Natural Deduction and Normalization Proofs for the Intersection Type Discipline
Abstract
Refining and extending previous work by Retoré, we develop a systematic approach to intersection types via natural deduction. We show how a step of beta reduction can be seen as performing, at the level of typing derivations, Prawitz reductions in parallel. Then we derive as immediate consequences of Subject Reduction the main theorems about normalization for intersection types: for system D, strong normalization, for system Omega, the leftmost reduction termination for terms typable without Omega.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2019
- DOI:
- 10.48550/arXiv.1904.10106
- arXiv:
- arXiv:1904.10106
- Bibcode:
- 2019arXiv190410106A
- Keywords:
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- Computer Science - Logic in Computer Science
- E-Print:
- In Proceedings DCM 2018 and ITRS 2018, arXiv:1904.09561