def strengthen2(a_inits:List[Expr], g_inits:List[Expr],
a_safeties:List[Expr], g_safeties:List[Expr],
a_livenesses:List[Expr], g_livenesses:List[Expr]) \
-> Expr:
"""
Assumes input expressions are not weirdos.
Splits safety into two types (+init):
formulas of the form G(..) and others.
:return: conjunction of:
init -> init
init & non_G_safety -> (g_state W !a_state)
init & non_G_safety & G(state) -> non_G_safety
init & orig_safety & liveness -> liveness
"""
# TODO: init are classified as non_state, _as_should_be4_correctness, but may be better way
a_init = and_expr(a_inits)
g_init = and_expr(g_inits)
a_state = and_expr(map(lambda e: e.arg, filter(lambda e: e.name=='G', a_safeties)))
g_state = and_expr(map(lambda e: e.arg, filter(lambda e: e.name=='G', g_safeties)))
a_non_state = and_expr(filter(lambda e: e.name!='G', a_safeties))
g_non_state = and_expr(filter(lambda e: e.name!='G', g_safeties))
safety_init = a_init >> g_init
safety_weak = (a_init & a_non_state) >> BinOp.W(g_state, ~a_state)
safety_other = (a_init & a_non_state & UnaryOp.G(a_state)) >> g_non_state
a_liveness = and_expr(a_livenesses)
g_liveness = and_expr(g_livenesses)
liveness = (a_init & a_non_state & UnaryOp.G(a_state) & a_liveness) >> g_liveness
logging.debug('a_state: ' + str(ConverterToLtl2BaFormatVisitor().dispatch(a_state)))
logging.debug('g_state: ' + str(g_state))
logging.debug('a_non_state: ' + str(a_non_state))
logging.debug('g_non_state: ' + str(g_non_state))
logging.debug('a_liveness: ' + str(a_liveness))
logging.debug('g_liveness: ' + str(g_liveness))
return safety_init & safety_weak & safety_other & liveness
def strengthen1(a_inits:List[Expr], g_inits:List[Expr],
a_safeties:List[Expr], g_safeties:List[Expr],
a_livenesses:List[Expr], g_livenesses:List[Expr]) \
-> Expr:
"""
PRE: a_safeties and g_safeties are iterable of _safety_ formulas and not transition formulas
(thus, they are of the form G(..))
"""
a_init = and_expr(a_inits)
g_init = and_expr(g_inits)
a_safety = and_expr(a_safeties)
g_safety = and_expr(g_safeties)
a_liveness = and_expr(a_livenesses)
g_liveness = and_expr(g_livenesses)
init_expr = a_init >> g_init
safety_implication = (a_init & a_safety) >> g_safety
liveness_expr = (a_init & a_safety & a_liveness) >> g_liveness
return init_expr & safety_implication & liveness_expr
