
Re: Mathematica and Lisp
Posted:
Jan 14, 2013 11:28 PM


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}];
s//InputForm
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 1dimensional 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 http://www.dbaileyconsultancy.co.uk

