Replace x, but not x[a] [duplicate]

Question

I want to replace all occurences of the symbol x with x[a], as long as it is not in the form x[a].

In other words, I am looking for magicReplacementRule in

x[a] + x /. magicReplacementRule
--> x[a] + x[a]

I tried

x[a] + x /. Except[x[a], x] -> x[a]

but the result was x[a][a] + x[a].

Answer 1

Use Replace instead of ReplaceAll with the option Heads -> False.

Replace[x[a] + x, x -> y, {0, Infinity}, Heads -> False]

{0, Infinity} here is a level specification which tells Replace to replace everywhere, just like ReplaceAll. You can drop Heads -> False because it's the default setting for Replace, but I wanted to point out the option which controls this behaviour.

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Update: It appears that since version 10, All can be used as a substitute for the {0, Infinity} level specification:

Replace[x[a] + x, x -> y, All]

Answer 2

In the depth-first preorder traversal of ReplaceAll complete expressions are matched before heads therefore one can use a skip rule⁽¹⁾⁽²⁾. Since you also want to replace x with x[a], the pattern to be skipped, you can use a single rule with Alternatives:

{x[a], x} /. x[a] | x -> x[a]

{x[a], x[a]}

( Since Plus[x[a], x[a]] evaluates to 2 x[a] I used List in the example above. )

Answer 3

because the x you want to replace is in the last level of the expression you can use:

Replace[Sin[x] + x[a] + x, x -> y, {-1}]
    (*y + Sin[y] + x[a]*)