def test_simplify(self):
algebra1 = BooleanAlgebra()
algebra2 = BooleanAlgebra()
a = algebra1.Symbol('a')
b = algebra1.Symbol('b')
c = algebra1.Symbol('c')
_0 = algebra1.FALSE
_1 = algebra1.TRUE
# Idempotence
self.assertEqual(a, (a & a).simplify())
# Idempotence + Associativity
self.assertEqual(a | b, (a | (a | b)).simplify())
# Annihilation
self.assertEqual(_0, (a & _0).simplify())
self.assertEqual(_1, (a | _1).simplify())
# Identity
self.assertEqual(a, (a & _1).simplify())
self.assertEqual(a, (a | _0).simplify())
# Complementation
self.assertEqual(_0, (a & ~a).simplify())
self.assertEqual(_1, (a | ~a).simplify())
# Absorption
self.assertEqual(a, (a & (a | b)).simplify())
self.assertEqual(a, (a | (a & b)).simplify())
self.assertEqual(b & a, ((b & a) | (b & a & c)).simplify())
# Elimination
self.assertEqual(a, ((a & ~b) | (a & b)).simplify())
expected = algebra1.parse('(a&b)|(b&c)|(a&c)')
result = algebra1.parse('(~a&b&c) | (a&~b&c) | (a&b&~c) | (a&b&c)', simplify=True)
self.assertEqual(expected, result)
expected = algebra1.parse('(a&b)|(b&c)|(a&c)')
result = algebra2.parse('(~a&b&c) | (a&~b&c) | (a&b&~c) | (a&b&c)', simplify=True)
self.assertEqual(expected, result)
expected = algebra1.parse('b&d')
result = algebra1.parse('(a&b&c&d) | (b&d)', simplify=True)
self.assertEqual(expected, result)
expected = algebra1.parse('b&d')
result = algebra2.parse('(a&b&c&d) | (b&d)', simplify=True)
self.assertEqual(expected, result)
expected = algebra1.parse('(~b&~d&a) | (~c&~d&b) | (a&c&d)', simplify=True)
result = algebra1.parse('''(~a&b&~c&~d) | (a&~b&~c&~d) | (a&~b&c&~d) |
(a&~b&c&d) | (a&b&~c&~d) | (a&b&c&d)''', simplify=True)
self.assertEqual(expected.pretty(), result.pretty())
expected = algebra1.parse('(~b&~d&a) | (~c&~d&b) | (a&c&d)', simplify=True)
result = algebra2.parse('''(~a&b&~c&~d) | (a&~b&~c&~d) | (a&~b&c&~d) |
(a&~b&c&d) | (a&b&~c&~d) | (a&b&c&d)''', simplify=True)
self.assertEqual(expected.pretty(), result.pretty())
def test_simplify(self):
algebra = BooleanAlgebra()
a = algebra.Symbol('a')
self.assertEqual(~a, ~a)
assert algebra.Symbol('a') == algebra.Symbol('a')
self.assertNotEqual(a, algebra.parse('~~a'))
self.assertEqual(a, (~~a).simplify())
self.assertEqual(~a, (~~~a).simplify())
self.assertEqual(a, (~~~~a).simplify())
self.assertEqual((~(a & a & a)).simplify(), (~(a & a & a)).simplify())
self.assertEqual(a, algebra.parse('~~a', simplify=True))
algebra2 = BooleanAlgebra()
self.assertEqual(a, algebra2.parse('~~a', simplify=True))
def test_simplify_complex_expression_parsed_with_simplify(self):
# FIXME: THIS SHOULD NOT FAIL
algebra = BooleanAlgebra()
a = algebra.Symbol('a')
b = algebra.Symbol('b')
c = algebra.Symbol('c')
d = algebra.Symbol('d')
test_expression_str = '''
(~a&~b&~c&~d) | (~a&~b&~c&d) | (~a&b&~c&~d) |
(~a&b&c&d) | (~a&b&~c&d) | (~a&b&c&~d) |
