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Re: Mathematica and Lisp

• To: mathgroup at smc.vnet.net
• Subject: [mg120049] Re: Mathematica and Lisp
• From: David Bailey <dave at removedbailey.co.uk>
• Date: Wed, 6 Mar 2013 06:04:51 -0500 (EST)
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On 06/03/2013 03:13, Richard Fateman wrote:
> On 3/5/2013 1:16 AM, David Bailey wrote:
> <snip>
>>
>> It is important to realise that anyone can understand any expression
>> involving operators by using Hold and FullForm:
>>
>> (f @@@ g) // Hold // FullForm
>>
>> Hold[Apply[f,g,List[1]]]
>
> I, of course, would suggest that one NOT use
> (f@@@g)//Hold//FullForm
>
> but
>
> FullForm[Hold[f@@@g]]
>
> 1. My form is clearer, not using any additional mysterious-to-the-novice
> infix operations like //.
>
> 2. It is even shorter, using 2 fewer characters, as written.
>
> 3. It apparently requires less thought, because even you were, at least
> for the moment,  unsure of the precedence of // and so you inserted the
> entirely unnecessary ()   around f@@g.
Yes, I never use @@@, and convert it to an equivalent whenever I 
encounter it - but it is there for those that like it.
>
> 4. There is really no question of the precedence in my form.
>

So perhaps we should extend your principle to maths itself? Why risk 
students getting confused about the meaning of a + b c + d or f(a+b)- 
better to teach students to use a notation equivalent to FullForm! This 
principle would be even more useful when they got to calculus, where 
notations like dy/dx and integrals are hopelessly ambiguous in that the 
terminating dx looks superficially as if it could commute with the 
integrand! These notations probably often encourage students to perform 
invalid manipulations - but even so, most people value them!

I guess Mathematicians themselves realised why operator notation is so 
useful a long time back. It reduces the clutter and helps people to 
concentrate on what matters. Ultimately the choice between FullForm and 
operator form is a psychological question - not a math or computer 
science one. Those of us who do a lot of programming, also value 
operators that assist with that task too.

The Mathematica language offers users a lot of choice - which you seem 
to abhor because some people don't choose to use it your way!

David Bailey
http://www.dbaileyconsultancy.co.uk

• References:
  • Re: Mathematica and Lisp
    • From: Richard Fateman <fateman@cs.berkeley.edu>