[plt-scheme] Newbie Lambda( ) (???????????)

----- Original Message ----- 
From: "Matthias Felleisen" <matthias at ccs.neu.edu>
To: "Carl Eastlund" <carl.eastlund at gmail.com>
Cc: <plt-scheme at list.cs.brown.edu>
Sent: Friday, February 13, 2009 8:23 PM
Subject: Re: [plt-scheme] Newbie Lambda( ) (???????????)


>
> Jesus, just to make sure. In case you have studied calculus,  functions 
> returning functions is very old. For example,
>
>   d/dx : (Real -> Real) -> (Real -> Real)
>
> Conventional mathematicians, though, tend to be afraid of the concept  and 
> therefore call these things 'operators' and 'functionals' and  other 
> hideous names.

If, as you say, mathematiciens use other names for the concept, that does 
not imply they are afraid of the concept. Ever heard of tensor operators in 
quantum mechanics? Did you ever see the beautiful graphical algebra of 
Yutsis and El Baz?
I am inclined to disagree on this point. Mho, Jos

>
> Now you are ahead of these people. You have taken the first step to a 
> land where all this is easy to understand, normal, and
>
>  .. HIGHLY PRODUCTIVE.
>
> (Think callbacks for GUIs and such stuff.)
>
> -- Matthias
>
>
>
>
>
>
>
> On Feb 13, 2009, at 2:13 PM, Carl Eastlund wrote:
>
>> On Fri, Feb 13, 2009 at 1:35 PM, Jesus Boadas <jboadas at gmail.com>  wrote:
>>> Thanks I understand now, this is new to me. My usual functions  only 
>>> return
>>> values, never could imagine that a function could return a function
>>
>> Functions can, indeed, return functions.  In fact, functions
>> themselves are values, so your function that returns a function is
>> still returning a value.  It just happens to be a more interesting
>> value than a number or a string.
>>
>>> I was doing some research and this is called higher order  functions or 
>>> I am in a
>>> mistake?.
>>
>> That is correct.  Higher order functions are functions whose inputs
>> and/or outputs are also functions.  They are commonplace in Scheme and
>> many similar programming languages.
>>
>> --Carl
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