def test_str_to_int():
r = parse('a = "hehe"')
g = tx.Tree.from_recursive_ast(r)
var_str2int = {'a': ['hehe', 'haha']}
tx.sub_constants(g, var_str2int)
f = g.to_recursive_ast()
s = f.flatten()
assert s == '( a = 0 )'
x = '(loc = "s2") -> X((((env_alice = "left") && (env_bob = "bright"))))'
var_str2int = {
'loc': ['s0', 's2'],
'env_alice': ['left', 'right'],
'env_bob': ['bleft', 'bright']}
r = parse(x)
print(repr(r))
g = tx.Tree.from_recursive_ast(r)
print(g)
tx.sub_constants(g, var_str2int)
print(str(g))
f = g.to_recursive_ast()
print(repr(f))
s = f.flatten()
print(s)
assert s == ('( ( loc = 1 ) -> '
'( X ( ( env_alice = 0 ) & ( env_bob = 1 ) ) ) )')
def test_str_to_int():
r = parse('a = "hehe"')
g = tx.Tree.from_recursive_ast(r)
var_str2int = {'a': ['hehe', 'haha']}
tx.sub_constants(g, var_str2int)
f = g.to_recursive_ast()
s = f.flatten()
assert s == '( a = 0 )'
x = '(loc = "s2") -> X((((env_alice = "left") && (env_bob = "bright"))))'
var_str2int = {
'loc': ['s0', 's2'],
'env_alice': ['left', 'right'],
'env_bob': ['bleft', 'bright']
}
r = parse(x)
print(repr(r))
g = tx.Tree.from_recursive_ast(r)
print(g)
tx.sub_constants(g, var_str2int)
print(str(g))
f = g.to_recursive_ast()
print(repr(f))
s = f.flatten()
print(s)
assert s == ('( ( loc = 1 ) -> '
'( X ( ( env_alice = 0 ) & ( env_bob = 1 ) ) ) )')
def parse_parse_test(formula, expected_length):
# If expected_length is None, then the formula is malformed, and
# thus we expect parsing to fail.
if expected_length is not None:
assert len(parse(formula)) == expected_length
else:
with pytest.raises(Exception):
parse(formula)
def generate_JTLV_LTL(spec):
"""Return the LTLSPEC for JTLV.
It takes as input a GRSpec object. N.B., assumes all variables
are Boolean (i.e., atomic propositions).
"""
formula = spec.to_canon()
parse(formula) # Raises exception if syntax error
specLTL = spec.to_jtlv()
logger.debug(''.join([str(x) for x in specLTL]) )
assumption = specLTL[0]
guarantee = specLTL[1]
assumption = re.sub(r'\b'+'True'+r'\b', 'TRUE', assumption)
guarantee = re.sub(r'\b'+'True'+r'\b', 'TRUE', guarantee)
assumption = re.sub(r'\b'+'False'+r'\b', 'FALSE', assumption)
guarantee = re.sub(r'\b'+'False'+r'\b', 'FALSE', guarantee)
assumption = assumption.replace('==', '=')
guarantee = guarantee.replace('==', '=')
assumption = assumption.replace('&&', '&')
guarantee = guarantee.replace('&&', '&')
assumption = assumption.replace('||', '|')
guarantee = guarantee.replace('||', '|')
# Replace any environment variable var in spec with e.var and replace any
# system variable var with s.var
for var in spec.env_vars.keys():
assumption = re.sub(r'\b'+var+r'\b', 'e.'+var, assumption)
guarantee = re.sub(r'\b'+var+r'\b', 'e.'+var, guarantee)
for var in spec.sys_vars.keys():
assumption = re.sub(r'\b'+var+r'\b', 's.'+var, assumption)
guarantee = re.sub(r'\b'+var+r'\b', 's.'+var, guarantee)
# Assumption
ltl = 'LTLSPEC\n(\n'
if assumption:
ltl += assumption
else:
ltl += "TRUE"
ltl += '\n);\n'
# Guarantee
ltl += '\nLTLSPEC\n(\n'
if guarantee:
ltl += guarantee
else:
ltl += "TRUE"
ltl += '\n);'
return ltl
def replace_dependent_vars(spec, bool2form):
logger.debug('replacing dependent variables using map:\n\t' +
str(bool2form))
vs = dict(spec.env_vars)
vs.update(spec.sys_vars)
logger.debug('variables:\n\t' + str(vs))
bool2subtree = dict()
for boolvar, formula in bool2form.iteritems():
logger.debug('checking var: ' + str(boolvar))
if boolvar in vs:
assert vs[boolvar] == 'boolean'
logger.debug(str(boolvar) + ' is indeed Boolean')
else:
logger.debug('spec does not contain var: ' + str(boolvar))
tree = parser.parse(formula)
bool2subtree[boolvar] = tx.Tree.from_recursive_ast(tree)
for s in {'env_init', 'env_safety', 'env_prog',
'sys_init', 'sys_safety', 'sys_prog'}:
part = getattr(spec, s)
new = []
for clause in part:
logger.debug('replacing in clause:\n\t' + clause)
tree = spec.ast(clause)
g = tx.Tree.from_recursive_ast(tree)
tx.sub_bool_with_subtree(g, bool2subtree)
f = g.to_recursive_ast().flatten()
new.append(f)
logger.debug('caluse tree after replacement:\n\t' + f)
setattr(spec, s, new)
def parse_parse_check(formula, expected_length):
