def test_grouping(self):
for n_str in self.numbers:
assert vexpr.Number(float(n_str)) == parser.parse("(" + n_str +
")")
for v in self.variables:
assert vexpr.Variable(v) == parser.parse("(" + v + ")")
def test_loop(self):
assert isinstance(
parser.parse(" [{?false++{s:=1; s:=2;}}*] true ").program,
vexpr.Loop)
assert isinstance(
parser.parse(" 1=1 -> [{?false++{s:=1; s:=2;}}*] true "),
vexpr.Imply)
assert isinstance(
parser.parse(" [{?false++{s:=1; s:=2;}}*; x:=15] true "),
vexpr.Box)
assert isinstance(
parser.parse(
" 1=1 -> [{?false++{s:=1; s:=2;}}*@invariant(1=1&2=2, false)] true "
),
vexpr.Imply,
)
def test_power(self):
assert isinstance(parser.parse("x^2"), vexpr.Power)
assert isinstance(parser.parse("2^2"), vexpr.Power)
assert isinstance(parser.parse("x^(2)"), vexpr.Power)
assert isinstance(parser.parse("(x)^2"), vexpr.Power)
assert isinstance(parser.parse("(-x)^2"), vexpr.Power)
assert isinstance(parser.parse("x^-2"), vexpr.Power)
assert isinstance(parser.parse("x^(-x)"), vexpr.Power)
def test_plus(self):
assert isinstance(parser.parse("a+b+c+d"), vexpr.Plus)
assert isinstance(parser.parse("(x + x)^2"), vexpr.Power)
assert isinstance(parser.parse("x+x^2"), vexpr.Plus)
assert isinstance(parser.parse("(x*x*y)+x"), vexpr.Plus)
assert isinstance(parser.parse("-x+-(x*-y*-x)"), vexpr.Plus)
assert isinstance(parser.parse("(x*x*-y)+-x"), vexpr.Plus)
assert isinstance(parser.parse("x*y+y*x"), vexpr.Plus)
def test_minus(self):
assert isinstance(parser.parse("a-b-c-d"), vexpr.Minus)
assert isinstance(parser.parse("(x-x)^2"), vexpr.Power)
assert isinstance(parser.parse("x-x^2"), vexpr.Minus)
assert isinstance(parser.parse("(x*x*y)-x"), vexpr.Minus)
assert isinstance(parser.parse("-x--(x*-y*-x)"), vexpr.Minus)
assert isinstance(parser.parse("(x*x*-y)--x"), vexpr.Minus)
assert isinstance(parser.parse("x*y-y*x"), vexpr.Minus)
def test_box(self):
assert isinstance(parser.parse(" [x:=12 + 2;] true "), vexpr.Box)
assert isinstance(parser.parse(" [?false] true "), vexpr.Box)
assert isinstance(parser.parse(" [?false;] true "), vexpr.Box)
assert isinstance(parser.parse(" [?false++s:=1;] true "), vexpr.Box)
assert isinstance(parser.parse(" [?false;++s:=1;] true "), vexpr.Box)
assert isinstance(parser.parse(" [?false++s:=1;] true "), vexpr.Box)
assert isinstance(parser.parse(" [?false++{s:=1; s:=2;}] true "),
vexpr.Box)
def test_previously_failed(self):
assert isinstance(parser.parse("x^2 <= 1/2"), vexpr.Formula)
assert isinstance(parser.parse("x^2 <= 1/2 & y^2 <= 1/3"),
vexpr.Formula)
assert isinstance(
parser.parse(
"1=1 -> [ {x'=1, v'=a, z' = \n 12 & true}] 1=1 "),
vexpr.Imply,
)
assert isinstance(
parser.parse(
"x^2 <= 1/2 & y^2 <= 1/3 -> [ {x'=-x - (1117*y)/500}]true"),
vexpr.Imply,
)
assert isinstance(
parser.parse("""
x^2 <= 1/2 & y^2 <= 1/3 -> [ {x'=-x - (1117*y)/500 + (439*y^3)/200 - (333*y^5)/500, y'=x + (617*y)/500 - (439*y^3)/200 + (333*y^5)/500} ] (x - 4*y < 8)
"""),
vexpr.Formula,
)
def test_whitespaces(self):
assert isinstance(parser.parse(" a <= b"), vexpr.LessEq)
assert isinstance(parser.parse(" a"), vexpr.Variable)
