Subject:      Re: Arrays and general functions

Reginald Meeson writes

> Interesting discussion, but it seems to me that Haskell already
> provides the best of both worlds, namely

>   a. Efficient implementation of arrays as data objects, with indexing
>      as a projection function; and

(Actually, efficient seems a little hopeful here).

Rats, my Haskell manual is home, so correct me if the following
is wrong... Actually, let me pose this as a question (then I
don't have to get so embarrassed later!)

Let's say I have an array arr and at some index i I want to update
it to be x.  That is, I want to define

upd arr i x 

to return a new array equal to arr everywhere except i where the
value of the result is x.  It seems to me that there is no
way to write this function without decomposing arr into a list
and rebuilding an array.  Am I right?  (I will be pleased to be wrong!)

>From the APL/Nial/Array Theory world, it is a travesty to be forced
to perform such a decomposition.  There are enough optimization problems
without mixing lists into it.  

This, of course, is not to say that it is not convenient or perhaps
necessary to be able to convert lists into arrays.  It is very convenient
for monolithic array operations, such as building tables for lookup
functions, etc, but it also seems like there ought to be some kind
of support for incremental array operations, like update.

Dave Barton writes:

> I am interested in how the lack of a distinction gets in the way of
> your reading and understanding programs, however.

(where the distinction is between arrays as rules and arrays
as general functions).

My apologies for not being more sensitive to your application
before my first response.  I have an interest in the
optimization of incremental array operations (see above) and
don't tend to think of arrays as fixed tables.  

The first area that pops into mind where I am more comfortable
with having the distinction is graph theory.  Now perhaps
it has something to do with the way it was taught to me, but
I like thinking of the arrays as data objects rather than functions,
and it helps me in thinking about what an algorithm is doing and
how much the algorithm costs.

On the other hand, I am not sure how important this is or how 
long it would take me to forget or drop my dependence on the


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