# If expected_length is None, then the formula is malformed, and
# thus we expect parsing to fail.
if expected_length is not None:
assert len(parse(formula)) == expected_length
else:
nt.assert_raises(Exception, parse, formula)
def check_var_name_conflict(f, varname):
t = parser.parse(f)
g = Tree.from_recursive_ast(t)
v = {x.value for x in g.variables}
if varname in v:
raise ValueError('var name "{v}" already used'.format(v=varname))
return v
def replace_dependent_vars(spec, bool2form):
logger.debug('replacing dependent variables using map:\n\t' +
str(bool2form))
vs = dict(spec.env_vars)
vs.update(spec.sys_vars)
logger.debug('variables:\n\t' + str(vs))
bool2subtree = dict()
for boolvar, formula in bool2form.items():
logger.debug('checking var: ' + str(boolvar))
if boolvar in vs:
assert vs[boolvar] == 'boolean'
logger.debug(str(boolvar) + ' is indeed Boolean')
else:
logger.debug('spec does not contain var: ' + str(boolvar))
tree = parser.parse(formula)
bool2subtree[boolvar] = tx.Tree.from_recursive_ast(tree)
for s in {'env_init', 'env_safety', 'env_prog',
'sys_init', 'sys_safety', 'sys_prog'}:
part = getattr(spec, s)
new = []
for clause in part:
logger.debug('replacing in clause:\n\t' + clause)
tree = spec.ast(clause)
g = tx.Tree.from_recursive_ast(tree)
tx.sub_bool_with_subtree(g, bool2subtree)
f = g.to_recursive_ast().flatten()
new.append(f)
logger.debug('caluse tree after replacement:\n\t' + f)
setattr(spec, s, new)
def parse_parse_check(formula, expected_length):
# If expected_length is None, then the formula is malformed, and
# thus we expect parsing to fail.
if expected_length is not None:
assert len(parse(formula)) == expected_length
else:
nt.assert_raises(Exception, parse, formula)
def check_var_name_conflict(f, varname):
t = parser.parse(f)
g = Tree.from_recursive_ast(t)
v = {x.value for x in g.variables}
if varname in v:
raise ValueError('var name "{v}" already used'.format(v=varname))
return v
def lexer_token_precedence_test():
s = 'False'
r = parse(s)
assert isinstance(r, ast.nodes.Bool)
assert r.value == 'False'
s = 'a'
r = parse(s)
assert isinstance(r, ast.nodes.Var)
assert r.value == 'a'
s = 'x = "a"'
r = parse(s)
assert isinstance(r, ast.nodes.Binary)
assert r.operator == '='
x, a = r.operands
assert isinstance(x, ast.nodes.Var)
assert x.value == 'x'
assert isinstance(a, ast.nodes.Str)
assert a.value == 'a'
s = 'y = 1'
r = parse(s)
assert isinstance(r, ast.nodes.Binary)
assert r.operator == '='
y, n = r.operands
assert isinstance(y, ast.nodes.Var)
assert y.value == 'y'
assert isinstance(n, ast.nodes.Num)
assert n.value == '1'
s = '[] a'
r = parse(s)
assert isinstance(r, ast.nodes.Unary)
assert r.operator == 'G'
assert isinstance(r.operands[0], ast.nodes.Var)
assert r.operands[0].value == 'a'
s = 'a U b'
r = parse(s)
assert isinstance(r, ast.nodes.Binary)
assert r.operator == 'U'
assert isinstance(r.operands[0], ast.nodes.Var)
assert r.operands[0].value == 'a'
assert isinstance(r.operands[1], ast.nodes.Var)
assert r.operands[1].value == 'b'
s = '( a )'
r = parse(s)
assert isinstance(r, ast.nodes.Var)
s = "(a ' = 1)"
r = parse(s)
assert isinstance(r, ast.nodes.Comparator)
assert r.operator == '='
x = r.operands[0]
assert isinstance(x, ast.nodes.Unary)
assert x.operator == 'X'
assert isinstance(x.operands[0], ast.nodes.Var)
assert x.operands[0].value == 'a'