assert isinstance(parser.parse(" a <= b "), vexpr.LessEq)
assert isinstance(parser.parse(" a "), vexpr.Variable)
assert isinstance(parser.parse("a <= b "), vexpr.LessEq)
assert isinstance(parser.parse("a "), vexpr.Variable)
def test_base_formulas(self):
asdf = parser.parse("true")
assert isinstance(asdf, vexpr.TrueF)
assert isinstance(parser.parse("false"), vexpr.FalseF)
assert isinstance(parser.parse("a < b"), vexpr.Less)
assert isinstance(parser.parse("a>b"), vexpr.Greater)
assert isinstance(parser.parse("a>= b"), vexpr.GreaterEq)
assert isinstance(parser.parse("a <= b"), vexpr.LessEq)
def test_ode(self):
assert isinstance(parser.parse("[{x'=1&true}]1=1"), vexpr.Box)
assert isinstance(parser.parse("[{x'=1,v'=a & true}] 1=1 "), vexpr.Box)
assert isinstance(parser.parse("[{x'=1, v'=a, z'=12 & true}] 1=1 "),
vexpr.Box)
assert isinstance(
parser.parse("[{x'=1, v'=a, z' = \n 12 & true}] 1=1 "),
vexpr.Box)
assert isinstance(
parser.parse(
"1=1 -> [{x'=1, v'=a, z' = \n 12 & true}] 1=1 "),
vexpr.Imply,
)
assert isinstance(
parser.parse(
"1=1 -> [{x'=1, v'=a, z' = \n 12 & true}@invariant(true)] 1=1 "
),
vexpr.Imply,
)
def test_numbers(self):
for n_str in self.numbers:
assert vexpr.Number(float(n_str)) == parser.parse(n_str)
def test_imply(self):
assert isinstance(parser.parse("1=1 -> false -> true"), vexpr.Imply)
def test_mult(self):
assert isinstance(parser.parse("(x*x)^2"), vexpr.Power)
assert isinstance(parser.parse("x*x^2"), vexpr.Times)
assert isinstance(parser.parse("x * x*y*x"), vexpr.Times)
assert isinstance(parser.parse("-x*x*-y*-x"), vexpr.Times)
assert isinstance(parser.parse("-(x*x*-y)*-x"), vexpr.Times)
def test_divide(self):
assert isinstance(parser.parse("(x/x)^2"), vexpr.Power)
assert isinstance(parser.parse("x/x^2"), vexpr.Divide)
assert isinstance(parser.parse("x / x*y*x"), vexpr.Divide)
assert isinstance(parser.parse("-x/x/-y/-x"), vexpr.Divide)
assert isinstance(parser.parse("-(x/x/-y)/-x"), vexpr.Divide)
def test_equiv(self):
assert isinstance(parser.parse("1=1 <-> false"), vexpr.Equiv)
def test_choice_seq_precedence(self):
r = parser.parse(" [?false++s:=1; s:=2;] true ")
assert isinstance(r.program, vexpr.Choice)
assert isinstance(r, vexpr.Box)
def test_neg(self):
for v in self.variables:
neg_variable = parser.parse("-" + v)
assert isinstance(neg_variable, vexpr.Neg)
assert vexpr.Variable(v) == neg_variable.child
assert isinstance(parser.parse("-x^(-x)"), vexpr.Neg)
def test_variables(self):
for v in self.variables:
assert vexpr.Variable(v) == parser.parse(v)
def test_exists(self):
assert isinstance(
parser.parse(r" r <= 0 -> \exists f (x=f -> [{x'=r+x^2}]x=f)"),
vexpr.Imply,
)
def test_assign(self):
assert isinstance(parser.parse(" [x:=12 + 2;] true "), vexpr.Box)
def test_not(self):
assert isinstance(parser.parse("!false"), vexpr.Not)
assert isinstance(parser.parse("! true"), vexpr.Not)
def test_and(self):
assert isinstance(parser.parse("(true)&(true)"), vexpr.And)
assert isinstance(parser.parse("true & true"), vexpr.And)
assert isinstance(parser.parse("true & true & true & true"),
vexpr.And)
