV8))
abb = Symbol("abb", ArrayType(BV8, BV8))
nested_a = Symbol("a_arb_aii",
ArrayType(ArrayType(REAL, BV8), ARRAY_INT_INT))
rf = Symbol("rf", FunctionType(REAL, [REAL, REAL]))
rg = Symbol("rg", FunctionType(REAL, [REAL]))
ih = Symbol("ih", FunctionType(INT, [REAL, INT]))
ig = Symbol("ig", FunctionType(INT, [INT]))
bf = Symbol("bf", FunctionType(BOOL, [BOOL]))
bg = Symbol("bg", FunctionType(BOOL, [BOOL]))
bv3 = Symbol("bv3", BVType(3))
bv8 = Symbol("bv8", BV8)
bv16 = Symbol("bv16", BV16)
result = [
# Formula, is_valid, is_sat, is_qf
Example(hr="(x & y)",
expr=And(x, y),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BOOL),
Example(hr="(x <-> y)",
expr=Iff(x, y),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BOOL),
Example(hr="((x | y) & (! (x | y)))",
expr=And(Or(x, y), Not(Or(x, y))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BOOL),
Example(hr="(x & (! y))",
expr=And(x, Not(y)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BOOL),
Example(hr="(False -> True)",
expr=Implies(FALSE(), TRUE()),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BOOL),
Example(hr="((x | y) & (! (x | y)))",
expr=And(Or(x, y), Not(Or(x, y))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BOOL),
#
# LIA
#
Example(hr="((q < p) & (x -> y))",
expr=And(GT(p, q), Implies(x, y)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_IDL),
Example(hr="(((p + q) = 5) & (q < p))",
expr=And(Equals(Plus(p, q), Int(5)), GT(p, q)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LIA),
Example(hr="((q <= p) | (p <= q))",
expr=Or(GE(p, q), LE(p, q)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_IDL),
Example(hr="(! (p < (q * 2)))",
expr=Not(LT(p, Times(q, Int(2)))),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LIA),
Example(hr="(p < (p - (5 - 2)))",
expr=GT(Minus(p, Minus(Int(5), Int(2))), p),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_IDL),
Example(hr="((x ? 7 : ((p + -1) * 3)) = q)",
expr=Equals(
Ite(x, Int(7), Times(Plus(p, Int(-1)), Int(3))), q),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LIA),
Example(hr="(p < (q + 1))",
expr=LT(p, Plus(q, Int(1))),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LIA),
#
# LRA
#
Example(hr="((s < r) & (x -> y))",
expr=And(GT(r, s), Implies(x, y)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_RDL),
Example(hr="(((r + s) = 28/5) & (s < r))",
expr=And(Equals(Plus(r, s), Real(Fraction("5.6"))),
GT(r, s)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LRA),
Example(hr="((s <= r) | (r <= s))",
expr=Or(GE(r, s), LE(r, s)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_RDL),
Example(hr="(! ((r * 2.0) < (s * 2.0)))",
expr=Not(LT(Div(r, Real((1, 2))), Times(s, Real(2)))),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LRA),
Example(hr="(! (r < (r - (5.0 - 2.0))))",
expr=Not(GT(Minus(r, Minus(Real(5), Real(2))), r)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_RDL),
Example(hr="((x ? 7.0 : ((s + -1.0) * 3.0)) = r)",
expr=Equals(
Ite(x, Real(7), Times(Plus(s, Real(-1)), Real(3))), r),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LRA),
#
# EUF
#
Example(hr="(bf(x) <-> bg(x))",
expr=Iff(Function(bf, (x, )), Function(bg, (x, ))),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_UF),
Example(hr="(rf(5.0, rg(r)) = 0.0)",
expr=Equals(Function(rf, (Real(5), Function(rg, (r, )))),
Real(0)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_UFLRA),
Example(hr="((rg(r) = (5.0 + 2.0)) <-> (rg(r) = 7.0))",
expr=Iff(Equals(Function(rg, [r]), Plus(Real(5), Real(2))),
Equals(Function(rg, [r]), Real(7))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_UFLRA),
Example(
hr="((r = (s + 1.0)) & (rg(s) = 5.0) & (rg((r - 1.0)) = 7.0))",
expr=And([
Equals(r, Plus(s, Real(1))),
Equals(Function(rg, [s]), Real(5)),
Equals(Function(rg, [Minus(r, Real(1))]), Real(7))
]),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_UFLRA),
#
# BV
#
Example(hr="((1_32 & 0_32) = 0_32)",
expr=Equals(BVAnd(BVOne(32), BVZero(32)), BVZero(32)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((! 2_3) = 5_3)",
expr=Equals(BVNot(BV("010")), BV("101")),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((! bv3) = 5_3)",
expr=Equals(BVNot(bv3), BV("101")),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((7_3 xor 0_3) = 0_3)",
expr=Equals(BVXor(BV("111"), BV("000")), BV("000")),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
Example(hr="((7_3 xor bv3) = (6_3 xor bv3))",
expr=Equals(BVXor(BV("111"), bv3), BVXor(BV("110"), bv3)),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
Example(hr="((bv8::bv8) u< 0_16)",
expr=BVULT(BVConcat(bv8, bv8), BVZero(16)),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
Example(hr="((bv8::bv8) u< (bv8::9_8))",
expr=BVULT(BVConcat(bv8, bv8), BVConcat(bv8, BV(9, 8))),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="(1_32[0:7] = 1_8)",
expr=Equals(BVExtract(BVOne(32), end=7), BVOne(8)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="(0_8 u< (((bv8 + 1_8) * 5_8) u/ 5_8))",
expr=BVUGT(
BVUDiv(BVMul(BVAdd(bv8, BVOne(8)), BV(5, width=8)),
BV(5, width=8)), BVZero(8)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="(0_16 u<= bv16)",
expr=BVUGE(bv16, BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="(0_16 s<= bv16)",
expr=BVSGE(bv16, BVZero(16)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(
hr="((0_32 u< (5_32 u% 2_32)) & ((5_32 u% 2_32) u<= 1_32))",
expr=And(
BVUGT(BVURem(BV(5, width=32), BV(2, width=32)),
BVZero(32)),
BVULE(BVURem(BV(5, width=32), BV(2, width=32)),
BVOne(32))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((((1_32 + (- 1_32)) << 1_32) >> 1_32) = 1_32)",
expr=Equals(
BVLShr(BVLShl(BVAdd(BVOne(32), BVNeg(BVOne(32))), 1),
1), BVOne(32)),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
Example(hr="((1_32 - 1_32) = 0_32)",
expr=Equals(BVSub(BVOne(32), BVOne(32)), BVZero(32)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
# Rotations
Example(hr="(((1_32 ROL 1) ROR 1) = 1_32)",
expr=Equals(BVRor(BVRol(BVOne(32), 1), 1), BVOne(32)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((bv16 ROL 1) = (bv16 ROR 2))",
expr=Equals(BVRol(bv16, 1), BVRor(bv16, 2)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
# Extensions
Example(hr="((0_5 ZEXT 11) = (0_1 SEXT 15))",
expr=Equals(BVZExt(BVZero(5), 11), BVSExt(BVZero(1), 15)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((bv8 ZEXT 19) = (bv16 SEXT 11))",
expr=Equals(BVZExt(bv8, 19), BVSExt(bv16, 11)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((bv16 - bv16) = 0_16)",
expr=Equals(BVSub(bv16, bv16), BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((bv16 - bv16)[0:7] = bv8)",