y = r.operands[1]
assert isinstance(y, ast.nodes.Num)
assert y.value == '1'
def lexer_token_precedence_test():
s = 'False'
r = parse(s)
assert isinstance(r, ast.nodes.Bool)
assert r.value == 'False'
s = 'a'
r = parse(s)
assert isinstance(r, ast.nodes.Var)
assert r.value == 'a'
s = 'x = "a"'
r = parse(s)
assert isinstance(r, ast.nodes.Binary)
assert r.operator == '='
x, a = r.operands
assert isinstance(x, ast.nodes.Var)
assert x.value == 'x'
assert isinstance(a, ast.nodes.Str)
assert a.value == 'a'
s = 'y = 1'
r = parse(s)
assert isinstance(r, ast.nodes.Binary)
assert r.operator == '='
y, n = r.operands
assert isinstance(y, ast.nodes.Var)
assert y.value == 'y'
assert isinstance(n, ast.nodes.Num)
assert n.value == '1'
s = '[] a'
r = parse(s)
assert isinstance(r, ast.nodes.Unary)
assert r.operator == 'G'
assert isinstance(r.operands[0], ast.nodes.Var)
assert r.operands[0].value == 'a'
s = 'a U b'
r = parse(s)
assert isinstance(r, ast.nodes.Binary)
assert r.operator == 'U'
assert isinstance(r.operands[0], ast.nodes.Var)
assert r.operands[0].value == 'a'
assert isinstance(r.operands[1], ast.nodes.Var)
assert r.operands[1].value == 'b'
s = '( a )'
r = parse(s)
assert isinstance(r, ast.nodes.Var)
s = "(a ' = 1)"
r = parse(s)
assert isinstance(r, ast.nodes.Comparator)
assert r.operator == '='
x = r.operands[0]
assert isinstance(x, ast.nodes.Unary)
assert x.operator == 'X'
assert isinstance(x.operands[0], ast.nodes.Var)
assert x.operands[0].value == 'a'
y = r.operands[1]
assert isinstance(y, ast.nodes.Num)
assert y.value == '1'
def test_to_labeled_graph():
f = ('( ( p & q ) U ( ( q | ( ( p -> w ) & ( ! ( z -> b ) ) ) ) & '
'( G ( X g ) ) ) )')
tree = parse(f)
assert len(tree) == 18
nodes = {'p', 'q', 'w', 'z', 'b', 'g', 'G', 'U', 'X', '&', '|', '!', '->'}
g = tx.Tree.from_recursive_ast(tree)
h = tx.ast_to_labeled_graph(g, detailed=False)
labels = {d['label'] for u, d in h.nodes(data=True)}
assert labels == nodes
def test_to_labeled_graph():
f = ('( ( p & q ) U ( ( q | ( ( p -> w ) & ( ! ( z -> b ) ) ) ) & '
'( G ( X g ) ) ) )')
tree = parse(f)
assert len(tree) == 18
nodes = {'p', 'q', 'w', 'z', 'b', 'g', 'G',
'U', 'X', '&', '|', '!', '->'}
g = tx.Tree.from_recursive_ast(tree)
h = tx.ast_to_labeled_graph(g, detailed=False)
labels = {d['label'] for u, d in h.nodes_iter(data=True)}
assert labels == nodes
def full_name_operators_test():
formulas = {
'always eventually p': '( G ( F p ) )',
'ALwaYs EvenTUAlly(p)': '( G ( F p ) )',
('(p and q) UNtIl (q or ((p -> w) and '
'not (z implies b))) and always next g'):
('( ( ( p & q ) U ( q | ( ( p -> w ) & '
'( ! ( z -> b ) ) ) ) ) & ( G ( X g ) ) )')}
for f, correct in formulas.items():
tree = parse(f, full_operators=True)
# g.write('hehe.png')
assert tree.flatten() == correct, tree.flatten()
def full_name_operators_test():
formulas = {
'always eventually p':
'( G ( F p ) )',
'ALwaYs EvenTUAlly(p)':
'( G ( F p ) )',
('(p and q) UNtIl (q or ((p -> w) and '
'not (z implies b))) and always next g'):
('( ( ( p & q ) U ( q | ( ( p -> w ) & '
'( ! ( z -> b ) ) ) ) ) & ( G ( X g ) ) )')
}
for f, correct in formulas.items():
tree = parse(f, full_operators=True)
# g.write('hehe.png')
assert tree.flatten() == correct, tree.flatten()
def infer_constants(formula, variables):
"""Enclose all non-variable names in quotes.
