User-defined Product with blocked variable and syntax hightlighting

Question

I want to define a new Product but for NonCommutativeMultiply, which I do something like this:

NCMProduct[expr_, iterator_] := NonCommutativeMultiply @@ Table[expr, iterator]

Is there any way for Mathematica to Block the iterator automatically to the scope of NCMProduct like it would for Product?

So then I could use things like:

i = 3; NCMProduct[f[i], {i, 5}] Product[f[i], {i, 5}]

In this case, Product will Block out i and the fact that I have assigned to i doesn't matter, but NCMProduct doesn't know that i is going to be Blocked inside its definition, and hence I get Table::itraw, which isn't the behaviour I want. I'd also like to have nice syntax highlighting for my NCMProduct showing that i is Blocked in the front end if possible!

Answer 1

Your problem is an evaluation leak, which is fixed with:

SetAttributes[NCMProduct, HoldAll];

NCMProduct[expr_,iterator_] := NonCommutativeMultiply @@ Table[expr, iterator]

Your example:

i = 3;
NCMProduct[f[i], {i, 5}]

f[1] ** f[2] ** f[3] ** f[4] ** f[5]

As for syntax coloring, the easiest thing to do is to copy the syntax information for Product:

SyntaxInformation[NCMProduct] = SyntaxInformation[Product];

Here is a screen shot showing the syntax coloring: