def pushquants(f): # print('pushquant({0})'.format(f)) if is_quantified(f): arg = f.args[0] if arg.op == OP_NOT: return ~pushquants(Quantifier(opposite(f.op), f.vars, arg.args[0])) elif is_quantified(arg): arg1 = pushquants(arg) # did pushquants have any effect? if arg1 == arg: # # if no, see if changing the order of the quants has an effect # arg2 = Quantifier(f.op, f.vars, arg.args[0]) # arg2_ = pushquants(arg2) # if arg2 == arg2_: # return Quantifier(f.op, f.vars, arg1) # else: # return Quantifier(arg.op, arg.vars, arg2_) return Quantifier(f.op, f.vars, arg1) else: return pushquants(Quantifier(f.op, f.vars, arg1)) elif arg.op in [OP_AND, OP_OR]: arg1 = arg.args[0] arg2 = arg.args[1] variable = f.vars[0] if variable in fvars(arg1) and variable in fvars(arg2): if ((arg.op == OP_AND and f.op == OP_FORALL) or (arg.op == OP_OR and f.op == OP_EXISTS)): return pushquants(Expr(arg.op, Quantifier(f.op, f.vars, arg1), Quantifier(f.op, f.vars, arg2))) else: return Quantifier(f.op, f.vars, pushquants(arg)) if variable in fvars(arg1): return pushquants(Expr(arg.op, Quantifier(f.op, f.vars, arg1), arg2)) if variable in fvars(arg2): return pushquants(Expr(arg.op, arg1, Quantifier(f.op, f.vars, arg2))) else: get_log().warning('Dropped quantifier "{0} : {1}" from "{2}"' .format(f.op, f.vars, f)) return arg elif arg.op == OP_IMPLIES: arg1 = arg.args[0] arg2 = arg.args[1] variable = f.vars[0] if variable in fvars(arg1) and variable in fvars(arg2): return Quantifier(f.op, f.vars, pushquants(arg)) elif variable in fvars(arg1): quant = opposite(f.op) return (pushquants(Quantifier(quant, variable, arg1)) >> pushquants(arg2)) elif variable in fvars(arg2): return (pushquants(arg1) >> pushquants(Quantifier(f.op, variable, arg2))) else: get_log().warning('Dropped quantifier "{0} : {1}" from "{2}"' .format(f.op, f.vars, f)) return (pushquants(arg1) >> pushquants(arg2)) elif arg.op == OP_IMPLIED_BY: arg1 = arg.args[0] arg2 = arg.args[1] variable = f.vars[0] if variable in fvars(arg1) and variable in fvars(arg2): return Quantifier(f.op, f.vars, pushquants(arg)) elif variable in fvars(arg1): return (pushquants(Quantifier(f.op, variable, arg1)) << pushquants(arg2)) elif variable in fvars(arg2): quant = opposite(f.op) return (pushquants(arg1) << pushquants(Quantifier(quant, variable, arg2))) else: get_log().warning('Dropped quantifier "{0} : {1}" from "{2}"' .format(f.op, f.vars, f)) return (pushquants(arg1) << pushquants(arg2)) else: return Quantifier(f.op, f.vars[0], pushquants(f.args[0])) elif f.op == OP_NOT: return ~pushquants(f.args[0]) elif f.op in BINARY_LOGIC_OPS: return Expr(f.op, *[pushquants(x) for x in f.args]) else: return f
def pullquants(f): # print('pullquants({0})'.format(str(f))) if f.op == OP_AND: arg1 = pullquants(f.args[0]) arg2 = pullquants(f.args[1]) if arg1.op == OP_FORALL and arg2.op == OP_FORALL: return rename_and_pull(f, OP_FORALL, arg1.vars[0], arg2.vars[0], arg1.args[0], arg2.args[0]) elif is_quantified(arg1): return rename_and_pull(f, arg1.op, arg1.vars[0], None, arg1.args[0], arg2) elif is_quantified(arg2): return rename_and_pull(f, arg2.op, None, arg2.vars[0], arg1, arg2.args[0]) else: return (arg1 & arg2) elif f.op == OP_OR: arg1 = pullquants(f.args[0]) arg2 = pullquants(f.args[1]) if arg1.op == OP_EXISTS and arg2.op == OP_EXISTS: return rename_and_pull(f, OP_EXISTS, arg1.vars[0], arg2.vars[0], arg1.args[0], arg2.args[0]) elif is_quantified(arg1): return rename_and_pull(f, arg1.op, arg1.vars[0], None, arg1.args[0], arg2) elif is_quantified(arg2): return rename_and_pull(f, arg2.op, None, arg2.vars[0], arg1, arg2.args[0]) else: return (arg1 | arg2) elif f.op == OP_IMPLIES: arg1 = pullquants(f.args[0]) arg2 = pullquants(f.args[1]) if is_quantified(arg1): return rename_and_pull(f, opposite(arg1.op), arg1.vars[0], None, arg1.args[0], arg2) elif is_quantified(arg2): return rename_and_pull(f, arg2.op, None, arg2.vars[0], arg1, arg2.args[0]) else: return (arg1 >> arg2) elif f.op == OP_IMPLIED_BY: arg1 = pullquants(f.args[0]) arg2 = pullquants(f.args[1]) if is_quantified(arg1): return rename_and_pull(f, arg1.op, arg1.vars[0], None, arg1.args[0], arg2) elif is_quantified(arg2): return rename_and_pull(f, opposite(arg2.op), None, arg2.vars[0], arg1, arg2.args[0]) else: return (arg1 << arg2) elif f.op == OP_EQUIVALENT: arg1 = pullquants(f.args[0]) arg2 = pullquants(f.args[1]) return pullquants((arg1 >> arg2) & (arg1 << arg2)) elif f.op == OP_NOT: arg = pullquants(f.args[0]) if is_quantified(arg): return Quantifier(opposite(arg.op), f.vars, ~(arg.args[0])) else: return (~arg) else: return f