Second-Order Simple Grammars
Higher-order notations for trees have a venerable history from the 1970s and 1980s when schemes (that is, functional programs without interpretations) and their relationship to formal language theory were first studied. Included are higher-order recursion schemes and pushdown automata. Automata and language theory study finitely presented mechanisms for generating languages. Instead of language generators, one can view them as process calculi, propagators of possibly infinite labelled transition systems. Recently, model-checking techniques have been successfully extended to these higher-order notations in the deterministic case [18,9,8,21].
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