Relating higher-order and first-order rewriting
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ArticleDescription: 1 archivo (435,2 KB)Subject(s): Online resources: Summary: We define a formal encoding from higher-order rewriting into first-order rewriting modulo an equational theory E. In particular, we obtain a characterization of the class of higher-order rewriting systems which can be encoded by first-order rewriting modulo an empty equational theory (that is, E = ∅). This class includes of course the λ-calculus. Our technique does not rely on the use of a particular substitution calculus but on an axiomatic framework of explicit substitutions capturing the notion of substitution in an abstract way. The axiomatic framework specifies the properties to be verified by a substitution calculus used in the translation. Thus, our encoding can be viewed as a parametric translation from higher-order rewriting into first-order rewriting, in which the substitution calculus is the parameter of the translation.
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We define a formal encoding from higher-order rewriting into first-order rewriting modulo an equational theory E. In particular, we obtain a characterization of the class of higher-order rewriting systems which can be encoded by first-order rewriting modulo an empty equational theory (that is, E = ∅). This class includes of course the λ-calculus. Our technique does not rely on the use of a particular substitution calculus but on an axiomatic framework of explicit substitutions capturing the notion of substitution in an abstract way. The axiomatic framework specifies the properties to be verified by a substitution calculus used in the translation. Thus, our encoding can be viewed as a parametric translation from higher-order rewriting into first-order rewriting, in which the substitution calculus is the parameter of the translation.
Journal of Logic and Computation, 15(6), pp. 901-947