Any SML coders able to translate this to Python?

[Chris Angelico]

On Thu, Sep 6, 2018 at 6:44 PM, Marko Rauhamaa <marko at pacujo.net> wrote:
> Chris Angelico <rosuav at gmail.com>:
>
>> On Thu, Sep 6, 2018 at 2:29 PM, Marko Rauhamaa <marko at pacujo.net> wrote:
>>> Marko Rauhamaa <marko at pacujo.net> (Marko Rauhamaa):
>>>> Steven D'Aprano <steve+comp.lang.python at pearwood.info>:
>>>>> I have this snippet of SML code which I'm trying to translate to Python:
>>>>>
>>>>> fun isqrt n = if n=0 then 0
>>>>>              else let val r = isqrt (n/4)
>>>>>                   in
>>>>>                     if n < (2*r+1)^2 then 2*r
>>>>>                     else 2*r+1
>>>>>                   end
>>>> [...]
>>>> You must make sure "r" doesn't leak outside its syntactic context so:
>>>>
>>>> def isqrt(n):
>>>>     if n == 0:
>>>>         return 0
>>>>     else:
>>>>         def f2398478957():
>>>>             r = isqrt(n//4)
>>>>             if n < (2*r+1)**2:
>>>>                 return 2*r
>>>>             else:
>>>>                 return 2*r+1
>>>>         return f2398478957()
>>>
>>> Actually, this is a more direct translation:
>>>
>>>    def isqrt(n):
>>>        if n == 0:
>>>            return 0
>>>        else:
>>>            def f2398478957(r):
>>>                if n < (2*r+1)**2:
>>>                    return 2*r
>>>                else:
>>>                    return 2*r+1
>>>            return f2398478957(isqrt(n//4))
>>>
>>
>> I don't understand why you created that nested function instead of
>> something simple like renaming the variable. Is there a difference
>> here?
>
> Yes, in understanding the semantics of "let."
>
> "let" is used to introduce local bindings in some functional programming
> languages. I must admit I'm not fully versed in ML but it looks like the
> analogue in Lisp variants. This is how the above function would be
> written in Scheme:
>
>    (define (isqrt n)
>       (if (= n 0)
>           0
>           (let ((r (isqrt (quotient n 4))))
>             (if (< n (expt (1+ (* 2 r)) 2))
>                 (* 2 r)
>                 (1+ (* 2 r))))))
>
> Now, Lisp's "let" can be implemented/defined using "lambda":
>
>    (let ((X A) (Y B) ...) . BODY)
>
>    =>
>
>    ((lambda (X Y ...) . BODY) A B ...)
>
> which gives us:
>
>    (define (isqrt n)
>       (if (= n 0)
>           0
>           ((lambda (r)
>             (if (< n (expt (1+ (* 2 r)) 2))
>                 (* 2 r)
>                 (1+ (* 2 r))))
>            (isqrt (quotient n 4)))))
>
> Python does have a limited form of "lambda" and even a conditional
> expression so--as others have mentioned--this particular function could
> be translated pretty directly into Python using its lambda.
>
> More generally and idiomatically, though, Python's functions are named.
> So that explains the version I give above.

And even more idiomatically, Python doesn't require a new scope just
for a new variable. So a much more idiomatic translation would be to
simply ensure that the inner variable can't collide, and then ignore
the function boundary. And I'm not sure if there even is a name
collision. What's the issue with scoping at all here? What's the inner
function actually achieving?

ChrisA