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We define some decomposition schema of the derivation trees of an arithmetic infix grammar into a set of subtrees. From the parenthesis nesting of an arithmetic expression this decomposition determines a cover of its derivation tree by a set of subtrees with known syntactic properties. We define from this a recursive interpretation actor. Roughly speaking, for a given arithmetic expression, this interpreter creates one actor for each of the subtrees in its derivation tree decomposition, each created actor being in charge of local (i.e., concerning its own subtree only) parsing and semantic tasks which involve synchronization with the other actors.