Summary: Preliminary Report. Final version to appear in:
c A. Abel & B. Pientka
This work is licensed under the
Creative Commons Attribution License.
Explicit Substitutions for Contextual Type Theory
Theoretical Computer Science, Ludwig-Maximilians-University Munich, Germany
School of Computer Science, McGill University, Montreal, Canada
In this paper, we present an explicit substitution calculus which distinguishes between ordinary bound
variables and meta-variables. Its typing discipline is derived from contextual modal type theory. We
first present a dependently typed lambda calculus with explicit substitutions for ordinary variables
and explicit meta-substitutions for meta-variables. We then present a weak head normalization pro-
cedure which performs both substitutions lazily and in a single pass thereby combining substitution
walks for the two different classes of variables. Finally, we describe a bidirectional type checking
algorithm which uses weak head normalization and prove soundness.
Keywords: Explicit substitutions, Meta-variables, Logical framework, Contextual modal type