@param formula: well-formed LTL formula
@type formula: C{str} or L{LTL_AST}
@param variables: domains of variables, or only their names.
If the domains are given, then they are checked
for ambiguities as for example a variable name
duplicated as a possible value in the domain of
a string variable (the same or another).
If the names are given only, then a warning is raised,
because ambiguities cannot be checked in that case,
since they depend on what domains will be used.
@type variables: C{dict} as accepted by L{GRSpec} or
container of C{str}
@return: C{formula} with all string literals not in C{variables}
enclosed in double quotes
@rtype: C{str}
"""
if isinstance(variables, dict):
for var in variables:
other_vars = dict(variables)
other_vars.pop(var)
_check_var_conflicts({var}, other_vars)
else:
logger.error('infer constants does not know the variable domains.')
warnings.warn(
'infer_constants can give an incorrect result '
'depending on the variable domains.\n'
'If you give the variable domain definitions as dict, '
'then infer_constants will check for ambiguities.')
tree = parser.parse(formula)
old2new = dict()
for u in tree:
if u.type != 'var':
continue
if str(u) in variables:
continue
# Var (so NAME token) but not a variable
# turn it into a string constant
old2new[u] = nodes.Const(str(u))
nx.relabel_nodes(tree, old2new, copy=False)
return str(tree)
def infer_constants(formula, variables):
"""Enclose all non-variable names in quotes.
@param formula: well-formed LTL formula
@type formula: C{str} or L{LTL_AST}
@param variables: domains of variables, or only their names.
If the domains are given, then they are checked
for ambiguities as for example a variable name
duplicated as a possible value in the domain of
a string variable (the same or another).
If the names are given only, then a warning is raised,
because ambiguities cannot be checked in that case,
since they depend on what domains will be used.
@type variables: C{dict} as accepted by L{GRSpec} or
container of C{str}
@return: C{formula} with all string literals not in C{variables}
enclosed in double quotes
@rtype: C{str}
"""
if isinstance(variables, dict):
for var in variables:
other_vars = dict(variables)
other_vars.pop(var)
_check_var_conflicts({var}, other_vars)
else:
logger.error('infer constants does not know the variable domains.')
warnings.warn(
'infer_constants can give an incorrect result '
'depending on the variable domains.\n'
'If you give the variable domain definitions as dict, '
'then infer_constants will check for ambiguities.')
tree = parser.parse(formula)
old2new = dict()
for u in tree:
if u.type != 'var':
continue
if str(u) in variables:
continue
# Var (so NAME token) but not a variable
# turn it into a string constant
old2new[u] = nodes.Const(str(u))
nx.relabel_nodes(tree, old2new, copy=False)
return str(tree)
def to_gr1c(self):
"""Dump to gr1c specification string.
Cf. L{interfaces.gr1c}.