(a&~b&~c&d) | (~a&b&c&d) | (a&~b&c&d) | (a&b&c&d)
'''
parsed = algebra.parse(test_expression_str, simplify=True)
test_expression = ((~a & ~b & ~c & ~d) | (~a & ~b & ~c & d) |
(~a & b & ~c & ~d) | (~a & b & c & d) |
(~a & b & ~c & d) | (~a & b & c & ~d) |
(a & ~b & ~c & d) | (~a & b & c & d) |
(a & ~b & c & d) | (a & b & c & d)).simplify()
# we have a different simplify behavior for expressions built from python expressions
# vs. expression built from an object tree vs. expression built from a parse
self.assertEqual(parsed.pretty(), test_expression.pretty())
def test_dual(self):
algebra = BooleanAlgebra()
self.assertEqual(algebra.AND(algebra.Symbol('a'), algebra.Symbol('b')).dual, algebra.OR)
self.assertEqual(algebra.OR(algebra.Symbol('a'), algebra.Symbol('b')).dual, algebra.AND)
self.assertEqual(algebra.parse('a|b').dual, algebra.AND)
self.assertEqual(algebra.parse('a&b').dual, algebra.OR)
def test_parse_with_mixed_operators_multilines_and_custom_symbol(self):
class MySymbol(Symbol):
pass
expr_str = '''(a or ~ b +_c ) and
d & ( ! e_
| (my * g OR 1 or 0) ) AND that '''
algebra = BooleanAlgebra(Symbol_class=MySymbol)
expr = algebra.parse(expr_str)
expected = algebra.AND(
algebra.OR(
algebra.Symbol('a'),
algebra.NOT(algebra.Symbol('b')),
algebra.Symbol('_c'),
),
algebra.Symbol('d'),
algebra.OR(
algebra.NOT(algebra.Symbol('e_')),
algebra.OR(
algebra.AND(
algebra.Symbol('my'),
algebra.Symbol('g'),
),
algebra.TRUE,
algebra.FALSE,
),
),
algebra.Symbol('that'),
)
self.assertEqual(expected.pretty(), expr.pretty())
self.assertEqual(expected, expr)
def test_parse_invalid_nested_and_should_raise_a_proper_exception(self):
algebra = BooleanAlgebra()
expr = '''a (and b)'''
try:
algebra.parse(expr)
except ParseError as pe:
assert pe.error_code == PARSE_INVALID_NESTING
def test_parse_side_by_side_symbols_raise_exception(self):
algebra = BooleanAlgebra()
expr_str = 'a b'
try:
algebra.parse(expr_str)
except ParseError as pe:
assert pe.error_code == PARSE_INVALID_SYMBOL_SEQUENCE
def test_parse_side_by_side_symbols_with_parens_raise_exception(self):
algebra = BooleanAlgebra()
expr_str = '(a) (b)'
try:
algebra.parse(expr_str)
except ParseError as pe:
assert pe.error_code == PARSE_INVALID_NESTING
def test_allowing_additional_characters_in_tokens(self):
algebra = BooleanAlgebra(allowed_in_token=('.', '_', '-', '+'))
test_expr = 'l-a AND b+c'
expr = algebra.parse(test_expr)
expected = algebra.AND(algebra.Symbol('l-a'), algebra.Symbol('b+c'))
self.assertEqual(expected, expr)
def test_parse_side_by_side_symbols_should_raise_exception_but_not2(self):
algebra = BooleanAlgebra()
expr_str = '(a or b) c'
try:
algebra.parse(expr_str)
except ParseError as pe:
assert pe.error_code == PARSE_INVALID_EXPRESSION
def test_parse(self):
algebra = BooleanAlgebra()
a, b, c = algebra.Symbol('a'), algebra.Symbol('b'), algebra.Symbol('c')
