[Haskell-beginners] Is "step by step" the most natural style of thought?

[Michael Mossey]

Daniel Fischer wrote:
> Am Dienstag 20 Oktober 2009 04:48:50 schrieb Michael Mossey:
>>
>> Eliminating variables and working with function combinations has benefits.
> 
> But it's not unconditionally a good thing. If you exaggerate it, it's pure obfuscation.
> Nevertheless, playing around with eliminating variables and using combinators 
> even beyond the border of obfuscation is a good exercise.
> You gain understanding and a feeling of when it's better to stop by that.
> 

I think I understand.

Another way to put my point is that learning Haskell has trained my eye to 
notice when a particular variable is flopping around in six different 
places. I programmed for twenty years or more in imperative languages (in a 
business setting, not academia) and no one ever said, "Hey we've got too 
many repetitions of x! Let's see what the underlying abstraction REALLY is."


>> The one suggestion I've seen here that seems to be right on the money is
>>
>> liftM2 (&&) (< 0.5) (> -0.5)
> 
> May I offer
> 
> (&&) <$> (< 0.5) <*> (> -0.5)
> 
> ? It works on Applicative Functors (doesn't need the full force of Monads).
> 
>> Although that might seem less clear to a beginner, it is actually _more_
>> clear than the lambda function in some ways. It's easier to work with proof
>> at a more abstract level like this, and strange as it may seem, what I seem
>> to observe in expert users of Haskell is that their brains will pick up
>> what this is doing faster than the lambda function.
> 
> In this small example, both are immediately clear, you need more complicated lambda 
> expressions to get a measurable difference :)

Yeah, pretty small example, but based on what I've read in "Real World 
Haskell" and "Craft of Functional Programming," the authors find a lot of 
"strange-looking" (to the imperative programmer's eye) function combinators 
to be the most natural way of expressing the solution, and from time to 
time I find my thoughts aligning with them, and I realize how much less 
thought it takes.

This raises the question: is "step by step" thinking the "most natural" way 
to think about a mathematical problem? My hunch is "no." There are multiple 
modes of thought, and no reason to eliminate cognitive models that involve 
imagery, imaginary things moving and sliding through space... or analogies 
to the more common physical world... or the list is endless. I like the way 
Haskell resonates with a larger set of thinking styles.

Mike