expr=Equals(BVExtract(BVSub(bv16, bv16), 0, 7), bv8),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((bv16[0:7] bvcomp bv8) = 1_1)",
expr=Equals(BVComp(BVExtract(bv16, 0, 7), bv8), BVOne(1)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((bv16 bvcomp bv16) = 0_1)",
expr=Equals(BVComp(bv16, bv16), BVZero(1)),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
Example(hr="(bv16 s< bv16)",
expr=BVSLT(bv16, bv16),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
Example(hr="(bv16 s< 0_16)",
expr=BVSLT(bv16, BVZero(16)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((bv16 s< 0_16) | (0_16 s<= bv16))",
expr=Or(BVSGT(BVZero(16), bv16), BVSGE(bv16, BVZero(16))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="(bv16 u< bv16)",
expr=BVULT(bv16, bv16),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
Example(hr="(bv16 u< 0_16)",
expr=BVULT(bv16, BVZero(16)),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
Example(hr="((bv16 | 0_16) = bv16)",
expr=Equals(BVOr(bv16, BVZero(16)), bv16),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((bv16 | 5_16) = bv16)",
expr=Equals(BVOr(bv16, BV(5, 16)), bv16),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((bv16 & 0_16) = 0_16)",
expr=Equals(BVAnd(bv16, BVZero(16)), BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((bv16 & 7_16) = 0_16)",
expr=Equals(BVAnd(bv16, BV(7, 16)), BVZero(16)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((0_16 s< bv16) & ((bv16 s/ 65535_16) s< 0_16))",
expr=And(BVSLT(BVZero(16), bv16),
BVSLT(BVSDiv(bv16, SBV(-1, 16)), BVZero(16))),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((0_16 s< bv16) & ((bv16 s% 1_16) s< 0_16))",
expr=And(BVSLT(BVZero(16), bv16),
BVSLT(BVSRem(bv16, BVOne(16)), BVZero(16))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_BV),
Example(hr="((bv16 u% 1_16) = 0_16)",
expr=Equals(BVURem(bv16, BVOne(16)), BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((bv16 u% bv16) = 0_16)",
expr=Equals(BVURem(bv16, bv16), BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((bv16 s% 1_16) = 0_16)",
expr=Equals(BVSRem(bv16, BVOne(16)), BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((bv16 s% bv16) = 0_16)",
expr=Equals(BVSRem(bv16, bv16), BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((bv16 s% (- 1_16)) = 0_16)",
expr=Equals(BVSRem(bv16, BVNeg(BVOne(16))), BVZero(16)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="(bv16 s< (- bv16))",
expr=BVSGT(BVNeg(bv16), bv16),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(hr="((bv16 a>> 0_16) = bv16)",
expr=Equals(BVAShr(bv16, BVZero(16)), bv16),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_BV),
Example(
hr="((0_16 s<= bv16) & ((bv16 a>> 1_16) = (bv16 >> 1_16)))",
expr=And(
BVSLE(BVZero(16), bv16),
Equals(BVAShr(bv16, BVOne(16)), BVLShr(bv16, BVOne(16)))),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BV),
#
# Quantification
#
Example(hr="(forall y . (x -> y))",
expr=ForAll([y], Implies(x, y)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.BOOL),
Example(hr="(forall p, q . ((p + q) = 0))",
expr=ForAll([p, q], Equals(Plus(p, q), Int(0))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.LIA),
Example(
hr="(forall r, s . (((0.0 < r) & (0.0 < s)) -> ((r - s) < r)))",
expr=ForAll([r, s],
Implies(And(GT(r, Real(0)), GT(s, Real(0))),
(LT(Minus(r, s), r)))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.LRA),
Example(hr="(exists x, y . (x -> y))",
expr=Exists([x, y], Implies(x, y)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.BOOL),
Example(hr="(exists p, q . ((p + q) = 0))",
expr=Exists([p, q], Equals(Plus(p, q), Int(0))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.LIA),
Example(hr="(exists r . (forall s . (r < (r - s))))",
expr=Exists([r], ForAll([s], GT(Minus(r, s), r))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.LRA),
Example(hr="(forall r . (exists s . (r < (r - s))))",
expr=ForAll([r], Exists([s], GT(Minus(r, s), r))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.LRA),
Example(hr="(x & (forall r . ((r + s) = 5.0)))",
expr=And(x, ForAll([r], Equals(Plus(r, s), Real(5)))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.LRA),
Example(hr="(exists x . ((x <-> (5.0 < s)) & (s < 3.0)))",
expr=Exists([x],
(And(Iff(x, GT(s, Real(5))), LT(s, Real(3))))),
is_valid=False,
is_sat=True,
logic=pysmt.logics.LRA),
#
# UFLIRA
#
Example(hr="((p < ih(r, q)) & (x -> y))",
expr=And(GT(Function(ih, (r, q)), p), Implies(x, y)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_UFLIRA),
Example(
hr=
"(((p - 3) = q) -> ((p < ih(r, (q + 3))) | (ih(r, p) <= p)))",
expr=Implies(
Equals(Minus(p, Int(3)), q),
Or(GT(Function(ih, (r, Plus(q, Int(3)))), p),
LE(Function(ih, (r, p)), p))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_UFLIRA),
Example(
hr=
"(((ToReal((p - 3)) = r) & (ToReal(q) = r)) -> ((p < ih(ToReal((p - 3)), (q + 3))) | (ih(r, p) <= p)))",
expr=Implies(
And(Equals(ToReal(Minus(p, Int(3))), r),
Equals(ToReal(q), r)),
Or(
GT(
Function(
ih,
(ToReal(Minus(p, Int(3))), Plus(q, Int(3)))),
p), LE(Function(ih, (r, p)), p))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_UFLIRA),
Example(
hr=
"(! (((ToReal((p - 3)) = r) & (ToReal(q) = r)) -> ((p < ih(ToReal((p - 3)), (q + 3))) | (ih(r, p) <= p))))",
expr=Not(
Implies(
And(Equals(ToReal(Minus(p, Int(3))), r),
Equals(ToReal(q), r)),
Or(
GT(
Function(ih, (ToReal(Minus(
p, Int(3))), Plus(q, Int(3)))), p),
LE(Function(ih, (r, p)), p)))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_UFLIRA),
Example(
hr=
"""("Did you know that any string works? #yolo" & "10" & "|#somesolverskeepthe||" & " ")""",
expr=And(Symbol("Did you know that any string works? #yolo"),
Symbol("10"), Symbol("|#somesolverskeepthe||"),
Symbol(" ")),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_BOOL),
#
# Arrays
#
Example(hr="((q = 0) -> (aii[0 := 0] = aii[0 := q]))",
expr=Implies(
Equals(q, Int(0)),
Equals(Store(aii, Int(0), Int(0)),
Store(aii, Int(0), q))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_ALIA),
Example(hr="(aii[0 := 0][0] = 0)",
expr=Equals(Select(Store(aii, Int(0), Int(0)), Int(0)),
Int(0)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_ALIA),
Example(hr="((Array{Int, Int}(0)[1 := 1] = aii) & (aii[1] = 0))",
expr=And(Equals(Array(INT, Int(0), {Int(1): Int(1)}), aii),
Equals(Select(aii, Int(1)), Int(0))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.get_logic_by_name("QF_ALIA*")),
Example(hr="((Array{Int, Int}(0)[1 := 3] = aii) & (aii[1] = 3))",
expr=And(Equals(Array(INT, Int(0), {Int(1): Int(3)}), aii),
Equals(Select(aii, Int(1)), Int(3))),