"""
def _to_gr1c_print_vars(vardict):
output = ""
for variable, domain in vardict.items():
if domain == "boolean":
output += " " + variable
elif isinstance(domain, tuple) and len(domain) == 2:
output += " " + variable + " [" + str(domain[0]) + ", " + str(domain[1]) + "]"
else:
raise ValueError("Domain type unsupported by gr1c: " + str(domain))
return output
tmp = finite_domain2ints(self)
if tmp is not None:
return tmp.to_gr1c()
output = "ENV:" + _to_gr1c_print_vars(self.env_vars) + ";\n"
output += "SYS:" + _to_gr1c_print_vars(self.sys_vars) + ";\n"
output += "ENVINIT: " + "\n& ".join(["(" + parser.parse(s).to_gr1c() + ")" for s in self.env_init]) + ";\n"
if len(self.env_safety) == 0:
output += "ENVTRANS:;\n"
else:
output += (
"ENVTRANS: " + "\n& ".join(["[](" + parser.parse(s).to_gr1c() + ")" for s in self.env_safety]) + ";\n"
)
if len(self.env_prog) == 0:
output += "ENVGOAL:;\n\n"
else:
output += (
"ENVGOAL: " + "\n& ".join(["[]<>(" + parser.parse(s).to_gr1c() + ")" for s in self.env_prog]) + ";\n\n"
)
output += "SYSINIT: " + "\n& ".join(["(" + parser.parse(s).to_gr1c() + ")" for s in self.sys_init]) + ";\n"
if len(self.sys_safety) == 0:
output += "SYSTRANS:;\n"
else:
output += (
"SYSTRANS: " + "\n& ".join(["[](" + parser.parse(s).to_gr1c() + ")" for s in self.sys_safety]) + ";\n"
)
if len(self.sys_prog) == 0:
output += "SYSGOAL:;\n"
else:
output += (
"SYSGOAL: " + "\n& ".join(["[]<>(" + parser.parse(s).to_gr1c() + ")" for s in self.sys_prog]) + ";\n"
)
return output
def str_to_grspec(f):
"""Return `GRSpec` from LTL formula `f` as `str`.
Formula `f` must be in the form:
A -> G
where each of A, G is a conjunction of terms: `B`, `[]C`, `[]<>B`.
For more details on `B, C`, see [split_gr1].
@type f: `str`
@rtype: [GRSpec]
"""
t = parser.parse(f)
assert t.operator == '->'
env, sys = t.operands
d = {'assume': split_gr1(env), 'assert': split_gr1(sys)}
return GRSpec(env_init=d['assume']['init'],
env_safety=d['assume']['G'],
env_prog=d['assume']['GF'],
sys_init=d['assert']['init'],
sys_safety=d['assert']['G'],
sys_prog=d['assert']['GF'])
def str_to_grspec(f):
"""Return `GRSpec` from LTL formula `f` as `str`.
Formula `f` must be in the form:
A -> G
where each of A, G is a conjunction of terms: `B`, `[]C`, `[]<>B`.
For more details on `B, C`, see [split_gr1].
@type f: `str`
@rtype: [GRSpec]
"""
t = parser.parse(f)
assert t.operator == '->'
env, sys = t.operands
d = {'assume': split_gr1(env),
'assert': split_gr1(sys)}
return GRSpec(env_init=d['assume']['init'],
env_safety=d['assume']['G'],
env_prog=d['assume']['GF'],
sys_init=d['assert']['init'],
sys_safety=d['assert']['G'],
sys_prog=d['assert']['GF'])
def synthesize(formula, env_vars=None, sys_vars=None):
"""Return Moore transducer if C{formula} is realizable.
Variable C{dict}s have variable names as keys and their type as
value. The types should be 'boolean'. These parameters are only
used if formula is of type C{str}. Else, the variable dictionaries
associated with the L{LTL} or L{GRSpec} object are used.
@param formula: linear temporal logic formula
@type formula: C{str}, L{LTL}, or L{GRSpec}
@param env_vars: uncontrolled variables (inputs); used only if
C{formula} is of type C{str}
@type env_vars: C{dict} or None
@param sys_vars: controlled variables (outputs); used only if
C{formula} is of type C{str}
@type sys_vars: C{dict} or None
@return: symbolic Moore transducer
(guards are conjunctions, not sets)
@rtype: L{MooreMachine}
"""
if isinstance(formula, GRSpec):
env_vars = formula.env_vars
sys_vars = formula.sys_vars
elif isinstance(formula, LTL):
env_vars = formula.input_variables
sys_vars = formula.output_variables
all_vars = dict(env_vars)
all_vars.update(sys_vars)
if not all(v == 'boolean' for v in all_vars.itervalues()):
raise TypeError(
'all variables should be Boolean:\n{v}'.format(v=all_vars))
if isinstance(formula, GRSpec):
f = translate(formula, 'wring')
else:
T = parse(str(formula))
f = translate_ast(T, 'wring').flatten(env_vars=env_vars,
sys_vars=sys_vars)
# dump partition file
s = '.inputs {inp}\n.outputs {out}'.format(
inp=' '.join(env_vars),
out=' '.join(sys_vars)
)
with open(IO_PARTITION_FILE, 'w') as fid:
fid.write(s)
# call lily
try:
p = subprocess.Popen([LILY, '-f', f, '-syn', IO_PARTITION_FILE],
stdout=subprocess.PIPE, stderr=subprocess.STDOUT)
out = p.stdout.read()
except OSError as e:
if e.errno == os.errno.ENOENT:
raise Exception(
'lily.pl not found in path.\n'
'See the Lily docs for setting PERL5LIB and PATH.')
