list of polynomial functions

[Scott David Daniels]

Fredrik Lundh wrote:
> Tim Chase wrote:
>>> The `i` is the problem.  It's not evaluated when the lambda
>>> *definition* is executed but when the lambda function is
>>> called.  And then `i` is always == `n`.  You have to
>>> explicitly bind it as default value in the lambda definition:
>>>
>>>      polys.append(lambda x, i=i: polys[i](x)*x)
>>>
>>> Then it works.
>>
>> Just to sate my curiosity, why can the lambda find "polys", but not 
>> find "i"?  If what you're describing is the case, then it seems to me 
>> that the following code should work too:
> 
> it's not that it cannot find it, it's that if you use a closure, i will 
> have the same value for all lambdas.
> 
>> There's some subtle behavior here that I'm missing.
> 
> lexical closures bind to names, default arguments bind to values.

Just to be a bit more explicit:
In code like:
     def make_polys(n):
         """Make a list of polynomial functions up to order n."""
         p = lambda x: 1
         polys = [p]
         for i in range(n):
             polys.append(lambda x: polys[i](x)*x)
         i=3

The lambda-defined functions will be called after the for loop is done,
at which time the "i" (from the surrounding environment) will have a
value of 3.  Hope this makes it a bit clearer.

--Scott David Daniels
scott.daniels at acm.org