is_valid=False,
is_sat=True,
logic=pysmt.logics.get_logic_by_name("QF_ALIA*")),
Example(hr="((Array{Real, Int}(10) = ari) & (ari[6/5] = 0))",
expr=And(Equals(Array(REAL, Int(10)), ari),
Equals(Select(ari, Real((6, 5))), Int(0))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.get_logic_by_name("QF_AUFBVLIRA*")),
Example(
hr=
"((Array{Real, Int}(0)[1.0 := 10][2.0 := 20][3.0 := 30][4.0 := 40] = ari) & (! ((ari[0.0] = 0) & (ari[1.0] = 10) & (ari[2.0] = 20) & (ari[3.0] = 30) & (ari[4.0] = 40))))",
expr=And(
Equals(
Array(
REAL, Int(0), {
Real(1): Int(10),
Real(2): Int(20),
Real(3): Int(30),
Real(4): Int(40)
}), ari),
Not(
And(Equals(Select(ari, Real(0)), Int(0)),
Equals(Select(ari, Real(1)), Int(10)),
Equals(Select(ari, Real(2)), Int(20)),
Equals(Select(ari, Real(3)), Int(30)),
Equals(Select(ari, Real(4)), Int(40))))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.get_logic_by_name("QF_AUFBVLIRA*")),
Example(
hr=
"((Array{Real, Int}(0)[1.0 := 10][2.0 := 20][3.0 := 30][4.0 := 40][5.0 := 50] = ari) & (! ((ari[0.0] = 0) & (ari[1.0] = 10) & (ari[2.0] = 20) & (ari[3.0] = 30) & (ari[4.0] = 40) & (ari[5.0] = 50))))",
expr=And(
Equals(
Array(
REAL, Int(0), {
Real(1): Int(10),
Real(2): Int(20),
Real(3): Int(30),
Real(4): Int(40),
Real(5): Int(50)
}), ari),
Not(
And(Equals(Select(ari, Real(0)), Int(0)),
Equals(Select(ari, Real(1)), Int(10)),
Equals(Select(ari, Real(2)), Int(20)),
Equals(Select(ari, Real(3)), Int(30)),
Equals(Select(ari, Real(4)), Int(40)),
Equals(Select(ari, Real(5)), Int(50))))),
is_valid=False,
is_sat=False,
logic=pysmt.logics.get_logic_by_name("QF_AUFBVLIRA*")),
Example(
hr=
"((a_arb_aii = Array{Array{Real, BV{8}}, Array{Int, Int}}(Array{Int, Int}(7))) -> (a_arb_aii[arb][42] = 7))",
expr=Implies(
Equals(nested_a,
Array(ArrayType(REAL, BV8), Array(INT, Int(7)))),
Equals(Select(Select(nested_a, arb), Int(42)), Int(7))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.get_logic_by_name("QF_AUFBVLIRA*")),
Example(hr="(abb[bv8 := y_][bv8 := z_] = abb[bv8 := z_])",
expr=Equals(
Store(Store(abb, bv8, Symbol("y_", BV8)), bv8,
Symbol("z_", BV8)),
Store(abb, bv8, Symbol("z_", BV8))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_ABV),
Example(hr="((r / s) = (r * s))",
expr=Equals(Div(r, s), Times(r, s)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_NRA),
Example(hr="(2.0 = (r * r))",
expr=Equals(Real(2), Times(r, r)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_NRA),
Example(hr="((p ^ 2) = 0)",
expr=Equals(Pow(p, Int(2)), Int(0)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_NIA),
Example(hr="((r ^ 2.0) = 0.0)",
expr=Equals(Pow(r, Real(2)), Real(0)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_NRA),
Example(hr="((r * r * r) = 25.0)",
expr=Equals(Times(r, r, r), Real(25)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_NRA),
Example(hr="((5.0 * r * 5.0) = 25.0)",
expr=Equals(Times(Real(5), r, Real(5)), Real(25)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LRA),
Example(hr="((p * p * p) = 25)",
expr=Equals(Times(p, p, p), Int(25)),
is_valid=False,
is_sat=False,
logic=pysmt.logics.QF_NIA),
Example(hr="((5 * p * 5) = 25)",
expr=Equals(Times(Int(5), p, Int(5)), Int(25)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LIA),
Example(hr="(((1 - 1) * p * 1) = 0)",
expr=Equals(Times(Minus(Int(1), Int(1)), p, Int(1)),
Int(0)),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_LIA),
# Huge Fractions:
Example(
hr=
"((r * 1606938044258990275541962092341162602522202993782792835301376/7) = -20480000000000000000000000.0)",
expr=Equals(Times(r, Real(Fraction(2**200, 7))),
Real(-200**11)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_LRA),
Example(hr="(((r + 5.0 + s) * (s + 2.0 + r)) = 0.0)",
expr=Equals(
Times(Plus(r, Real(5), s), Plus(s, Real(2), r)),
Real(0)),
is_valid=False,
is_sat=True,
logic=pysmt.logics.QF_NRA),
Example(
hr=
"(((p + 5 + q) * (p - (q - 5))) = ((p * p) + (10 * p) + 25 + (-1 * q * q)))",
expr=Equals(
Times(Plus(p, Int(5), q), Minus(p, Minus(q, Int(5)))),
Plus(Times(p, p), Times(Int(10), p), Int(25),
Times(Int(-1), q, q))),
is_valid=True,
is_sat=True,
logic=pysmt.logics.QF_NIA),
]
return result
def test_bv_sle_symbols(self):
x, y = (Symbol(name, BVType(32)) for name in "xy")
f = BVSLE(x, y)
self.check_equal_and_valid(f, BVSLE(x, y))
def test_bv(self):
mgr = get_env().formula_manager
BV = mgr.BV
# Constants
one = BV(1, 32)
zero = BV(0, 32)
big = BV(127, 128)
binary = BV("111")
binary2 = BV("#b111")
binary3 = BV(0b111, 3) # In this case we need to explicit the width
self.assertEqual(binary, binary2)
self.assertEqual(binary2, binary3)
self.assertEqual(one, mgr.BVOne(32))
self.assertEqual(zero, mgr.BVZero(32))
# Type Equality
self.assertTrue(BV32 != BV128)
self.assertFalse(BV32 != BV32)
self.assertFalse(BV32 == BV128)
self.assertTrue(BV32 == BV32)
with self.assertRaises(ValueError):
# Negative numbers are not supported
BV(-1, 10)
with self.assertRaises(ValueError):
# Number should fit in the width
BV(10, 2)
# Variables
b128 = Symbol("b", BV128) # BV1, BV8 etc. are defined in pysmt.typing
b32 = Symbol("b32", BV32)
hexample = BV(0x10, 32)
#s_one = BV(-1, 32)
bcustom = Symbol("bc", BVType(42))
self.assertIsNotNone(hexample)
self.assertIsNotNone(bcustom)
#self.assertIsNotNone(s_one)
self.assertEqual(bcustom.bv_width(), 42)
self.assertEqual(hexample.constant_value(), 16)
#self.assertEqual(str(s_one), "-1_32")
not_zero32 = mgr.BVNot(zero)
not_b128 = mgr.BVNot(b128)
f1 = Equals(not_zero32, b32)
f2 = Equals(not_b128, big)
#print(f1)
#print(f2)
self.assertTrue(is_sat(f1, logic=QF_BV))
self.assertTrue(is_sat(f2, logic=QF_BV))
zero_and_one = mgr.BVAnd(zero, one)
zero_or_one = mgr.BVOr(zero, one)
zero_xor_one = mgr.BVXor(zero, one)
zero_xor_one.simplify()
self.assertTrue(zero_xor_one.is_bv_op())
# print(zero_and_one)
# print(zero_or_one)
# print(zero_xor_one)
f1 = Equals(zero_and_one, b32)
f2 = Equals(zero_or_one, b32)
f3 = Equals(zero_xor_one, b32)
f4 = Equals(zero_xor_one, one)
self.assertTrue(is_sat(f1, logic=QF_BV), f1)
self.assertTrue(is_sat(f2, logic=QF_BV), f2)
self.assertTrue(is_sat(f3, logic=QF_BV), f3)
self.assertTrue(is_valid(f4, logic=QF_BV), f4)
with self.assertRaises(TypeError):
mgr.BVAnd(b128, zero)
f = mgr.BVAnd(b32, zero)
f = mgr.BVOr(f, b32)
f = mgr.BVXor(f, b32)
f = Equals(f, zero)
self.assertTrue(is_sat(f, logic=QF_BV), f)
zero_one_64 = mgr.BVConcat(zero, one)
one_zero_64 = mgr.BVConcat(one, zero)
one_one_64 = mgr.BVConcat(one, one)
self.assertTrue(zero_one_64.bv_width() == 64)
f1 = Equals(mgr.BVXor(one_zero_64, zero_one_64), one_one_64)
self.assertTrue(is_sat(f1, logic=QF_BV), f1)
