Homogeneity Without Loss of Generality
Author Pawel Parys
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3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: Formal Structures for Computation and Deduction (FSCD) - License:
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- Publication Date: 2018-07-04
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Subject Classification
ACM Subject Classification
- Theory of computation → Rewrite systems
Keywords
- higher-order recursion schemes
- lambda-calculus
- homogeneous types
- safe schemes
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Abstract
We consider higher-order recursion schemes as generators of infinite trees. A sort (simple type) is called homogeneous when all arguments of higher order are taken before any arguments of lower order. We prove that every scheme can be converted into an equivalent one (i.e, generating the same tree) that is homogeneous, that is, uses only homogeneous sorts. Then, we prove the same for safe schemes: every safe scheme can be converted into an equivalent safe homogeneous scheme. Furthermore, we compare two definition of safe schemes: the original definition of Damm, and the modern one. Finally, we prove a lemma which illustrates usefulness of the homogeneity assumption. The results are known, but we prove them in a novel way: by directly manipulating considered schemes.
Cite As Get BibTex
Pawel Parys. Homogeneity Without Loss of Generality. In 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 108, pp. 27:1-27:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.FSCD.2018.27
BibTex
@InProceedings{parys:LIPIcs.FSCD.2018.27,
author = {Parys, Pawel},
title = {{Homogeneity Without Loss of Generality}},
booktitle = {3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)},
pages = {27:1--27:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-077-4},
ISSN = {1868-8969},
year = {2018},
volume = {108},
editor = {Kirchner, H\'{e}l\`{e}ne},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2018.27},
URN = {urn:nbn:de:0030-drops-91972},
doi = {10.4230/LIPIcs.FSCD.2018.27},
annote = {Keywords: higher-order recursion schemes, lambda-calculus, homogeneous types, safe schemes}
}
Author Details
Funding
Work supported by the National Science Centre, Poland (grant no. 2016/22/E/ST6/ 00041).
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