Strange behaviour of variables in Table

Question

I'm trying to work with some vectors and have run into a strange problem. An obvious way to define a difference of two vectors would be

dif[x_,y_] := x-y

I thought an equivalent way of doing this would be

dif[x_,y_] := Table[x-z,{z,{y}}][[1]]

However, using this second method, there is some strange behaviour. When I evaluate

dif[{x,z},{0,0}]

I get the result

{x,{0,0}}

which is clearly not what I wanted.

If I try evaluating

dif[{x,y},{0,0}]

instead, everything is ok, which leads me to think that the variable z in my definition of dif is treated as non-local. This seems pretty counterintuitive to me, as I was expecting z to act as a dummy variable.

What am I missing?

One solution that works is using Module. This is a bit unsatisfying though, as it seems to me z should be treated as local even without having to explicitly demand this.

Answer 1

Table doesn't scope the variable like that. This allows you to do things like this:

a = x^2;
Table[a, {x, 0, 3}]
(*{0, 1, 4, 9}*)

In your case you would like to scope z, which you can do via:

dif[x_, y_] := Module[{z}, Table[x - z, {z, {y}}][[1]]]

I think the relevant part of the doc is where it states: "Table effectively uses Block to localize values or variables."

So what it's doing is roughly evaluating: Block[{z=y},x-z], which means any z present in x will also get substituted. Though I think it could have been stated more clearly and properbly should have an example under possible issues.