# MG: BV indexes grow to the left.
# This is confusing and we should address this.
extraction = mgr.BVExtract(zero_one_64, 32, 63)
self.assertTrue(is_valid(Equals(extraction, zero)))
#print(extraction)
ult = mgr.BVULT(zero, one)
neg = mgr.BVNeg(one)
self.assertTrue(is_valid(ult, logic=QF_BV), ult)
test_eq = Equals(neg, one)
self.assertTrue(is_unsat(test_eq, logic=QF_BV))
# print(ult)
# print(neg)
f = zero
addition = mgr.BVAdd(f, one)
multiplication = mgr.BVMul(f, one)
udiv = mgr.BVUDiv(f, one)
self.assertTrue(is_valid(Equals(addition, one), logic=QF_BV), addition)
self.assertTrue(is_valid(Equals(multiplication, zero), logic=QF_BV),
multiplication)
self.assertTrue(is_valid(Equals(udiv, zero), logic=QF_BV), udiv)
# print(addition)
# print(multiplication)
# print(udiv)
three = mgr.BV(3, 32)
two = mgr.BV(2, 32)
reminder = mgr.BVURem(three, two)
shift_l_a = mgr.BVLShl(one, one)
shift_l_b = mgr.BVLShl(one, 1)
self.assertTrue(is_valid(Equals(reminder, one)), reminder)
self.assertEqual(shift_l_a, shift_l_b)
self.assertTrue(is_valid(Equals(shift_l_a, two)))
# print(reminder)
# print(shift_l_a)
# print(shift_l_b)
shift_r_a = mgr.BVLShr(one, one)
shift_r_b = mgr.BVLShr(one, 1)
self.assertEqual(shift_r_a, shift_r_b)
self.assertTrue(is_valid(Equals(shift_r_a, zero)))
rotate_l = mgr.BVRol(one, 3)
rotate_r = mgr.BVRor(rotate_l, 3)
self.assertTrue(is_valid(Equals(one, rotate_r)))
# print(rotate_l)
# print(rotate_r)
zero_ext = mgr.BVZExt(one, 64)
signed_ext = mgr.BVSExt(one, 64)
signed_ext2 = mgr.BVSExt(mgr.BVNeg(one), 64)
self.assertNotEqual(signed_ext2, signed_ext)
self.assertTrue(is_valid(Equals(zero_ext, signed_ext), logic=QF_BV))
# print(zero_ext)
# print(signed_ext)
x = Symbol("x")
g = And(x, mgr.BVULT(zero, one))
res = is_sat(g, logic=QF_BV)
self.assertTrue(res)
model = get_model(g, logic=QF_BV)
self.assertTrue(model[x] == TRUE())
gt_1 = mgr.BVUGT(zero, one)
gt_2 = mgr.BVULT(one, zero)
self.assertEqual(gt_1, gt_2)
gte_1 = mgr.BVULE(zero, one)
gte_2 = mgr.BVUGE(one, zero)
self.assertEqual(gte_1, gte_2)
self.assertTrue(is_valid(gte_2, logic=QF_BV))
ide = Equals(mgr.BVNeg(BV(10, 32)), mgr.SBV(-10, 32))
self.assertValid(ide, logic=QF_BV)
# These should work without exceptions
mgr.SBV(-2, 2)
mgr.SBV(-1, 2)
mgr.SBV(0, 2)
mgr.SBV(1, 2)
# Overflow and Underflow
with self.assertRaises(ValueError):
mgr.SBV(2, 2)
with self.assertRaises(ValueError):
mgr.SBV(-3, 2)
# These should work without exceptions
mgr.BV(0, 2)
mgr.BV(1, 2)
mgr.BV(2, 2)
mgr.BV(3, 2)
# Overflow
with self.assertRaises(ValueError):
mgr.BV(4, 2)
# No negative number allowed
with self.assertRaises(ValueError):
mgr.BV(-1, 2)
# SBV should behave as BV for positive numbers
self.assertEqual(mgr.SBV(10, 16), mgr.BV(10, 16))
return
def get_sts(self, params):
if len(params) != len(self.interface.split()):
Logger.error("Invalid parameters for clock behavior \"%s\"" %
(self.name))
clk = params[0]
cyclestr = params[1]
try:
cycle = int(cyclestr)
except:
Logger.error(
"Clock cycle should be an integer number instead of \"%s\"" %
cyclestr)
if (not type(clk) == FNode) or (not clk.is_symbol()):
Logger.error("Clock symbol \"%s\" not found" % (str(clk)))
init = []
invar = []
trans = []
vars = set([])
if clk.symbol_type().is_bv_type():
pos_clk = EqualsOrIff(clk, BV(1, 1))
neg_clk = EqualsOrIff(clk, BV(0, 1))
else:
pos_clk = clk
neg_clk = Not(clk)
if cycle < 1:
Logger.error(
"Deterministic clock requires at least a cycle of size 1")
if cycle == 1:
init.append(neg_clk)
trans.append(Iff(neg_clk, TS.to_next(pos_clk)))
if cycle > 1:
statesize = math.ceil(math.log(cycle) / math.log(2))
counter = Symbol("%s%s" % (clk.symbol_name(), CLOCK_COUNTER),
BVType(statesize))
# 0 counts
cycle -= 1
# counter = 0 & clk = 0
init.append(EqualsOrIff(counter, BV(0, statesize)))
init.append(neg_clk)
# counter <= cycle
invar.append(BVULE(counter, BV(cycle, statesize)))
# (counter < cycle) -> next(counter) = counter + 1
trans.append(
Implies(
BVULT(counter, BV(cycle, statesize)),
EqualsOrIff(TS.to_next(counter),
BVAdd(counter, BV(1, statesize)))))
# (counter >= cycle) -> next(counter) = 0
trans.append(
Implies(BVUGE(counter, BV(cycle, statesize)),
EqualsOrIff(TS.to_next(counter), BV(0, statesize))))
