On Saturday, March 7, 2015 at 5:04:02 AM UTC+5:30, Steven D'Aprano wrote:
> Rustom Mody wrote:
>
> > On Friday, March 6, 2015 at 10:13:55 PM UTC+5:30, Steven D'Aprano wrote:
> >> Rustom Mody wrote:
> >>
> >> > On Friday, March 6, 2015 at 3:57:12 AM UTC+5:30, rand...@fastmail.us
> >> > wrote:
> >> >> It's been brought up on Stack Overflow that the "in" operator (on
> >> >> tuples, and by my testing on dict and list, as well as dict lookup)
> >> >> uses object identity as a shortcut, and returns true immediately if
> >> >> the object being tested *is* an element of the container. However, the
> >> >> contains operation does not specify whether object identity or
> >> >> equality is to be used. In effect, the built-in container types use a
> >> >> hybrid test: "a is b or a == b".
> >> >>
> >> >> My question is, is this a *correct* implementation of the operator, or
> >> >> are objects "supposed to" use a basis of equality for these tests?
> >> >
> >> > nan is an illegal or bogus value.
> >>
> >> NANs *represent* bogus values, they aren't bogus themselves.
> >>
> >>
> >> > As usual legalizing the illegal is always fraught with increasing
> >> > conundrums.
> >> >
> >> > The most (to me) classic instance of this is denotational semantics.
> >> > In DS one tries to give semantics to programs by mapping programs to
> >> > math-functions across some domains
> >> >
> >> > However some programs crash. What should be the semantics of such a
> >> > program. We say its a partial function – undefined at the crash-points.
> >> > But partial functions are not nearly as tractable (to mathematicians!)
> >> > as total functions.
> >> > So we invent a bogus value ⊥ (called bottom) and totalize all
> >> > functions by mapping to this.
> >> >
> >> > Very nice…
> >> >
> >> > So nice in fact that we wish to add ⊥ to our programming language
> >> >
> >> > And now all hell breaks loose because the question x == ⊥ is the
> >> > halting problem.
> >>
> >> Oh nonsense. x == ⊥ is easily performed with the equivalent of:
> >>
> >> type(x) == BottomType and bit_representation(x) == bit_representation(⊥)
> >
> > You dont grok your theory of computation very well do you?
> >
> > def foo(x): return x + x
> > def bar(x): return x + x
> > def baz(x): return 2*x
> >
> > One can imagine an implementation where
> > id(foo) == id(bar)
> > [I am assuming that id is a good enough approx to bit_representation]
> >
> > Can you imagine an implementation where
> > id(bar) == id(baz)
> > ?
>
> Not necessarily if x are floats. But I'll grant you that 2*x and x+x are
> computationally equivalent if x is an int. I'll also grant you that there
> are other functions which are computationally equivalent to x+x but
> immeasurably more complex, and that for the compiler to recognise all such
> functions is equivalent to the halting problem.
Good so far
>
> What does this have to do with the ability to perform an equality test
> against some ⊥ value?
What do you understand by ⊥ value?
>
> Your argument is analogous to this:
>
> "Somewhere, out in the immensity of space, floats an infinite number of
> haystacks. Inside just one of those haystacks is a single tiny needle.
> Since it is impossible to locate that needle, it is likewise impossible to
> locate this needle I hold between my fingers!"
Straw... er Hayman!
>
> You have made a claim that None is a reinvention of the ⊥ (bottom) pattern,
Ok
> and that it is impossible to evaluate x == ⊥ due to the Halting Problem.
That depends on how you answer my question above: What do mean by ⊥ value?
> Let's put that to the test:
>
> [steve@ando ~]$ python -c "x = 23; print x == None"
> False
>
>
> I was hoping to have time to make a cup of tea while Python tried to solve
> the Halting Problem, possibly even to go to the market, do some shopping,
> do my house work, watch a movie, and catch a good night's sleep, but it
> only took a small fraction of a second for x == None to complete.
You dont know the difference between analogy and identity?
>
> I can draw only two possible conclusions:
>
> (1) The halting problem, and therefore Godel's Incompleteness Theorem as
> well, are disproven and the very fundamentals of mathematics and logic are
> overturned; or
>
> (2) You are mistaken that evaluating x == ⊥ is equivalent to solving the
> Halting Problem.
>
>
> If I were a betting man, I know where I would put my money.
>
I'd put my money on (some variation of) "Syntax Error"
python3:
>>> x = 1
>>> x == ⊥
File "<stdin>", line 1
x == ⊥
^
SyntaxError: invalid character in identifier
python2
>>> x = 1
>>> x == ⊥
File "<stdin>", line 1
x == ⊥
^
SyntaxError: invalid syntax
Which is to say ⊥ does not exist in python.
So until you say what *you* mean by ⊥ we cannot evaluate where the rheostat
sits between
"You/I are wrong" … "You/I are confused" … "You/I are not even wrong"
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