else:
raise
dotf = open(DOTFILE, 'r')
fail_msg = 'Formula is not realizable'
if dotf.read(len(fail_msg)) == fail_msg:
return None
dotf.seek(0)
g = nx.read_dot(dotf)
dotf.close()
moore = lily_strategy2moore(g, env_vars, sys_vars)
return moore
def to_jtlv(self):
"""Return specification as list of two strings [assumption, guarantee].
Format is that of JTLV. Cf. L{interfaces.jtlv}.
"""
spec = ['', '']
desc_added = False
for env_init in self.env_init:
if (len(env_init) > 0):
if (len(spec[0]) > 0):
spec[0] += ' && \n'
if (not desc_added):
spec[0] += '-- valid initial env states\n'
desc_added = True
spec[0] += '\t' + parser.parse(env_init).to_jtlv()
desc_added = False
for env_safety in self.env_safety:
if (len(env_safety) > 0):
if (len(spec[0]) > 0):
spec[0] += ' && \n'
if (not desc_added):
spec[0] += '-- safety assumption on environment\n'
desc_added = True
env_safety = parser.parse(env_safety).to_jtlv()
spec[0] += '\t[](' +re.sub(r"next\s*\(", "next(", env_safety) +')'
desc_added = False
for prog in self.env_prog:
if (len(prog) > 0):
if (len(spec[0]) > 0):
spec[0] += ' && \n'
if (not desc_added):
spec[0] += '-- justice assumption on environment\n'
desc_added = True
spec[0] += '\t[]<>(' + parser.parse(prog).to_jtlv() + ')'
desc_added = False
for sys_init in self.sys_init:
if (len(sys_init) > 0):
if (len(spec[1]) > 0):
spec[1] += ' && \n'
if (not desc_added):
spec[1] += '-- valid initial system states\n'
desc_added = True
spec[1] += '\t' + parser.parse(sys_init).to_jtlv()
desc_added = False
for sys_safety in self.sys_safety:
if (len(sys_safety) > 0):
if (len(spec[1]) > 0):
spec[1] += ' && \n'
if (not desc_added):
spec[1] += '-- safety requirement on system\n'
desc_added = True
sys_safety = parser.parse(sys_safety).to_jtlv()
spec[1] += '\t[](' +re.sub(r"next\s*\(", "next(", sys_safety) +')'
desc_added = False
for prog in self.sys_prog:
if (len(prog) > 0):
if (len(spec[1]) > 0):
spec[1] += ' && \n'
if (not desc_added):
spec[1] += '-- progress requirement on system\n'
desc_added = True
spec[1] += '\t[]<>(' + parser.parse(prog).to_jtlv() + ')'
return spec
def test_has_operator():
t = parser.parse(' [](x & y) ')
g = transformation.Tree.from_recursive_ast(t)
assert gr1.has_operator(t, g, {'&'}) == '&'
assert gr1.has_operator(t, g, {'G'}) == 'G'
def test_has_operator():
t = parser.parse(' [](x & y) ')
g = transformation.Tree.from_recursive_ast(t)
assert gr1.has_operator(t, g, {'&'}) == '&'
assert gr1.has_operator(t, g, {'G'}) == 'G'
def split_gr1(f):
"""Return `dict` of GR(1) subformulae.
