[Python-ideas] str.startswith taking any iterator instead of just tuple

[Devin Jeanpierre]

On Sun, Jan 5, 2014 at 9:08 PM, Terry Reedy <tjreedy at udel.edu> wrote:
> On 1/5/2014 12:48 PM, Andrew Barnert wrote:
>>
>> On Jan 5, 2014, at 3:09, David Townshend
>> <aquavitae69 at gmail.com> wrote:
>>
>>> Reading this thread made me start to think about why a string is a
>>> sequence,
>
>
> Because a string is defined in math/language theory as a sequence of symbols
> from an alphabet. If you want to invent or define something else, such as an
> atomic symbol type, please use a different term. For example:

And sequences in math / CS are functions from the natural
numbers to elements of the sequence. Since isinstance(str,
types.FunctionType) isn't True, it must mean that Python strings
aren't strings.

But seriously, Python functions aren't functions, the set of Python
complex numbers is not the set of complex numbers, Python types aren't
types, and Python addition is not addition; mathematical terminology
in programming is evocative and
not actually literally true. Arguments based on trying to literally
copy math to the letter are flawed, probably irretrievably so.

The important feature of strings in math is not that they are
literally a sequence of characters, but that they correspond to a
sequence of characters isomorphically. You can represent them any way
you like, as long as you maintain that isomorphism, and the operations
with the right names do the right thing, etc. As evidence, observe
that not every programming language has its string type obey the
equivalent of Python's sequence interface or math's notion of
"sequence" per se (mapping naturals to elements). For example, Haskell
strings are linked lists; Rust strings are arrays behind the scenes
but don't expose it within the str type; etc.

It's not just strings, either, There are a multitude of ways of
defining the natural numbers -- maybe a natural number is a set of a
given structure (and which structure?), maybe it is a pair of integers
where the second integer is 1, maybe it is an infinite sequence of
rationals whose limit is a rational with denominator 1, maybe it is a
bitstring of arbitrary finite length. The usual construction in math
is the first, but Python uses the last one. To say Python doesn't
actually have natural numbers but does have strings, is absurd, but it
is what your logic points towards. If two things are equivalent,
everything said about one can be said about the other, and math is
about saying things about stuff, not about precise definitions of
structure -- those are chosen for convenience.

-- Devin