On 9/11/2015 8:40 PM, Alexander Belopolsky wrote:
The insanity I am dealing with now is specific to Python datetime which
wisely blocks any binary operation that involves naive and aware
datetimes, but allows comparisons and subtractions of datetimes with
different timezones. This is not an unusual situation given a limited
supply of binary operators, Python has to reuse them in less than ideal
ways. For example,
>>> a = 'a'
>>> b = 'b'
>>> c = 5
>>> (a + b) * c == a * c + b * c
False
is less than ideal if you hold the distributive law of arithmetic
sacred.
In mathematics, algebra is, put simply, the study of binary operations.
None of the laws for particular operations on particular sets is
'sacred'. They are simply facts. Or possibly axioms whose consequences
are to be explored. A mathematician has no problem with 'a'+'b' !=
'b'+'a'. After closure, associativity is the most 'basic' operation,
but non-associative operations are studied.
The equality relation, mapping pairs of members of a set to True or
False is a different matter. Being an equivalence relation is
fundamental to both normal logic, algebraic proofs, and the definition
of sets. It is also required for the 'proper' operation of Python's
sets. (Lets leave nans out of the discussion).
Similarly, '-' is reused in datetime for two different
operation: if s and t are datetimes with the same tzinfo, s - t tells
you how far to move hands on the local clock to arrive at s when you
start at t. This is clearly a very useful operation that forms the
basis of everything else that we do in datetime. Note that for this
operation, it does not matter what kind of time your clock is showing or
whether it is running at all. We are not asking how long one needs to
wait to see s after t was shown. We are just asking how far to turn the
knob on the back of the clock. This operation does not make sense when
s and t have different tzinfos, so in this case a '-' is reused for a
different operation. This operation is much more involved. We require
an existence of some universal time (UTC) and a rule to convert s and t
to that time and define s - t as s.astimezone(UTC) - t.timezone(UTC).
In the later expression '-' is taken in the "turns of the knob" sense
because the operands are in the same timezone (UTC).
Datetime members, are rather unusual beasts. They are triples consisting
of a member of a discrete sequence (with some odd gaps), a tz tag, and a
0/1 fold tag. The tz tags divide datetimes into equivalence classes.
The '-' operation is also unusual in being defined differently for pairs
in the same or different equivalence classes.
Clearly, when we "abuse" the mathematical notation in this way,
Mathematicians wildly overload operater/relation symbols. '=' is the
only one I can think of with more-or-less universal properties.
we cannot expect mathematical identities
which are context dependent
to hold
in a different context. Right.
and it is easy to find for
example, aware datetimes u, t, and s such that (t - u) - (s - u) ≠ t - s.
Datetime '-' (subtraction) should be documented as an unusual overloaded
use which does not have the normal properties that the naive might expect.
Within the constraint on '=', there are two choices for designing an
operation.
1. Define the operation the way you want, and live with the consequent
properties (or absence of properties).
2. Decide the properties you require, and live with the consequent
restriction on the definition.
--
Terry Jan Reedy
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