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Re: Mathematica and Lisp

On 14/01/2013 05:01, Richard Fateman wrote:

> David has a point:  to some extent Mathematica "does Lisp wrong".  Lisp
> has lists but also arrays and hashtables.  Mathematica uses the term
> List, but the implementation is as an array. Then there is a SparseArray
> which is also not an array but a hashtable.

Actually, I don't think sparse arrays are based on hash tables. You can 
see the internal structure of a SparaseArray object thus:

  s = SparseArray[{{1, 1} -> 1, {2, 2} -> 2, {3, 3} -> 3, {1, 3} -> 4}];


SparseArray[Automatic, {3, 3}, 0, {1, {{0, 2, 3, 4}, {{1}, {3}, {2}, 
{3}}}, {1, 4, 2, 3}}]

The approach seems to be to index down one dimension, and then follow a 
list of entries for the other dimension. I am not sure what happens in 
the 1-dimensional case, but if you dump the structure out in the same 
way, it clearly isn't a hash table.

Incidentally, this really is the internal structure of a sparse array - 
you can replace the head of a sparse array, manipulate the structure and 
reassemble a sparse array if necessary!

Of course, It makes you wonder why sparse arrays do not use hash tables!

I am less convinced that LISP did get it right - they just got there 
first! Variants of LISP had to add arrays and hash tables to the basic 
language, which obviously traded language simplicity for performance on 
larger problems. Mathematica seems to have kept its original design (at 
least in this area) over the years, even though internally, lists now 
come in two flavors!

I also like the way in which Mathematica does not force people to use 
functional programming. I find many situations in which functional 
programming gives no perceptible gain, and can render an algorithm more 
obscure. Perhaps that is because I learned Fortran as my first computer 
language :)

I do tend to agree that teaching Mathematica as a first programming 
language, would be a bad idea, because so much happens behind the scene 
- for example the way in which multiple definitions for a function get 
reordered to improve efficiency. I would imagine that some students 
would get a hazy idea of what the were asking the computer to do, or how 
expensive it might be.

David Bailey

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