self.assertEqual(algebra.parse('0'), algebra.FALSE)
self.assertEqual(algebra.parse('(0)'), algebra.FALSE)
self.assertEqual(algebra.parse('1') , algebra.TRUE)
self.assertEqual(algebra.parse('(1)'), algebra.TRUE)
self.assertEqual(algebra.parse('a'), a)
self.assertEqual(algebra.parse('(a)'), a)
self.assertEqual(algebra.parse('(a)'), a)
self.assertEqual(algebra.parse('~a'), algebra.parse('~(a)'))
self.assertEqual(algebra.parse('~(a)'), algebra.parse('(~a)'))
self.assertEqual(algebra.parse('~a'), ~a)
self.assertEqual(algebra.parse('(~a)'), ~a)
self.assertEqual(algebra.parse('~~a', simplify=True), (~~a).simplify())
self.assertEqual(algebra.parse('a&b'), a & b)
self.assertEqual(algebra.parse('~a&b'), ~a & b)
self.assertEqual(algebra.parse('a&~b'), a & ~b)
self.assertEqual(algebra.parse('a&b&c'), algebra.parse('a&b&c'))
self.assertEqual(algebra.parse('a&b&c'), algebra.AND(a, b, c))
self.assertEqual(algebra.parse('~a&~b&~c'), algebra.parse('~a&~b&~c'))
self.assertEqual(algebra.parse('~a&~b&~c'), algebra.AND(~a, ~b, ~c))
self.assertEqual(algebra.parse('a|b'), a | b)
self.assertEqual(algebra.parse('~a|b'), ~a | b)
self.assertEqual(algebra.parse('a|~b'), a | ~b)
self.assertEqual(algebra.parse('a|b|c'), algebra.parse('a|b|c'))
self.assertEqual(algebra.parse('a|b|c'), algebra.OR(a, b, c))
self.assertEqual(algebra.parse('~a|~b|~c'), algebra.OR(~a, ~b, ~c))
self.assertEqual(algebra.parse('(a|b)'), a | b)
self.assertEqual(algebra.parse('a&(a|b)', simplify=True), (a & (a | b)).simplify())
self.assertEqual(algebra.parse('a&(a|~b)', simplify=True), (a & (a | ~b)).simplify())
self.assertEqual(algebra.parse('(a&b)|(b&((c|a)&(b|(c&a))))', simplify=True), ((a & b) | (b & ((c | a) & (b | (c & a))))).simplify())
self.assertEqual(algebra.parse('(a&b)|(b&((c|a)&(b|(c&a))))', simplify=True), algebra.parse('a&b | b&(c|a)&(b|c&a)', simplify=True))
def test_or(self):
algebra = BooleanAlgebra()
exp = algebra.parse("a|b|c")
for a in [True, False]:
for b in [True, False]:
for c in [True, False]:
self.assertEqual(exp(a=a, b=b, c=c), a or b or c)
def test_init(self):
algebra = BooleanAlgebra()
self.assertRaises(TypeError, algebra.NOT)
self.assertRaises(TypeError, algebra.NOT, 'a', 'b')
algebra.NOT(algebra.Symbol('a'))
self.assertEqual(algebra.FALSE, (algebra.NOT(algebra.TRUE)).simplify())
self.assertEqual(algebra.TRUE, (algebra.NOT(algebra.FALSE)).simplify())
def test_and(self):
algebra = BooleanAlgebra()
exp = algebra.parse("a&b&c")
for a in [True, False]:
for b in [True, False]:
for c in [True, False]:
self.assertEqual(exp(a=a, b=b, c=c), a and b and c)
def test_normalize(self):
algebra = BooleanAlgebra()
expr = algebra.parse("a&b")
self.assertEqual(algebra.dnf(expr), expr)
self.assertEqual(algebra.cnf(expr), expr)
expr = algebra.parse("a|b")
self.assertEqual(algebra.dnf(expr), expr)
self.assertEqual(algebra.cnf(expr), expr)
expr = algebra.parse("(a&b)|(c&b)")
result_dnf = algebra.parse("(a&b)|(b&c)")
result_cnf = algebra.parse("b&(a|c)")
self.assertEqual(algebra.dnf(expr), result_dnf)
self.assertEqual(algebra.cnf(expr), result_cnf)
expr = algebra.parse("(a|b)&(c|b)")
result_dnf = algebra.parse("b|(a&c)")
result_cnf = algebra.parse("(a|b)&(b|c)")
self.assertEqual(algebra.dnf(expr), result_dnf)
self.assertEqual(algebra.cnf(expr), result_cnf)
expr = algebra.parse('((s|a)&(s|b)&(s|c)&(s|d)&(e|c|d))|(a&e&d)')
result = algebra.normalize(expr, expr.AND)
expected = algebra.parse('(a|s)&(b|e|s)&(c|d|e)&(c|e|s)&(d|s)')
self.assertEqual(result, expected)
def test_cancel(self):
algebra = BooleanAlgebra()
a = algebra.Symbol('a')
self.assertEqual(~a, (~a).cancel())
self.assertEqual(a, algebra.parse('~~a').cancel())
self.assertEqual(~a, algebra.parse('~~~a').cancel())
self.assertEqual(a, algebra.parse('~~~~a').cancel())
def test_parse_raise_ParseError9(self):
algebra = BooleanAlgebra()
expr = '+ l-a'
try:
algebra.parse(expr)
self.fail("Exception should be raised when parsing '%s'" % expr)
except ParseError as pe:
assert pe.error_code == PARSE_INVALID_OPERATOR_SEQUENCE
def test_composite(self):
algebra = BooleanAlgebra()
exp = algebra.parse("!(a|b&(a|!c))")
for a in [True, False]:
for b in [True, False]:
for c in [True, False]:
self.assertEqual(exp(a=a, b=b, c=c),
not (a or b and (a or not c)))
def test_demorgan(self):
algebra = BooleanAlgebra()
a = algebra.Symbol('a')
b = algebra.Symbol('b')
self.assertEqual(algebra.parse('~(a&b)').demorgan(), ~a | ~b)
self.assertEqual(
algebra.parse('~(a|b|c)').demorgan(), algebra.parse('~a&~b&~c'))
self.assertEqual(algebra.parse('~(~a&b)').demorgan(), a | ~b)
def test_printing(self):
parse = BooleanAlgebra().parse
self.assertEqual(str(parse('a&a')), 'a&a')
self.assertEqual(repr(parse('a&a')), "AND(Symbol('a'), Symbol('a'))")
self.assertEqual(str(parse('a|a')), 'a|a')
self.assertEqual(repr(parse('a|a')), "OR(Symbol('a'), Symbol('a'))")
self.assertEqual(str(parse('(a|b)&c')), '(a|b)&c')
self.assertEqual(repr(parse('(a|b)&c')), "AND(OR(Symbol('a'), Symbol('b')), Symbol('c'))")
def test_subs_default(self):
algebra = BooleanAlgebra()
a, b, c = algebra.Symbol('a'), algebra.Symbol('b'), algebra.Symbol('c')
expr = a & b | c
self.assertEqual(expr.subs({}, default=algebra.TRUE).simplify(), algebra.TRUE)
self.assertEqual(expr.subs({a: algebra.FALSE, c: algebra.FALSE}, default=algebra.TRUE).simplify(), algebra.FALSE)
self.assertEqual(algebra.TRUE.subs({}, default=algebra.FALSE).simplify(), algebra.TRUE)
self.assertEqual(algebra.FALSE.subs({}, default=algebra.TRUE).simplify(), algebra.FALSE)
def test_parse_raise_ParseError7(self):
algebra = BooleanAlgebra()
expr = 'l-a AND'
try:
algebra.parse(expr)