# (!clk) & (counter < cycle) -> next(!clk)
trans.append(
Implies(And(neg_clk, BVULT(counter, BV(cycle, statesize))),
TS.to_next(neg_clk)))
# (!clk) & (counter >= cycle) -> next(clk)
trans.append(
Implies(And(neg_clk, BVUGE(counter, BV(cycle, statesize))),
TS.to_next(pos_clk)))
# (clk) & (counter < cycle) -> next(clk)
trans.append(
Implies(And(pos_clk, BVULT(counter, BV(cycle, statesize))),
TS.to_next(pos_clk)))
# (clk) & (counter >= cycle) -> next(!clk)
trans.append(
Implies(And(pos_clk, BVUGE(counter, BV(cycle, statesize))),
TS.to_next(neg_clk)))
vars.add(counter)
ts = TS("Clock Behavior")
ts.vars, ts.init, ts.invar, ts.trans = vars, And(init), And(
invar), And(trans)
Logger.log(
"Adding clock behavior \"%s(%s)\"" %
(self.name, ", ".join([str(p) for p in params])), 1)
return ts
def test_infix_extended(self):
p, r, x, y = self.p, self.r, self.x, self.y
get_env().enable_infix_notation = True
self.assertEqual(Plus(p, Int(1)), p + 1)
self.assertEqual(Plus(r, Real(1)), r + 1)
self.assertEqual(Times(r, Real(1)), r * 1)
self.assertEqual(Minus(p, Int(1)), p - 1)
self.assertEqual(Minus(r, Real(1)), r - 1)
self.assertEqual(Times(r, Real(1)), r * 1)
self.assertEqual(Plus(r, Real(1.5)), r + 1.5)
self.assertEqual(Minus(r, Real(1.5)), r - 1.5)
self.assertEqual(Times(r, Real(1.5)), r * 1.5)
self.assertEqual(Plus(r, Real(1.5)), 1.5 + r)
self.assertEqual(Times(r, Real(1.5)), 1.5 * r)
with self.assertRaises(PysmtTypeError):
foo = p + 1.5
self.assertEqual(Not(x), ~x)
self.assertEqual(Times(r, Real(-1)), -r)
self.assertEqual(Times(p, Int(-1)), -p)
self.assertEqual(Xor(x, y), x ^ y)
self.assertEqual(And(x, y), x & y)
self.assertEqual(Or(x, y), x | y)
self.assertEqual(Or(x, TRUE()), x | True)
self.assertEqual(Or(x, TRUE()), True | x)
self.assertEqual(And(x, TRUE()), x & True)
self.assertEqual(And(x, TRUE()), True & x)
self.assertEqual(Iff(x, y), x.Iff(y))
self.assertEqual(And(x, y), x.And(y))
self.assertEqual(Or(x, y), x.Or(y))
self.assertEqual(Ite(x, TRUE(), FALSE()), x.Ite(TRUE(), FALSE()))
with self.assertRaises(Exception):
x.Ite(1, 2)
self.assertEqual(6 - r, Plus(Times(r, Real(-1)), Real(6)))
# BVs
# BV_CONSTANT: We use directly python numbers
#
# Note: In this case, the width is implicit (yikes!) The
# width of the constant is inferred by the use of a
# symbol or operator that enforces a bit_width.
#
# This works in very simple cases. For complex
# expressions it is advisable to create a shortcut for
# the given BVType.
const1 = 3
const2 = 0b011
const3 = 0x3
# Since these are python numbers, the following holds
self.assertEqual(const1, const2)
self.assertEqual(const1, const3)
# However, we cannot use infix pySMT Equals, since const1 is a
# python int!!!
with self.assertRaises(AttributeError):
const1.Equals(const2)
# We use the usual syntax to build a constant with a fixed width
const1_8 = self.mgr.BV(3, width=8)
# In actual code, one can simply create a macro for this:
_8bv = lambda v: self.mgr.BV(v, width=8)
const1_8b = _8bv(3)
self.assertEqual(const1_8, const1_8b)
# Equals forces constants to have the width of the operand
self.assertEqual(const1_8.Equals(const1),
self.mgr.Equals(const1_8, const1_8b))
# Symbols
bv8 = self.mgr.FreshSymbol(BV8)
bv7 = self.mgr.FreshSymbol(BVType(7))
self.assertEqual(bv8.Equals(const1), bv8.Equals(const1_8))
# BV_AND,
self.assertEqual(bv8 & const1, self.mgr.BVAnd(bv8, const1_8))
self.assertEqual(const1 & bv8, self.mgr.BVAnd(bv8, const1_8))
self.assertEqual(const1 & bv8, self.mgr.BVAnd(bv8, const1_8))
# BV_XOR,
self.assertEqual(bv8 ^ const1, self.mgr.BVXor(bv8, const1_8))
self.assertEqual(const1 ^ bv8, self.mgr.BVXor(bv8, const1_8))
# BV_OR,
self.assertEqual(bv8 | const1, self.mgr.BVOr(bv8, const1_8))
self.assertEqual(const1 | bv8, self.mgr.BVOr(bv8, const1_8))
# BV_ADD,
self.assertEqual(bv8 + const1, self.mgr.BVAdd(bv8, const1_8))
self.assertEqual(const1 + bv8, self.mgr.BVAdd(bv8, const1_8))
# BV_SUB,
self.assertEqual(bv8 - const1, self.mgr.BVSub(bv8, const1_8))
self.assertEqual(const1 - bv8, self.mgr.BVSub(const1_8, bv8))
# BV_MUL,
self.assertEqual(bv8 * const1, self.mgr.BVMul(bv8, const1_8))
self.assertEqual(const1 * bv8, self.mgr.BVMul(bv8, const1_8))