The formula `f` is assumed to be a conjunction of expressions
of the form:
`B`, `[]C` or `[]<>B`
where:
- `C` can contain "next"
- `B` cannot contain "next"
@param f: temporal logic formula
@type f: `str` or AST
@return: conjunctions of formulae A, B as `str`, grouped by keys:
`'init', 'G', 'GF'`
@rtype: `dict` of `str`: `list` of `str`
"""
# TODO: preprocess by applying syntactic identities: [][] = [] etc
try:
f + 's'
t = parser.parse(f)
except TypeError:
t = f
g = tx.Tree.from_recursive_ast(t)
# collect boundary of conjunction operators
Q = [g.root]
b = list() # use lists to preserve as much given syntactic order
while Q:
u = Q.pop()
# terminal ?
if not g.succ.get(u):
b.append(u)
continue
# operator
if u.operator == '&':
# use `u.operands` instead of `g.successors`
# to preserve original order
Q.extend(u.operands)
else:
b.append(u)
d = {'init': list(), 'G': list(), 'GF': list()}
for u in b:
# terminal ?
if not g.succ.get(u):
d['init'].append(u)
continue
# some operator
if u.operator != 'G':
d['init'].append(u)
continue
# G
(v, ) = u.operands
# terminal in G ?
if not g.succ.get(v):
d['G'].append(v)
continue
# some operator in G
if v.operator == 'F':
(w, ) = v.operands
d['GF'].append(w)
else:
# not a GF
d['G'].append(v)
# assert only admissible temporal operators
ops = {'G', 'F', 'U', 'V', 'R'}
operators = {'G': ops}
ops = set(ops)
ops.add('X')
operators.update(init=ops, GF=ops)
for part, f in d.items():
ops = operators[part]
for u in f:
op = has_operator(u, g, ops)
if op is None:
continue
raise AssertionError(('found inadmissible operator "{op}" '
'in "{f}" formula').format(op=op, f=u))
# conjoin (except for progress)
init = ' & '.join(u.flatten() for u in reversed(d['init']))
d['init'] = [init]
safe = ' & '.join(u.flatten() for u in reversed(d['G']))
d['G'] = [safe]
# flatten individual progress formulae
d['GF'] = [u.flatten() for u in d['GF']]
return d
def split_gr1(f):
"""Return `dict` of GR(1) subformulae.
The formula `f` is assumed to be a conjunction of expressions
of the form:
`B`, `[]C` or `[]<>B`
where:
- `C` can contain "next"
- `B` cannot contain "next"
@param f: temporal logic formula
@type f: `str` or AST
@return: conjunctions of formulae A, B as `str`, grouped by keys:
`'init', 'G', 'GF'`
@rtype: `dict` of `str`: `list` of `str`
"""
# TODO: preprocess by applying syntactic identities: [][] = [] etc
try:
f + 's'
t = parser.parse(f)
except TypeError:
t = f
g = tx.Tree.from_recursive_ast(t)
# collect boundary of conjunction operators
Q = [g.root]
b = list() # use lists to preserve as much given syntactic order
while Q:
u = Q.pop()
# terminal ?
if not g.succ.get(u):
b.append(u)
continue
# operator
if u.operator == '&':
# use `u.operands` instead of `g.successors`
# to preserve original order
Q.extend(u.operands)
else:
b.append(u)
d = {'init': list(), 'G': list(), 'GF': list()}
for u in b:
# terminal ?
if not g.succ.get(u):
d['init'].append(u)
continue
# some operator
if u.operator != 'G':
d['init'].append(u)
continue
# G
(v,) = u.operands
# terminal in G ?
if not g.succ.get(v):
d['G'].append(v)
continue
# some operator in G
if v.operator == 'F':
(w,) = v.operands
d['GF'].append(w)
else:
# not a GF
d['G'].append(v)
# assert only admissible temporal operators
ops = {'G', 'F', 'U', 'V', 'R'}
operators = {'G': ops}
ops = set(ops)
ops.add('X')
operators.update(init=ops, GF=ops)
for part, f in d.iteritems():
ops = operators[part]
for u in f:
op = has_operator(u, g, ops)
if op is None:
continue
raise AssertionError((
'found inadmissible operator "{op}" '
'in "{f}" formula').format(
op=op, f=u))
# conjoin (except for progress)
init = ' & '.join(u.flatten() for u in reversed(d['init']))
d['init'] = [init]
safe = ' & '.join(u.flatten() for u in reversed(d['G']))
d['G'] = [safe]
# flatten individual progress formulae
d['GF'] = [u.flatten() for u in d['GF']]
return d