self.fail("Exception should be raised when parsing '%s'" % expr)
except ParseError as pe:
assert pe.error_code == PARSE_UNKNOWN_TOKEN
def test_printing(self):
algebra = BooleanAlgebra()
a = algebra.Symbol('a')
self.assertEqual(str(~a), '~a')
self.assertEqual(repr(~a), "NOT(Symbol('a'))")
expr = algebra.parse('~(a&a)')
self.assertEqual(str(expr), '~(a&a)')
self.assertEqual(repr(expr), "NOT(AND(Symbol('a'), Symbol('a')))")
def test_subtract(self):
parse = BooleanAlgebra().parse
expr = parse('a&b&c')
p1 = parse('b&d')
p2 = parse('a&c')
result = parse('b')
self.assertEqual(expr.subtract(p1, simplify=True), expr)
self.assertEqual(expr.subtract(p2, simplify=True), result)
def test_order(self):
algebra = BooleanAlgebra()
x = algebra.Symbol(1)
y = algebra.Symbol(2)
self.assertTrue(x < ~x)
self.assertTrue(~x > x)
self.assertTrue(~x < y)
self.assertTrue(y > ~x)
def test_parse_invalid_nested_and_should_raise_a_proper_exception(self):
algebra = BooleanAlgebra()
expr = '''a (and b)'''
with self.assertRaises(ParseError) as context:
algebra.parse(expr)
self.assertEqual(context.exception.error_code,
PARSE_INVALID_NESTING)
def test_subs(self):
algebra = BooleanAlgebra()
a, b, c = algebra.Symbol('a'), algebra.Symbol('b'), algebra.Symbol('c')
expr = a & b | c
self.assertEqual(expr.subs({a: b}).simplify(), b | c)
self.assertEqual(expr.subs({a: a}).simplify(), expr)
self.assertEqual(expr.subs({a: b | c}).simplify(), algebra.parse('(b|c)&b|c').simplify())
self.assertEqual(expr.subs({a & b: a}).simplify(), a | c)
self.assertEqual(expr.subs({c: algebra.TRUE}).simplify(), algebra.TRUE)
def test_get_symbols_return_all_symbols_in_original_order(self):
alg = BooleanAlgebra()
exp = alg.parse('a and b or True and a and c')
assert [
alg.Symbol('a'),
alg.Symbol('b'),
alg.Symbol('a'),
alg.Symbol('c')
] == exp.get_symbols()
def test_order(self):
algebra = BooleanAlgebra()
x, y, z = algebra.Symbol(1), algebra.Symbol(2), algebra.Symbol(3)
self.assertTrue(algebra.AND(x, y) < algebra.AND(x, y, z))
self.assertTrue(not algebra.AND(x, y) > algebra.AND(x, y, z))
self.assertTrue(algebra.AND(x, y) < algebra.AND(x, z))
self.assertTrue(not algebra.AND(x, y) > algebra.AND(x, z))
self.assertTrue(algebra.AND(x, y) < algebra.AND(y, z))
self.assertTrue(not algebra.AND(x, y) > algebra.AND(y, z))
self.assertTrue(not algebra.AND(x, y) < algebra.AND(x, y))
self.assertTrue(not algebra.AND(x, y) > algebra.AND(x, y))
def test_distributive(self):
algebra = BooleanAlgebra()
a = algebra.Symbol('a')
b = algebra.Symbol('b')
c = algebra.Symbol('c')
d = algebra.Symbol('d')
e = algebra.Symbol('e')
self.assertEqual((a & (b | c)).distributive(), (a & b) | (a & c))
t1 = algebra.AND(a, (b | c), (d | e))
t2 = algebra.OR(algebra.AND(a, b, d), algebra.AND(a, b, e), algebra.AND(a, c, d), algebra.AND(a, c, e))
self.assertEqual(t1.distributive(), t2)
