From Higher-Order to First-Order Rewriting

We show how higher-order rewriting may be encoded into first-order rewriting modulo an equational theory Ɛ. We obtain a characterization of the class of higher-order rewriting systems which can be encoded by first-order rewriting modulo an empty theory (that is, Ɛ = θ). This class includes of course the λ-calculus. Our technique does not rely on a particular substitution calculus but on a set of abstract properties to be verified by the substitution calculus used in the translation.

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