[Python-Dev] Recommend accepting PEP 312 -- Simple Implicit Lambda

[Kay Schluehr]

Reinhold Birkenfeld wrote:

>>
>>                lambda x,y: x+y*y
>>                lambda x,y: y**2+x
>>
>> are essentialy the same functions with different implementations [1].
> 
> 
> Except that they are not. Think of __pow__, think of __add__ and __radd__.

You know the difference between the concept of a function and it's 
infinitely many representations? That's why formal definitions exist.

> 
> Reinhold
> 
> 

Just for refresh:

"Formally, a function f from a set X of input values to a set Y of 
possible output values (written as f : X -> Y) is a relation between X 
and Y which satisfies:

    1. f is total, or entire: for all x in X, there exists a y in Y such 
that x f y (x is f-related to y), i.e. for each input value, there is at 
least one output value in Y.

    2. f is many-to-one, or functional: if x f y and x f z, then y = z. 
i.e., many input values can be related to one output value, but one 
input value cannot be related to many output values.

A more concise expression of the above definition is the following: a 
function from X to Y is a subset f of the cartesian product X × Y, such 
that for each x in X, there is a unique y in Y such that the ordered 
pair (x, y) is in f."

http://en.wikipedia.org/wiki/Function_%28mathematics%29

Kay