# BV_NOT:
# !!!WARNING!!! Cannot be applied to python constants!!
# This results in a negative number
with self.assertRaises(PysmtValueError):
_8bv(~const1)
# For symbols and expressions this works as expected
self.assertEqual(~bv8, self.mgr.BVNot(bv8))
# BV_NEG -- Cannot be applied to 'infix' constants
self.assertEqual(-bv8, self.mgr.BVNeg(bv8))
# BV_EXTRACT -- Cannot be applied to 'infix' constants
self.assertEqual(bv8[0:7], self.mgr.BVExtract(bv8, 0, 7))
self.assertEqual(bv8[:7], self.mgr.BVExtract(bv8, end=7))
self.assertEqual(bv8[0:], self.mgr.BVExtract(bv8, start=0))
self.assertEqual(bv8[7], self.mgr.BVExtract(bv8, start=7, end=7))
# BV_ULT,
self.assertEqual(bv8 < const1, self.mgr.BVULT(bv8, const1_8))
# BV_ULE,
self.assertEqual(bv8 <= const1, self.mgr.BVULE(bv8, const1_8))
# BV_UGT
self.assertEqual(bv8 > const1, self.mgr.BVUGT(bv8, const1_8))
# BV_UGE
self.assertEqual(bv8 >= const1, self.mgr.BVUGE(bv8, const1_8))
# BV_LSHL,
self.assertEqual(bv8 << const1, self.mgr.BVLShl(bv8, const1_8))
# BV_LSHR,
self.assertEqual(bv8 >> const1, self.mgr.BVLShr(bv8, const1_8))
# BV_UDIV,
self.assertEqual(bv8 / const1, self.mgr.BVUDiv(bv8, const1_8))
# BV_UREM,
self.assertEqual(bv8 % const1, self.mgr.BVURem(bv8, const1_8))
# The following operators use the infix syntax left.Operator.right
# These includes all signed operators
# BVSLT,
self.assertEqual(self.mgr.BVSLT(bv8, const1_8), bv8.BVSLT(const1_8))
#BVSLE,
self.assertEqual(self.mgr.BVSLE(bv8, const1_8), bv8.BVSLE(const1_8))
#BVComp
self.assertEqual(self.mgr.BVComp(bv8, const1_8), bv8.BVComp(const1_8))
#BVSDiv
self.assertEqual(self.mgr.BVSDiv(bv8, const1_8), bv8.BVSDiv(const1_8))
#BVSRem
self.assertEqual(self.mgr.BVSRem(bv8, const1_8), bv8.BVSRem(const1_8))
#BVAShr
self.assertEqual(self.mgr.BVAShr(bv8, const1_8), bv8.BVAShr(const1_8))
#BVNand
self.assertEqual(self.mgr.BVNand(bv8, const1_8), bv8.BVNand(const1_8))
#BVNor
self.assertEqual(self.mgr.BVNor(bv8, const1_8), bv8.BVNor(const1_8))
#BVXnor
self.assertEqual(self.mgr.BVXnor(bv8, const1_8), bv8.BVXnor(const1_8))
#BVSGT
self.assertEqual(self.mgr.BVSGT(bv8, const1_8), bv8.BVSGT(const1_8))
#BVSGE
self.assertEqual(self.mgr.BVSGE(bv8, const1_8), bv8.BVSGE(const1_8))
#BVSMod
self.assertEqual(self.mgr.BVSMod(bv8, const1_8), bv8.BVSMod(const1_8))
#BVRol,
self.assertEqual(self.mgr.BVRol(bv8, steps=5), bv8.BVRol(5))
#BVRor,
self.assertEqual(self.mgr.BVRor(bv8, steps=5), bv8.BVRor(5))
#BVZExt,
self.assertEqual(self.mgr.BVZExt(bv8, increase=4), bv8.BVZExt(4))
#BVSExt,
self.assertEqual(self.mgr.BVSExt(bv8, increase=4), bv8.BVSExt(4))
#BVRepeat,
self.assertEqual(self.mgr.BVRepeat(bv8, count=5), bv8.BVRepeat(5))
def Reg(in_, clk, clr, rst, arst, out, initval, clk_posedge, arst_posedge):
# INIT: out = initval
# do_arst = Ite(arst_posedge, (!arst & arst'), (arst & !arst'))
# do_clk = Ite(clk_posedge, (!clk & clk'), (clk & !clk'))
# inr = Ite(clr, 0, Ite(rst, initval, in))
# if Modules.functional
# TRANS: out' = Ite(do_clk, Ite(clr, 0, Ite(rst, initval, in)), Ite(rst, initval, in))
# INVAR: True
# trans gives priority to clr signal over rst
# else
# act_trans = (out' = inr)
# pas_trans = (out' = out)
# TRANS: (!do_arst -> ((do_clk -> act_trans) & (!do_clk -> pas_trans))) & (do_arst -> (out' = initval))
# INVAR: True
# trans gives priority to clr signal over rst
vars_ = [in_, clk, clr, rst, arst, out]
comment = "Reg (in, clk, clr, rst, arst, out) = (%s, %s, %s, %s, %s, %s)" % (
tuple([str(x) for x in vars_]))
Logger.log(comment, 3)
init = TRUE()
trans = TRUE()
invar = TRUE()
initvar = None
basename = SEP.join(out.symbol_name().split(
SEP)[:-1]) if SEP in out.symbol_name() else out.symbol_name()
initname = basename + SEP + INIT
if initval is not None and not Modules.symbolic_init:
if out.symbol_type() == BOOL:
binitval = FALSE() if initval == 0 else TRUE()
else:
binitval = BV(initval, out.symbol_type().width)
initvar = binitval
else:
if out.symbol_type() == BOOL:
initvar = Symbol(initname, BOOL)
else:
initvar = Symbol(initname, BVType(out.symbol_type().width))
trans = And(trans, EqualsOrIff(initvar, TS.get_prime(initvar)))
vars_.append(initvar)
init = And(init, EqualsOrIff(out, initvar))
if arst_posedge is not None:
arst_posedge0 = False if arst_posedge else True
arst_posedge1 = True if arst_posedge else False
else:
arst_posedge0 = False
arst_posedge1 = True
if clk_posedge is not None:
clk_posedge0 = False if clk_posedge else True
clk_posedge1 = True if clk_posedge else False
else:
clk_posedge0 = False
clk_posedge1 = True
if clr is not None:
if clr.symbol_type() == BOOL:
clr0 = Not(clr)
clr1 = clr
else:
clr0 = EqualsOrIff(clr, BV(0, 1))
clr1 = EqualsOrIff(clr, BV(1, 1))
else:
clr0 = TRUE()
clr1 = FALSE()
if rst is not None:
if rst.symbol_type() == BOOL:
rst0 = Not(rst)
rst1 = rst
else:
rst0 = EqualsOrIff(rst, BV(0, 1))
rst1 = EqualsOrIff(rst, BV(1, 1))
else:
rst0 = TRUE()
rst1 = FALSE()
if arst is not None:
if arst.symbol_type() == BOOL:
arst0 = Not(arst)
arst1 = arst
else:
arst0 = EqualsOrIff(arst, BV(0, 1))
arst1 = EqualsOrIff(arst, BV(1, 1))
else:
arst0 = TRUE()
arst1 = FALSE()
if clk.symbol_type() == BOOL:
clk0 = Not(clk)
clk1 = clk
else:
clk0 = EqualsOrIff(clk, BV(0, 1))
clk1 = EqualsOrIff(clk, BV(1, 1))
if Modules.abstract_clock:
do_clk = TRUE()
else:
do_clk = And(TS.to_next(clk1), clk0) if clk_posedge1 else And(
TS.to_next(clk0), clk1)
if out.symbol_type() == BOOL:
out0 = FALSE()
else:
out0 = BV(0, out.symbol_type().width)
inr = Ite(clr1, out0, Ite(rst1, initvar, in_))
do_arst = And(TS.to_next(arst1), arst0) if arst_posedge1 else And(
TS.to_next(arst0), arst1)
ndo_arst = Not(do_arst)
ndo_clk = Not(do_clk)
act_trans = EqualsOrIff(inr, TS.get_prime(out))
