Implementing a normalizer using sized heterogeneous types (2006)
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| Venue: | In Workshop on Mathematically Structured Functional Programming, MSFP |
| Citations: | 7 - 1 self |
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@INPROCEEDINGS{Abel06implementinga,
author = {Andreas Abel},
title = {Implementing a normalizer using sized heterogeneous types},
booktitle = {In Workshop on Mathematically Structured Functional Programming, MSFP},
year = {2006}
}
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Abstract
In the simply-typed lambda-calculus, a hereditary substitution replaces a free variable in a normal form r by another normal form s of type a, removing freshly created redexes on the fly. It can be defined by lexicographic induction on a and r, thus, giving rise to a structurally recursive normalizer for the simply-typed lambda-calculus. We generalize this scheme to simultaneous substitutions, preserving its simple termination argument. We further implement hereditary simultaneous substitutions in a functional programming language with sized heterogeneous inductive types, Fωb, arriving at an interpreter whose termination can be tracked by the type system of its host programming language.
