PEP Deferral

Further consideration of this PEP has been deferred until Python 3.8 at the earliest.

Abstract

Inspired by PEP 335, and building on the circuit breaking protocol described in PEP 532, this PEP proposes a change to the definition of chained comparisons, where the comparison chaining will be updated to use the left-associative circuit breaking operator (else) rather than the logical disjunction operator (and) if the left hand comparison returns a circuit breaker as its result.

While there are some practical complexities arising from the current handling of single-valued arrays in NumPy, this change should be sufficient to allow elementwise chained comparison operations for matrices, where the result is a matrix of boolean values, rather than raising ValueError or tautologically returning True (indicating a non-empty matrix).

Relationship with other PEPs

This PEP has been extracted from earlier iterations of PEP 532, as a follow-on use case for the circuit breaking protocol, rather than an essential part of its introduction.

The specific proposal in this PEP to handle the element-wise comparison use case by changing the semantic definition of comparison chaining is drawn directly from Guido’s rejection of PEP 335.

Specification

A chained comparison like 0 < x < 10 written as:

LEFT_BOUND LEFT_OP EXPR RIGHT_OP RIGHT_BOUND

is currently roughly semantically equivalent to:

_expr = EXPR
_lhs_result = LEFT_BOUND LEFT_OP _expr
_expr_result = _lhs_result and (_expr RIGHT_OP RIGHT_BOUND)

Using the circuit breaking concepts introduced in PEP 532, this PEP proposes that comparison chaining be changed to explicitly check if the left comparison returns a circuit breaker, and if so, use else rather than and to implement the comparison chaining:

_expr = EXPR
_lhs_result = LEFT_BOUND LEFT_OP _expr
if hasattr(type(_lhs_result), "__else__"):
    _expr_result = _lhs_result else (_expr RIGHT_OP RIGHT_BOUND)
else:
    _expr_result = _lhs_result and (_expr RIGHT_OP RIGHT_BOUND)

This allows types like NumPy arrays to control the behaviour of chained comparisons by returning suitably defined circuit breakers from comparison operations.

The expansion of this logic to an arbitrary number of chained comparison operations would be the same as the existing expansion for and.

Rationale

In ultimately rejecting PEP 335, Guido van Rossum noted [1]:

The NumPy folks brought up a somewhat separate issue: for them, the most common use case is chained comparisons (e.g. A < B < C).

To understand this observation, we first need to look at how comparisons work with NumPy arrays:

>>> import numpy as np
>>> increasing = np.arange(5)
>>> increasing
array([0, 1, 2, 3, 4])
>>> decreasing = np.arange(4, -1, -1)
>>> decreasing
array([4, 3, 2, 1, 0])
>>> increasing < decreasing
array([ True,  True, False, False, False], dtype=bool)

Here we see that NumPy array comparisons are element-wise by default, comparing each element in the left hand array to the corresponding element in the right hand array, and producing a matrix of boolean results.

If either side of the comparison is a scalar value, then it is broadcast across the array and compared to each individual element:

>>> 0 < increasing
array([False,  True,  True,  True,  True], dtype=bool)
>>> increasing < 4
array([ True,  True,  True,  True, False], dtype=bool)

However, this broadcasting idiom breaks down if we attempt to use chained comparisons:

>>> 0 < increasing < 4
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()

The problem is that internally, Python implicitly expands this chained comparison into the form:

>>> 0 < increasing and increasing < 4
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()

And NumPy only permits implicit coercion to a boolean value for single-element arrays where a.any() and a.all() can be assured of having the same result:

>>> np.array([False]) and np.array([False])
array([False], dtype=bool)
>>> np.array([False]) and np.array([True])
array([False], dtype=bool)
>>> np.array([True]) and np.array([False])
array([False], dtype=bool)
>>> np.array([True]) and np.array([True])
array([ True], dtype=bool)

The proposal in this PEP would allow this situation to be changed by updating the definition of element-wise comparison operations in NumPy to return a dedicated subclass that implements the new circuit breaking protocol and also changes the result array’s interpretation in a boolean context to always return False and hence never trigger the short-circuiting behaviour:

class ComparisonResultArray(np.ndarray):
    def __bool__(self):
        # Element-wise comparison chaining never short-circuits
        return False
    def _raise_NotImplementedError(self):
        msg = ("Comparison array truth values are ambiguous outside "
               "chained comparisons. Use a.any() or a.all()")
        raise NotImplementedError(msg)
    def __not__(self):
        self._raise_NotImplementedError()
    def __then__(self, result):
        self._raise_NotImplementedError()
    def __else__(self, result):
        return np.logical_and(self, other.view(ComparisonResultArray))

With this change, the chained comparison example above would be able to return:

>>> 0 < increasing < 4
ComparisonResultArray([ False,  True,  True,  True, False], dtype=bool)

Implementation

Actual implementation has been deferred pending in-principle interest in the idea of making the changes proposed in PEP 532.

…TBD…

References

[1]

PEP 335 rejection notification (https://mail.python.org/pipermail/python-dev/2012-March/117510.html)

Copyright

This document has been placed in the public domain under the terms of the CC0 1.0 license: https://creativecommons.org/publicdomain/zero/1.0/