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Re: Re: Sequential evaluation of lists

On Dec 23, 2004, at 7:58 AM, János wrote:

> It would be nice to have all List manipulation functions have an option
> Direction->Left or Direction->Right, just as Limit has +1 or -1. I even
> would like functional programming functions like Map or Apply have this
> option. Any seesaw type operation modeling would greatly benefit from
> it and nature has many.

MapIndexed can be used to map a function whose result depends on the 
distance from the first or last position in a list,  MapIndexed can 
also be used to make a version of Apply that depends on the position in 
the list.

> On Dec 22, 2004, at 4:53 AM, Ray Koopman wrote:
>> When I first started using Mathematica (v2), one of the features that
>> I found rather surprising is its sequential evaluation of lists, as in
>> In[1]:= x = 0; {x++,x++,x++}
>> Out[1]= {0,1,2}
>> I had expected a warning that such code should be avoided because
>> it presumed sequential evaluation, which could not be guaranteed,
>> and a recommendation to treat list elements as being evaluated in
>> parallel -- if not simultaneously then in no particular order.
>> However, so far I have found no exception to sequential evaluation
>> and no mention of it in any documentation. Have I missed something?

++ is not a functional operation by definition since it alters the 
value of its argument.  It is explicitly a procedural operation and 
using it explicitly assumes a known order of evaluation.  The 
functional equivalent of your statement that assumes no order of 
evaluation and thus no knowledge of global state beyond the arguments 
to the function is


Of course the existence of a globally accessible x and the ability to 
redefine its value through Set also breaks the functional programming 
paradigm, but Mathematica has never claimed to be a purely functional 
language, only to allow it as one of a variety of styles.  At any rate, 
given that Mathematica is not dogmatic about functional programming, 
and that ++ is explicitly not a functional operation there is no need 
for a warning because no rule is being broken.  Referring to the help 
browser, ++ is described in section 2.5.4 of The Mathematica Book which 
is titled "Special Forms of Assignment" which instructs the programmer 
that this is not functional programming since assignment of state is 
not allowed.  Furthermore the first phrase of said section is 
"Particularly when you write procedural programs in Mathematica,..." 
again informing the user that the assumptions of functional programming 
do not apply.

I believe ++ can be implemented in purely functional languages like 
Haskell using a construct called a monad but I don't really understand 
the details and since Mathematica is not purely functional it's not 
necessary to include the monad model anyway.



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