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Abstract: In this paper, we present an explicit substitution calculus whichdistinguishes between ordinary bound variables and meta-variables. Its typingdiscipline is derived from contextual modal type theory. We first present adependently typed lambda calculus with explicit substitutions for ordinaryvariables and explicit meta-substitutions for meta-variables. We then present aweak head normalization procedure which performs both substitutions lazily andin a single pass thereby combining substitution walks for the two differentclasses of variables. Finally, we describe a bidirectional type checkingalgorithm which uses weak head normalization and prove soundness.



Author: Andreas Abel Ludwig-Maximilians-University, Brigitte Pientka McGill University

Source: https://arxiv.org/







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