[Haskell] 2-D Plots, graphical representation of massive data
carette at mcmaster.ca
Fri Aug 27 11:42:56 EDT 2004
> One could create Haskell libraries that are matlab-like, but most of
> the advantages of haskell (ie stong typing) are not realizable in
> Haskell. To express even the most basic of matrix datatypes and
> operations requires dependent types.
Jerzy Karcmarczuk replied:
> I did not understand what is not realizable where...
Note that I did not say "not realizable" [this would be false], I only
claimed that most of the advantages of Haskell would be "lost". It has been
shown how to embed a dynamically typed language into a statically typed one.
An interesting embedding of Matlab-like functionality in Haskell would
really need to feel more like Haskell than Matlab!
This is not to say that embedding Matlab functionality into Haskell, even at
the cost of having that subset be dynamically typed, would not be quite
useful. Quite the contrary.
> I have the impression that the true calculus/math analysis percentage in
> Matlab programs
> is negligible. Look at the composition of Matlab toolboxes.
[This information is straight from Cleve Moler]. The main uses of Matlab
are in industry, not academia. And there, they use toolboxes, few use 'raw'
Matlab. The most propular toolbox is Simulink. And the mathematics of
Simulink is partly about matricies, but mostly it is about differential
equations. The interface just hides them from the user quite successfully.
> With symbolic packages, such
> as Maple or Mathematica it is a bit different, but statistically what
> counts is pure algebra +
> a good deal of visualization facilities. Actually, with the development
> of the Automatic
> differentiation techniques, one needs much less of symbolic processing
I do not understand this 'statistically what counts is pure algebra +
visualization' statement. That visualization is extremely important I
fully agree with. That the nitty-gritty of these systems is all implemented
using pure algebra, again agreed. But my experience is that what most users
want is to solve differential equations (or computing quadratures, but that
is clearly the same thing). Of course, what they really want is to not see
those DEs at all, but see control systems, circuits, chemical flows, etc.
All of which boil down to DEs.
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