Should "counters" used in Do, Table, ... within Module be declared as local?

Question

I have little to no understanding of how Mathematica handles scoping, so the question may seem a little bit funny.

What is the preferred way:

Test[] = Module[{},
   Do[Print["Hello ", i], {i, 5, 50, 5}];
   ];
Test[];

Or:

Test[] = Module[{i},
   Do[Print["Hello ", i], {i, 5, 50, 5}];
   ];
Test[];

First option is all you need. Mathematica handles scoping a couple of different ways. Table/Do/etc. create their own scope for an iterator, and I believe they use textual scoping just like With (but unlike Block and Module). This may help: http://reference.wolfram.com/language/guide/ScopingConstructs.html. In particular look at "Learning Resources". — mfvonh, Dec 02 '14 at 20:41
One way to test such things is to use, and show, an explicit setting for your symbol. Try for example this small variation on your code: Module[{i=-20}, Do[Print["Hello ", i], {i, 5, 50, 5}]; i]. Notice that the i at the end is the Module variable and is not related to the i of the loop. — Daniel Lichtblau, Dec 02 '14 at 20:48
@d125q I've added an answer but there's a good chance someone will provide a better one or a good link to a previous answer. Worth waiting before you accept. — mfvonh, Dec 02 '14 at 20:55
@mfvonh Actually Table & related functions use the same type of scoping as Block (not like With). Try Table[i = 1; Print[i], {i, 5}]. — Szabolcs, Dec 02 '14 at 21:00
for entertainment ask a "c" programmer what this does.. i = {4, 5}; Do[Do[ Print[ i ] , {i, i}], {i, i}] — george2079, Dec 02 '14 at 21:05

score 5 · Accepted Answer · edited Apr 13 '17 at 12:56

One type of scoping uses "textual" replacement, meaning the symbolic layer of evaluation is bypassed. For example:

With[{i = 1}, SymbolName[Unevaluated[i]]]

enter image description here

SymbolName[Unevaluated[1]]

This property of With makes it very handy sometimes, simply as a way to avoid evaluation where it is not wanted. I learned this myself in this question.

Compare that to:

Block[{i = 1}, SymbolName[Unevaluated[i]]]

i

Module[{i = 1}, SymbolName[Unevaluated[i]]]

i$24225

And turns out my comment above was inaccurate. Table does not use textual scoping:

Table[SymbolName[Unevaluated[i]], {i, 1, 1}]

{i}

Should "counters" used in Do, Table, ... within Module be declared as local?

1 Answers1