pas_trans = EqualsOrIff(out, TS.get_prime(out))
if Modules.functional:
f_outr = Ite(rst1, initvar, out)
f_inr = Ite(rst1, initvar, in_)
f_clr_rst = Ite(clr1, out0, f_inr)
trans = And(
trans,
EqualsOrIff(TS.get_prime(out), Ite(do_clk, f_clr_rst, f_outr)))
else:
trans = And(trans, And(Implies(ndo_arst, And(Implies(do_clk, act_trans), Implies(ndo_clk, pas_trans))), \
Implies(do_arst, EqualsOrIff(TS.get_prime(out), initvar))))
trans = simplify(trans)
ts = TS(comment)
ts.vars, ts.state_vars = set([v for v in vars_
if v is not None]), set([out])
ts.set_behavior(init, trans, invar)
return ts
def walk_int_to_bv(self, formula, args, **kwargs):
#pylint: disable=unused-argument
bv_type = BVType(formula.bv_width())
return self.walk_type_to_type(formula, args, INT, bv_type)
def __init__(self, value=SMYBOLIC, *, name=AUTOMATIC, prefix=AUTOMATIC):
if (name is not AUTOMATIC
or prefix is not AUTOMATIC) and value is not SMYBOLIC:
raise TypeError('Can only name symbolic variables')
elif name is not AUTOMATIC and prefix is not AUTOMATIC:
raise ValueError('Can only set either name or prefix not both')
elif name is not AUTOMATIC:
if not isinstance(name, str):
raise TypeError('Name must be string')
elif name in _name_table:
raise ValueError(f'Name {name} already in use')
elif _name_re.fullmatch(name):
warnings.warn(
'Name looks like an auto generated name, this might break things'
)
_name_table[name] = self
elif prefix is not AUTOMATIC:
name = _gen_name(prefix)
_name_table[name] = self
elif name is AUTOMATIC and value is SMYBOLIC:
name = _gen_name()
_name_table[name] = self
self._name = name
T = BVType(self.size)
if value is SMYBOLIC:
self._value = smt.Symbol(name, T)
elif isinstance(value, pysmt.fnode.FNode):
t = value.get_type()
if t is T:
self._value = value
else:
raise TypeError(f'Expected {T} not {t}')
elif isinstance(value, SMTBitVector):
if name is not AUTOMATIC and name != value.name:
warnings.warn(
'Changing the name of a SMTBitVector does not cause a new underlying smt variable to be created'
)
ext = self.size - value.size
if ext < 0:
warnings.warn('Truncating value from {} to {}'.format(
type(value), type(self)))
self._value = value[:self.size].value
elif ext > 0:
self._value = value.zext(ext).value
else:
self._value = value.value
elif isinstance(value, SMTBit):
self._value = smt.Ite(value.value, smt.BVOne(self.size),
smt.BVZero(self.size))
elif isinstance(value, tp.Sequence):
if len(value) != self.size:
raise ValueError('Iterable is not the correct size')
cls = type(self)
B1 = cls.unsized_t[1]
self._value = ft.reduce(lambda acc, elem: acc.concat(elem),
map(B1, value)).value
elif isinstance(value, int):
self._value = smt.BV(value % (1 << self.size), self.size)
elif hasattr(value, '__int__'):
value = int(value)
self._value = smt.BV(value, self.size)
else:
raise TypeError("Can't coerce {} to SMTBitVector".format(
type(value)))
self._value = smt.simplify(self._value)
assert self._value.get_type() is T
def walk_bv_extend(self, formula, args, **kwargs):
#pylint: disable=unused-argument
target_width = formula.bv_width()
if target_width < args[0].width or target_width < 0:
return None
return BVType(target_width)
def parse_string(self, strinput):
hts = HTS()
ts = TS()
nodemap = {}
node_covered = set([])
translist = []
initlist = []
invarlist = []
invar_props = []
ltl_props = []
def getnode(nid):
node_covered.add(nid)
if int(nid) < 0:
return Ite(BV2B(nodemap[str(-int(nid))]), BV(0,1), BV(1,1))
return nodemap[nid]
def binary_op(bvop, bop, left, right):
if (get_type(left) == BOOL) and (get_type(right) == BOOL):
return bop(left, right)
return bvop(B2BV(left), B2BV(right))
def unary_op(bvop, bop, left):
if (get_type(left) == BOOL):
return bop(left)
return bvop(left)
for line in strinput.split(NL):
linetok = line.split()
if len(linetok) == 0:
continue
if linetok[0] == COM:
continue
(nid, ntype, *nids) = linetok
if ntype == SORT:
(stype, *attr) = nids
if stype == BITVEC:
nodemap[nid] = BVType(int(attr[0]))
node_covered.add(nid)
if stype == ARRAY:
nodemap[nid] = ArrayType(getnode(attr[0]), getnode(attr[1]))
node_covered.add(nid)
if ntype == WRITE:
nodemap[nid] = Store(*[getnode(n) for n in nids[1:4]])
if ntype == READ:
nodemap[nid] = Select(getnode(nids[1]), getnode(nids[2]))
if ntype == ZERO:
nodemap[nid] = BV(0, getnode(nids[0]).width)
if ntype == ONE:
nodemap[nid] = BV(1, getnode(nids[0]).width)
if ntype == ONES:
width = getnode(nids[0]).width
nodemap[nid] = BV((2**width)-1, width)
if ntype == REDOR:
width = get_type(getnode(nids[1])).width
zeros = BV(0, width)
nodemap[nid] = BVNot(BVComp(getnode(nids[1]), zeros))
if ntype == REDAND:
width = get_type(getnode(nids[1])).width
ones = BV((2**width)-1, width)
nodemap[nid] = BVComp(getnode(nids[1]), ones)
if ntype == CONSTD:
width = getnode(nids[0]).width
nodemap[nid] = BV(int(nids[1]), width)
if ntype == CONST:
width = getnode(nids[0]).width
nodemap[nid] = BV(bin_to_dec(nids[1]), width)
if ntype == STATE:
if len(nids) > 1:
nodemap[nid] = Symbol(nids[1], getnode(nids[0]))
else:
nodemap[nid] = Symbol((SN%nid), getnode(nids[0]))
ts.add_state_var(nodemap[nid])
if ntype == INPUT:
if len(nids) > 1:
nodemap[nid] = Symbol(nids[1], getnode(nids[0]))
else:
nodemap[nid] = Symbol((SN%nid), getnode(nids[0]))
ts.add_input_var(nodemap[nid])
if ntype == OUTPUT:
if len(nids) > 2:
symbol = Symbol(nids[2], getnode(nids[0]))
else:
symbol = Symbol((SN%nid), getnode(nids[0]))
nodemap[nid] = EqualsOrIff(symbol, B2BV(getnode(nids[1])))
invarlist.append(nodemap[nid])
node_covered.add(nid)
ts.add_output_var(symbol)
if ntype == AND:
nodemap[nid] = binary_op(BVAnd, And, getnode(nids[1]), getnode(nids[2]))
if ntype == CONCAT:
