Oh look, another language (ceylon)
Steven D'Aprano
steve at pearwood.info
Tue Nov 19 08:00:21 CET 2013
On Mon, 18 Nov 2013 19:33:01 -0800, Rick Johnson wrote:
> I've never *really* been crazy about the plus operator concatenating
> strings anyhow, however, the semantics of "+" seem to navigate the
> "perilous waters of intuition" far better than "*".
>
> Addition of numeric types is well defined in maths: Take N inputs
> values and *reduce* them into a single value that represents the
> mathematical summation of all inputs.
Which sum would that be?
Addition of vectors, matrices, quaternions, tensors, something else?
Do you perhaps mean the Whitney Sum?
http://mathworld.wolfram.com/WhitneySum.html
Ah, no, you're talking about addition of Real numbered values, where
nothing can *possibly* go wrong:
py> 0.1 + 0.1 + 0.1 == 0.3
False
Hmmm. Oh well, at least we know that adding 1 to a number is guaranteed
to make it bigger:
py> 1e16 + 1 > 1e16
False
Surely though, the order you do the addition doesn't matter:
py> 1.5 + (1.3 + 1.9) == (1.5 + 1.3) + 1.9
False
Dammit maths, why do you hate us so???
So, explain to me again, what is the *precise* connection between the
mathematical definition of addition, as we learn about in school, and
what computers do?
> HOWEVER,
>
> Addition of strings (concatenation) requires interpreting the
> statement as a more simplistic "joining" process of : take N inputs
> and join them together in a *linear fashion* until they become a
> single value.
Ah, you mean like addition in base-1, otherwise known as the unary number
system, also known as a tally.
So if you want to add (decimal) 3 and 5 using base-1, we would write:
||| + |||||
and concatenating the tallies together gives:
||||||||
which if I'm not mistaken makes 8 in decimal.
> There is an inconsistency when applying the "*" operator between
> numerics and strings. In the case of numerics the rules are widely
> understood and quite logical, HOWEVER, in the case of "string products",
> not only are rules missing, any attempt to create a rule is illogical,
> AND, we've broken the consistency of the "*" interface!
A foolish consistency is the hobgoblin of little minds.
Just because you can't define a sensible meaning for str * str doesn't
mean you can't define a sensible meaning for str * int.
> py> "a" * "4"
> 'aaaa'
>
> Okay, that makes sense, but what about:
>
> py> "a" * "aaaa"
>
> That will haunt your nightmares!
You're easily terrified if you have nightmares about that. I can't
imagine what you would do if faced with the M-combinator applied to
itself.
> But even the previous example, whilst quite logical, is violating the
> "contract of transformations"
What contract of transformations?
--
Steven
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