The simple type theory of normalisation by evaluation (2001)
| Venue: | Proceedings of the First International Workshop on Reduction Strategies in Rewriting and Programming (WRS 2001), number 57 in Electronic Notes in Theoretical Computer Science |
| Citations: | 1 - 0 self |
BibTeX
@INPROCEEDINGS{Vestergaard01thesimple,
author = {René Vestergaard},
title = {The simple type theory of normalisation by evaluation},
booktitle = {Proceedings of the First International Workshop on Reduction Strategies in Rewriting and Programming (WRS 2001), number 57 in Electronic Notes in Theoretical Computer Science},
year = {2001},
publisher = {Elsevier Science}
}
Bookmark
 |
 |
 |
 |
 |
 |
OpenURL
Abstract
We develop the type theory of the Normalisation by Evaluation (NbE) algorithm for the λ-calculus in the simply-typed case. In particular, we show that the algorithm computes long β(η)-normal forms by means of Plotkin’s call-by-name and callby-value β-evaluation semantics. This is noteworthy (i) as the algorithm decides full βη-equality and (ii) as the algorithm so-far only has been presented in modeltheoretic terms. To showcase the effective means of the algorithm, we provide an environment machine implementation of the semantics: the NbE Machine. We also analyse the semantics and the environment machine in terms of strategies on the λ-calculus and subsequently address the untyped case. The proof burden is slight. 1
