Checking in some text. Most of this is simply an Appendix repeating
what David Ascher said in 1998 (before the starship bites the dust again).
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Guido van Rossum
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pep-0207.txt
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pep-0207.txt
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PEP: 207
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Title: Rich Comparisions
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Version: $Revision$
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Author: mal@lemburg.com (Marc-Andre Lemburg), guido@python.org (Guido van Rossum)
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Author: guido@python.org (Guido van Rossum), mal@lemburg.com (Marc-Andre Lemburg)
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Python-Version: 2.1
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Status: Incomplete
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Abstract
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This PEP proposes several new features for comparisons:
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- Allow separately overloading of <, >, <=, >=, ==, !=, both in
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classes and in C extensions.
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- Allow any of those overloaded operators to return something else
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besides a Boolean result.
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Motivation
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The main motivation comes from NumPy, whose users agree that A<B
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should return an array of elementwise comparison outcomes; they
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currently have to spell this as less(A,B) because A<B can only
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return a Boolean result or an exception.
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An additional motivation is that frequently, types don't have a
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natural ordering, but still need to be compared for equality.
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Currenlty such a type *must* implement comparison and thus assign
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an arbitrary ordering, just so that equality can be tested.
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More motivation can be found in the proposals listed under
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previous work below.
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Previous Work
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Rich Comparisons have been proposed before; in particular by David
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Ascher, after experience with Numerical Python:
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http://starship.python.net/crew/da/proposals/richcmp.html
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It is also included as an appendix. In this proposal, David also
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proposes the addition of an optional 3rd argument to cmp(), as in:
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cmp(a, b, "<") or cmp(a, b, "!=").
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Concerns
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- Backwards compatibility, both at the Python level (classes using
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__cmp__ need not be changed) and at the C level (extensions
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defining tp_compare need not be changed).
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- When A<B returns a matrix of elementwise comparisons, an easy
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mistake to make is to use this expression in a Boolean context.
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Without special precautions, it would always be true. This use
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should raise an exception instead.
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- If a class overrides x==y but nothing else, should x!=y be
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computed as not(x==y), or fail? (I think this is OK; David
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disagrees.)
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- Similarly, should we allow x<y to be calculated from y>x? (I
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think this is OK; David agrees.)
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- Similarly, should we allow x<=y to be calculated from not(x>y)?
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(I think this is *not* OK; neither does David.)
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- When using comparisons to generate elementwise comparisons, what
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to do about shortcut operators like A<B<C or ``A<B and C<D''?
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(David proposes a solution for A<B<C, but it means that ``if
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A<B:...'' will assume ``if true:...''.
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Solution
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To be done.
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Copyright
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This document has been placed in the public domain.
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Appendix
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Here, for posterity, is most of David Ascher's original proposal.
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It addresses almost all concerns.
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Abstract
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A new mechanism allowing comparisons of Python objects to return
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values other than -1, 0, or 1 (or raise exceptions) is
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proposed. This mechanism is entirely backwards compatible, and can
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be controlled at the level of the C PyObject type or of the Python
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class definition. There are three cooperating parts to the
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proposed mechanism:
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- the use of the last slot in the type object structure to store a
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pointer to a rich comparison function
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- the addition of special methods for classes
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- the addition of an optional argument to the builtin cmp()
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function.
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Motivation
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The current comparison protocol for Python objects assumes that
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any two Python objects can be compared (as of Python 1.5, object
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comparisons can raise exceptions), and that the return value for
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any comparison should be -1, 0 or 1. -1 indicates that the first
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argument to the comparison function is less than the right one, +1
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indicating the contrapositive, and 0 indicating that the two
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objects are equal. While this mechanism allows the establishment
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of a order relationship (e.g. for use by the sort() method of list
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objects), it has proven to be limited in the context of Numeric
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Python (NumPy).
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Specifically, NumPy allows the creation of multidimensional
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arrays, which support most of the numeric operators. Thus:
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x = array((1,2,3,4)) y = array((2,2,4,4))
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are two NumPy arrays. While they can be added elementwise,:
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z = x + y # z == array((3,4,7,8))
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they cannot be compared in the current framework - the released
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version of NumPy compares the pointers, (thus yielding junk
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information) which was the only solution before the recent
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addition of the ability (in 1.5) to raise exceptions in comparison
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functions.
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Even with the ability to raise exceptions, the current protocol
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makes array comparisons useless. To deal with this fact, NumPy
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includes several functions which perform the comparisons: less(),
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less_equal(), greater(), greater_equal(), equal(),
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not_equal(). These functions return arrays with the same shape as
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their arguments (modulo broadcasting), filled with 0's and 1's
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depending on whether the comparison is true or not for each
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element pair. Thus, for example, using the arrays x and y defined
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above:
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less(x,y)
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would be an array containing the numbers (1,0,0,0).
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The current proposal is to modify the Python object interface to
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allow the NumPy package to make it so that x < y returns the same
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thing as less(x,y). The exact return value is up to the NumPy
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package -- what this proposal really asks for is changing the
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Python core so that extension objects have the ability to return
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something other than -1, 0, 1, should their authors choose to do
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so.
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Current State of Affairs
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The current protocol is, at the C level, that each object type
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defines a tp_compare slot, which is a pointer to a function which
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takes two PyObject* references and returns -1, 0, or 1. This
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function is called by the PyObject_Compare() function defined in
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the C API. PyObject_Compare() is also called by the builtin
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function cmp() which takes two arguments.
