Behavior of expression evaluation in Plot

I'm confused with Mathematica's way of parsing expressions. I've been struggling with this for a while and never found an exhaustive answer, sometimes things don't parse the way I think they would and I don't really understand why.

As an example, with Mathematica 8:

(* A works *)
Manipulate[
  Plot[(y/a) /. {y -> (x - b)}, {x, 0, 2}, PlotRange -> {0, 1}],
  {a, 1, 2},
  {b, 0, 1}]

(* B doesn't work *)

Manipulate[
  Plot[(x/a) /. {x -> (x - b)}, {x, 0, 2}, PlotRange -> {0, 1}],
  {a, 1, 2},
  {b, 0, 1}]

(* C works *)
(x/a) /. {x -> (x - b)}
Manipulate[
  Plot[%, {x, 0, 2}, PlotRange -> {0, 1}],
  {a, 1, 2},

  {b, 0, 1}]

(* D doesn't work *)
test = (x/a) /. {x -> (x - b)}
Manipulate[
 Plot[test, {x, 0, 2}, PlotRange -> {0, 1}]
, {a, 1, 2}, {b, 0, 1}]

(* E works *)
test2[x_, a_, b_] = (x/a) /. {x -> (x - b)}

Manipulate[
  Plot[test2[x, a, b], {x, 0, 2}, PlotRange -> {0, 1}],
  {a, 1, 2},
  {b, 0, 1}]

Case A works, so the substitution is performed fine inside Plot and Manipulate.

But B doesn't, which I could understand as an issue trying to substitute a variable with an expression containing itself, but then, if you evaluate it beforehand, as in C, everything works again, so it has to be a problem with x being part of Plot, I guess.

Then if you assign the result of the substitution to a variable, you can't directly plot it, so it seems that variables are not evaluated if they are not functions (as in E, with pattern matching) inside Plot. But % is, so % is "special" as it gets evaluated inside plot while a standard symbol assigned to a value does not.

Can someone explain me all this? I guess it's related to the Hold attributes a function can have?

Comments

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