Source code for proveit.numbers.rounding.round
from proveit import (defaults, Function, InnerExpr, Literal, ProofFailure,
USE_DEFAULTS, relation_prover, equality_prover)
from proveit.logic import InSet
from proveit.numbers.number_sets import Integer, Natural, Real
from proveit.numbers.rounding.rounding_methods import (
apply_rounding_elimination, apply_rounding_extraction,
apply_shallow_simplification, rounding_deduce_in_number_set,
rounding_readily_provable_number_set)
[docs]class Round(Function):
# operator of the Round operation.
_operator_ = Literal(string_format='round', theory=__file__)
def __init__(self, A, *, styles=None):
Function.__init__(self, Round._operator_, A, styles=styles)
@equality_prover('shallow_simplified', 'shallow_simplify')
def shallow_simplification(self, *, must_evaluate=False,
**defaults_config):
'''
Returns a proven simplification equation for this Round
expression assuming the operands have been simplified.
For the trivial case Round(x) where the operand x is already
known to be or assumed to be an integer, derive and return this
Round expression equated with the operand itself: Round(x) = x.
Assumptions may be necessary to deduce necessary conditions for
the simplification. For the case where the operand is of the
form x = real + int, derive and return this Round expression
equated with Round(real) + int.
'''
return apply_shallow_simplification(self, must_evaluate=must_evaluate)
[docs] @equality_prover('rounding_eliminated', 'rounding_eliminate')
def rounding_elimination(self, **defaults_config):
'''
For the trivial case of Round(x) where the operand x is already
an integer, derive and return this Round expression equated
with the operand itself: Round(x) = x. Assumptions may be
necessary to deduce necessary conditions (for example, that x
actually is an integer) for the simplification.
This method is utilized by the do_reduced_simplification() method
only after the operand x is verified to already be proven
(or assumed) to be an integer.
For the case where the operand is of the form x = real + int,
see the rounding_extraction() method.
'''
from . import round_of_integer
return apply_rounding_elimination(self, round_of_integer)
[docs] @relation_prover
def deduce_in_number_set(self, number_set, **defaults_config):
'''
Given a number set number_set, attempt to prove that the given
Round expression is in that number set using the appropriate
closure theorem.
'''
from proveit.numbers.rounding import round_is_an_int
from proveit.numbers.rounding import round_real_pos_closure
return rounding_deduce_in_number_set(
self, number_set, round_is_an_int, round_real_pos_closure)
def readily_provable_number_set(self):
'''
Return the most restrictive number set we can readily
prove contains the evaluation of this number operation.
'''
return rounding_readily_provable_number_set(self)