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Re: Mathematica and Lisp
*To*: mathgroup at smc.vnet.net
*Subject*: [mg129452] Re: Mathematica and Lisp
*From*: David Bailey <dave at removedbailey.co.uk>
*Date*: Mon, 14 Jan 2013 23:31:05 -0500 (EST)
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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 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
http://www.dbaileyconsultancy.co.uk
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