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1. Changes to the C structure for type objects
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The last availabel slot in the PyTypeObject, reserved up to now
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for future expansion, is used to optionally store a pointer to a
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new comparison function, of type richcmpfunc defined by:
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typedef PyObject *(*richcmpfunc)
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Py_PROTO((PyObject *, PyObject *, int));
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This function takes three arguments. The first two are the objects
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to be compared, and the third is an integer corresponding to an
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opcode (one of LT, LE, EQ, NE, GT, GE). If this slot is left NULL,
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then rich comparison for that object type is not supported (except
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for class instances whose class provide the special methods
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described below).
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The above opcodes need to be added to the published Python/C API
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(probably under the names Py_LT, Py_LE, etc.)
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2. Additions of special methods for classes
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Classes wishing to support the rich comparison mechanisms must add
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one or more of the following new special methods:
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def __lt__(self, other):
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...
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def __le__(self, other):
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...
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def __gt__(self, other):
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...
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def __ge__(self, other):
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...
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def __eq__(self, other):
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...
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def __ne__(self, other):
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...
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Each of these is called when the class instance is the on the
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left-hand-side of the corresponding operators (<, <=, >, >=, ==,
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and != or <>). The argument other is set to the object on the
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right side of the operator. The return value of these methods is
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up to the class implementor (after all, that's the entire point of
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the proposal).
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If the object on the left side of the operator does not define an
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appropriate rich comparison operator (either at the C level or
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with one of the special methods, then the comparison is reversed,
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and the right hand operator is called with the opposite operator,
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and the two objects are swapped. This assumes that a < b and b > a
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are equivalent, as are a <= b and b >= a, and that == and != are
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commutative (e.g. a == b if and only if b == a).
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For example, if obj1 is an object which supports the rich
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comparison protocol and x and y are objects which do not support
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the rich comparison protocol, then obj1 < x will call the __lt__
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method of obj1 with x as the second argument. x < obj1 will call
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obj1's __gt__ method with x as a second argument, and x < y will
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just use the existing (non-rich) comparison mechanism.
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The above mechanism is such that classes can get away with not
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implementing either __lt__ and __le__ or __gt__ and
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__ge__. Further smarts could have been added to the comparison
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mechanism, but this limited set of allowed "swaps" was chosen
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because it doesn't require the infrastructure to do any processing
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(negation) of return values. The choice of six special methods was
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made over a single (e.g. __richcmp__) method to allow the
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dispatching on the opcode to be performed at the level of the C
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implementation rather than the user-defined method.
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3. Addition of an optional argument to the builtin cmp()
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The builtin cmp() is still used for simple comparisons. For rich
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comparisons, it is called with a third argument, one of "<", "<=",
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">", ">=", "==", "!=", "<>" (the last two have the same
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meaning). When called with one of these strings as the third
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argument, cmp() can return any Python object. Otherwise, it can
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only return -1, 0 or 1 as before.
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Chained Comparisons
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Problem
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It would be nice to allow objects for which the comparison returns
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something other than -1, 0, or 1 to be used in chained
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comparisons, such as:
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x < y < z
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Currently, this is interpreted by Python as:
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temp1 = x < y
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if temp1:
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return y < z
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else:
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return temp1
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Note that this requires testing the truth value of the result of
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comparisons, with potential "shortcutting" of the right-side
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comparison testings. In other words, the truth-value of the result
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of the result of the comparison determines the result of a chained
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operation. This is problematic in the case of arrays, since if x,
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y and z are three arrays, then the user expects:
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x < y < z
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to be an array of 0's and 1's where 1's are in the locations
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corresponding to the elements of y which are between the
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corresponding elements in x and z. In other words, the right-hand
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side must be evaluated regardless of the result of x < y, which is
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incompatible with the mechanism currently in use by the parser.
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Solution
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Guido mentioned that one possible way out would be to change the
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code generated by chained comparisons to allow arrays to be
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chained-compared intelligently. What follows is a mixture of his
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idea and my suggestions. The code generated for x < y < z would be
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equivalent to:
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temp1 = x < y
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if temp1:
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temp2 = y < z
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return boolean_combine(temp1, temp2)
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else:
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return temp1
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where boolean_combine is a new function which does something like
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the following:
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def boolean_combine(a, b):
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if hasattr(a, '__boolean_and__') or \
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hasattr(b, '__boolean_and__'):
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try:
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return a.__boolean_and__(b)
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except:
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return b.__boolean_and__(a)
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else: # standard behavior
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if a:
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return b
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else:
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return 0
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where the __boolean_and__ special method is implemented for
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C-level types by another value of the third argument to the
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richcmp function. This method would perform a boolean comparison
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of the arrays (currently implemented in the umath module as the
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logical_and ufunc).
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Thus, objects returned by rich comparisons should always test
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true, but should define another special method which creates
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boolean combinations of them and their argument.
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This solution has the advantage of allowing chained comparisons to
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work for arrays, but the disadvantage that it requires comparison
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arrays to always return true (in an ideal world, I'd have them
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always raise an exception on truth testing, since the meaning of
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testing "if a>b:" is massively ambiguous.
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The inlining already present which deals with integer comparisons
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would still apply, resulting in no performance cost for the most
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common cases.
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Local Variables:
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mode: indented-text
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