Infix-prefix coding problem

infix-prefix

We have some expressions, represented as a list where every term is either:
- A variable (e.g. A, B, C)
- A boolean operator (AND or OR)
- A nested expression (list)

You're presented an expression with infix operators, like:

  [A AND [B OR C]]

Can you transform these expressions so the operators are in prefix order? The output for this case is:

  [AND A [OR B C]] 

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If you can do that, let's try:

[A AND [B OR [C AND D]]] 
  -> [AND A [OR B [AND C D]]]
  
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How would you handle this?

[A AND B OR C AND D]

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Note: the representation of these expressions will be a little different depending on your language,
but the important thing is you don't need to worry about parsing and tokenizing the expression yourself;
it will already come nicely formatted. For example, in javascript it could look like:
  ["A", "AND", ["B", "OR", "C"]]