Second-Order Matching via Explicit Substitutions
نویسندگان
چکیده
Matching is a basic operation extensively used in computation. Second-order matching, in particular, provides an adequate environment for expressing program transformations and pattern recognition for automated deduction. The past few years have established the benefit of using explicit substitutions for theorem proving and higher-order unification. In this paper, we will make use of explicit substitutions to facilitate matching: we develop a second-order matching algorithm via the λσ-style of explicit substitutions. We introduce a convenient notation for matching in the λσ-calculus. This notation keeps the matching equations separated from the incremental graftings. We characterise an important class of second-order matching problems which is essential to prove termination of the algorithm. In addition, we illustrate how the algorithm works through some examples.
منابع مشابه
A ρ-calculus of explicit constraint application
Theoretical presentations of the ρ-calculus often treat the matching constraint computations as an atomic operation although matching constraints are explicitly expressed. Actual implementations have to take a more realistic view: computations needed in order to find the solutions of a matching equation can have an important impact on the (efficiency of the) calculus for some matching theories ...
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