nodemap[nid] = BVConcat(B2BV(getnode(nids[1])), B2BV(getnode(nids[2])))
if ntype == XOR:
nodemap[nid] = binary_op(BVXor, Xor, getnode(nids[1]), getnode(nids[2]))
if ntype == NAND:
bvop = lambda x,y: BVNot(BVAnd(x, y))
bop = lambda x,y: Not(And(x, y))
nodemap[nid] = binary_op(bvop, bop, getnode(nids[1]), getnode(nids[2]))
if ntype == IMPLIES:
nodemap[nid] = BVOr(BVNot(getnode(nids[1])), getnode(nids[2]))
if ntype == NOT:
nodemap[nid] = unary_op(BVNot, Not, getnode(nids[1]))
if ntype == UEXT:
nodemap[nid] = BVZExt(B2BV(getnode(nids[1])), int(nids[2]))
if ntype == OR:
nodemap[nid] = binary_op(BVOr, Or, getnode(nids[1]), getnode(nids[2]))
if ntype == ADD:
nodemap[nid] = BVAdd(B2BV(getnode(nids[1])), B2BV(getnode(nids[2])))
if ntype == SUB:
nodemap[nid] = BVSub(B2BV(getnode(nids[1])), B2BV(getnode(nids[2])))
if ntype == UGT:
nodemap[nid] = BVUGT(B2BV(getnode(nids[1])), B2BV(getnode(nids[2])))
if ntype == UGTE:
nodemap[nid] = BVUGE(B2BV(getnode(nids[1])), B2BV(getnode(nids[2])))
if ntype == ULT:
nodemap[nid] = BVULT(B2BV(getnode(nids[1])), B2BV(getnode(nids[2])))
if ntype == ULTE:
nodemap[nid] = BVULE(B2BV(getnode(nids[1])), B2BV(getnode(nids[2])))
if ntype == EQ:
nodemap[nid] = BVComp(getnode(nids[1]), getnode(nids[2]))
if ntype == NE:
nodemap[nid] = BVNot(BVComp(getnode(nids[1]), getnode(nids[2])))
if ntype == MUL:
nodemap[nid] = BVMul(B2BV(getnode(nids[1])), B2BV(getnode(nids[2])))
if ntype == SLICE:
nodemap[nid] = BVExtract(B2BV(getnode(nids[1])), int(nids[3]), int(nids[2]))
if ntype == SLL:
nodemap[nid] = BVLShl(getnode(nids[1]), getnode(nids[2]))
if ntype == SRA:
nodemap[nid] = BVAShr(getnode(nids[1]), getnode(nids[2]))
if ntype == SRL:
nodemap[nid] = BVLShr(getnode(nids[1]), getnode(nids[2]))
if ntype == ITE:
if (get_type(getnode(nids[2])) == BOOL) or (get_type(getnode(nids[3])) == BOOL):
nodemap[nid] = Ite(BV2B(getnode(nids[1])), BV2B(getnode(nids[2])), BV2B(getnode(nids[3])))
else:
nodemap[nid] = Ite(BV2B(getnode(nids[1])), getnode(nids[2]), getnode(nids[3]))
if ntype == NEXT:
if (get_type(getnode(nids[1])) == BOOL) or (get_type(getnode(nids[2])) == BOOL):
nodemap[nid] = EqualsOrIff(BV2B(TS.get_prime(getnode(nids[1]))), BV2B(getnode(nids[2])))
else:
nodemap[nid] = EqualsOrIff(TS.get_prime(getnode(nids[1])), getnode(nids[2]))
translist.append(getnode(nid))
if ntype == INIT:
if (get_type(getnode(nids[1])) == BOOL) or (get_type(getnode(nids[2])) == BOOL):
nodemap[nid] = EqualsOrIff(BV2B(getnode(nids[1])), BV2B(getnode(nids[2])))
else:
nodemap[nid] = EqualsOrIff(getnode(nids[1]), getnode(nids[2]))
initlist.append(getnode(nid))
if ntype == CONSTRAINT:
nodemap[nid] = BV2B(getnode(nids[0]))
invarlist.append(getnode(nid))
if ntype == BAD:
nodemap[nid] = getnode(nids[0])
invar_props.append(Not(BV2B(getnode(nid))))
if nid not in nodemap:
Logger.error("Unknown node type \"%s\""%ntype)
if Logger.level(1):
name = lambda x: str(nodemap[x]) if nodemap[x].is_symbol() else x
uncovered = [name(x) for x in nodemap if x not in node_covered]
uncovered.sort()
if len(uncovered) > 0:
Logger.warning("Unlinked nodes \"%s\""%",".join(uncovered))
if not self.symbolic_init:
init = simplify(And(initlist))
else:
init = TRUE()
trans = simplify(And(translist))
invar = simplify(And(invarlist))
ts.set_behavior(init, trans, invar)
hts.add_ts(ts)
return (hts, invar_props, ltl_props)
def add_free_var(self, free_var):
""" Creates the encoding for free_var """
# We create a BV variable
enc_val = FreshSymbol(BVType(SymbolicGrounding.MAX_BV))
self.fvars2encvars.add(free_var, enc_val)
return enc_val
def get_sts(self, name, params):
in_port, max_val, clk = list(params)
max_val = int(max_val)
zero = BV(0, 1)
one = BV(1, 1)
tracking = Symbol("%s.tracking" % name, BOOL)
end = Symbol("%s.end" % name, BOOL)
packet = Symbol("%s.packet" % name,
BVType(in_port.symbol_type().width))
max_width = math.ceil(math.log(max_val) / math.log(2))
max_bvval = BV(max_val, max_width)
count = Symbol("%s.count" % name, BVType(max_width))
pos_clk = And(EqualsOrIff(clk, zero),
EqualsOrIff(TS.to_next(clk), one))
neg_clk = Not(
And(EqualsOrIff(clk, zero), EqualsOrIff(TS.to_next(clk), one)))
init = []
init.append(EqualsOrIff(count, BV(0, max_width)))
init.append(EqualsOrIff(tracking, FALSE()))
init = And(init)
invar = EqualsOrIff(end, EqualsOrIff(max_bvval, count))
trans = []
# tracking -> next(tracking);
trans.append(Implies(tracking, TS.to_next(tracking)))
# tracking -> (next(packet) = packet);
trans.append(Implies(tracking, EqualsOrIff(TS.to_next(packet),
packet)))
# !tracking & next(tracking) -> (next(clk) = 0_1);
trans.append(
Implies(And(Not(tracking), TS.to_next(tracking)),
EqualsOrIff(TS.to_next(clk), zero)))
# ((clk = 0_1) & (next(clk) = 1_1) & next(tracking)) -> (packet = in);
trans.append(
Implies(And(pos_clk, TS.to_next(tracking)),
EqualsOrIff(packet, in_port)))
# ((clk = 0_1) & (next(clk) = 1_1) & tracking) -> (next(count) = (count + 1_8));
trans.append(
Implies(
And(pos_clk, tracking),
EqualsOrIff(TS.to_next(count), BVAdd(count, BV(1,
max_width)))))
# (!((clk = 0_1) & (next(clk) = 1_1))) -> (next(count) = count);
trans.append(Implies(neg_clk, EqualsOrIff(count, TS.to_next(count))))
# ((clk = 0_1) & (next(clk) = 1_1) & !tracking) -> (next(count) = count);
trans.append(
Implies(And(pos_clk, Not(tracking)),
EqualsOrIff(count, TS.to_next(count))))
trans = And(trans)
ts = TS()
ts.vars, ts.init, ts.invar, ts.trans = set(
[tracking, end, packet, count]), init, invar, trans
return ts
def test_bv_0_add(self):
x = Symbol("x", BVType(32))
f = BVAdd(BVZero(32), x)
self.check_equal_and_valid(f, x)
def test_bv_ult_zero(self):
x = Symbol("x", BVType(32))
f = BVULT(x, BVZero(32))
self.check_equal_and_valid(f, Bool(False))
