Help needed with grammar problem

hello everyone,
I'm facing a problem:


Among other rules, I have a syntax rule that goes E -> E R E , which
is of course a left recursion. now, this syntax rule is supposed to be
interpreted into a syntax subtree that is supposed to be binary and
created preorder, meaning I'd like the lefthand side E to become a
node of type R, which has two 'sons' of type E (each of which may
become another R itself and so on).


Simple left recursion elimination algorithms can't help me here,
because eventually it still comes down to inorder processing, which
gives me a non-binary tree (E may become a single node, three nodes,
five nodes and so on).


anyone?

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