Re: Very very basic question about Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg111222] Re: Very very basic question about Mathematica
- From: Leonid Shifrin <lshifr at gmail.com>
- Date: Sat, 24 Jul 2010 05:06:17 -0400 (EDT)
Just a correction to my previous reply:
During normal evaluation subexpressions are evaluated before expressions
( I wrote expressions before subexpressions, which is incorrect - this only
happens if evaluation of a particular (sub)expression is non-standard).
Regards,
Leonid
On Fri, Jul 23, 2010 at 12:17 AM, Leonid Shifrin <lshifr at gmail.com> wrote:
> Hi Sam,
>
> A short answer is that there are no functions in Mathematica, only
> expressions and
> replacement rules (except pure functions perhaps). When you define a
> "function" like
>
> s[x_, h_]:=x+h
>
> you really associate a certain global replacement rule with a symbol <s>.
> When
> evaluator sees a match, it rewrites according to this rule. There are no
> stack frames
> or activation records - it is a completely different mechanism that
> superficially resembles
> function calls (there is evaluation stack which is similar but not the
> same). So, <s>
> is always a Symbol.
>
> Generally, Mathematica at its hart is a rule-based engine, not a functional
> language. Functional
> layer sits already on top of it. So comparisons with Scheme or Lisp may be
> misleading. In
> particular, if you study Mathematica evaluation loop, you will see that the
> recursive part will be similar
> to Lisp (that expressions are evaluated before subexpressions normally),
> but the part related
> to rule application is not found in Lisp.You may want to check out some
> simple account explaining
> these things about Mathematica, perhaps some parts of the virtual book or
> documentation related to evaluation of expressions. I also dwelt somewhat on
> this in my book,
>
> www.mathprogramming-intro.org/
>
> Regarding Manipulate, this behavior is related to scoping (Manipulate is a
> scoping
> construct and you relationship between <s> and <h> was originally defined
> outside
> of the scope of Manipulate).
>
> Hope this helps.
>
> Regards,
> Leonid
>
>
>
> On Thu, Jul 22, 2010 at 1:44 PM, Sam Takoy <sam.takoy at yahoo.com> wrote:
>
>> Thanks to all who responded!
>>
>> May I belabor this point a little. I understand how to make Manipulate
>> work and I understand functions. (I am a product of Scheme from with
>> Mathematica seems to have borrowed a few ideas.)
>>
>> My question is much more formal: What are the building blocks of
>> Mathematica, the formal language. When you say
>>
>> s = x+h
>>
>> what is s?
>>
>> Is it an "expression"? Does s represent x+h wherever it appears
>> (assuming x and h are unassigned at the time of s=x+h)? Apparently not
>> always: yes in s/.h->5, but not in Manipulate.
>>
>> So here, then is my "model" of Mathematica:
>> In s = x+h, s is an "Expression"
>> In s[x_, h_]:=x+h, s is a "Function"
>>
>> Manipulate expects a "Function" so that answers my question.
>>
>> Then what is
>>
>> s[h_] := x + h? Is it an "Expression" or a "Function" of h with a
>> parameter x?
>>
>> Would then Manipulate[Plot[s[h], {x, 0, 1}, PlotRange -> {0, 1}], {h, 0,
>> 1}] work? (The answer is yes.) So apparently, Plot is happy with an
>> "Expression", but Manipulate wants a "Function"? Why?
>>
>> Also, in Manipulate[Plot[x+h, {x, 0, 1}, PlotRange -> {0, 1}], {h, 0,
>> 1}], x+h is no longer an "Expression", but is once again a "Function",
>> because of the context? Even though it's inside Plot which is happy with
>> an "Expression"?
>>
>> A personal note: I guess I'm a little frustrated that after a few months
>> of working with Mathematica, I still have to try things before I know
>> whether they'll work or not. I'm used to having a clear picture of the
>> grammar of the language that I'm working with, but I'm struggling here.
>>
>>
>> On 7/21/2010 7:14 AM, dr DanW wrote:
>> > I ran into this problem yesterday. I don't know exactly why it
>> > happens, I think it has something to do with the way Manipulate
>> > localizes variables. To solve it, I use a trick I found that lets me
>> > take an expression built up of global symbols and localize the
>> > symbols. Your trivial example:
>> >
>> > s = x + h
>> >
>> > Make a function out of it. The Evaluate[] is necessary to evaluate s,
>> > which replaces it with x+h
>> >
>> > sfnc = Function[{x, h}, Evaluate[s]]
>> >
>> > Now the Manipulate[] works fine
>> >
>> > Manipulate[Plot[sfnc[x, h], {x, 0, h}], {h, 0.1, 1}]
>> >
>> > I find myself using this trick a lot.
>> >
>> > Regards,
>> > Daniel
>> >
>>
>>
>>
>