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I've heard that Mathematica is usually faster when the code is list-based and/or uses a functional paradigm.

I'm still working on getting the hang of this; there are a lot of Ifs and Fors that I end up using in more complex code that probably shouldn't be there.

In general how do I go about writing more functional and list based code?

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  • $\begingroup$ This really has nothing to do with Mathematica. It is about functional programming. You basically have to learn to ask the computer what to do and not how to do it. i.e think in a higher abstract level, not implementation level. In addition, you think of functions as objects themselves as well just like data itself. But I think this question belongs to functional-programming tag here programmers.stackexchange.com/questions/tagged/… also see wiki en.wikipedia.org/wiki/Functional_programming $\endgroup$
    – Nasser
    Dec 17 '13 at 21:37
  • $\begingroup$ @Nasser Thing is, I am reasonably comfortable with Lisp. But Mathematica has its own style, and the problems faced are different. Plus, there are many in-built commands that work well with functional programming or lists. $\endgroup$
    – Manishearth
    Dec 17 '13 at 21:40
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    $\begingroup$ So this is like asking: I know OO programming in C++, but how to do OO programming in Java? well, you need have to learn new syntax and new commands in Java. The concept of OO programming do not change. Only the syntax changes. Same case here with functional programming and different languages. To learn the syntax of Mathematica is a very wide question. At least that is what I think. But you are free to ask anything you want, and others are free to answer :) $\endgroup$
    – Nasser
    Dec 17 '13 at 21:56
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    $\begingroup$ @Nasser, with all due respect, you have some one interested in learning Mathematica and you slap them in their face? I don't get it. $\endgroup$
    – carlosayam
    Dec 17 '13 at 22:12
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    $\begingroup$ Is this something you are after?: alternatives for loops $\endgroup$
    – Kuba ♦
    Dec 17 '13 at 22:14
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If you come from Lisp, note that Mathematica's approach to list manipulation is not through deconstruction operators like CAR and CDR and construction through CONS. And this is also different from traditional functional programming, in which most lists metaphors are actually derived from our old friend Lisp. Mathematica is very different.

Everything in Mathematica is an expression and certainly lists are. So deconstruction of expressions in Mathematica is achieved by using mainly pattern matching and some built-in operators. However, you usually don't need to disassemble a list (in the traditional sense) as Mathematica offers built-ins that are similar to the functional programming counterparts.

For List manipulation, I find Fold, FoldList, Map and MapThread probably the closest to FP - although there are many others which would be probably harder to achieve in FP but are built-ins in Mathematica. For example, look at Partition or even Transpose. Whereas in Lisp a list of lists is just that, Mathematica can transpose it as it were a matrix if you know that all items have the same length.

So, yes, you need to leave the FP list paradigm and embrace expressions in Mathematica!

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  • $\begingroup$ Hmm, this is interesting :) I haven't used Fold much but I can see how it would be useful here. (Also, I don't "come from" Lisp, I just am comfy with it but I am much more at ease with procedural things). $\endgroup$
    – Manishearth
    Dec 17 '13 at 22:24

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