LIPIcs.CSL.2013.101.pdf
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A characterization of the Taylor expansion of lambda-terms
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Computer Science Logic 2013 (CSL 2013)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Computer Science Logic (CSL) - License:
Creative Commons Attribution 3.0 Unported license
- Publication Date: 2013-09-02
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Pierre Boudes, Fanny He, and Michele Pagani. A characterization of the Taylor expansion of lambda-terms. In Computer Science Logic 2013 (CSL 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 23, pp. 101-115, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
https://doi.org/10.4230/LIPIcs.CSL.2013.101
https://doi.org/10.4230/LIPIcs.CSL.2013.101
Abstract
The Taylor expansion of lambda-terms, as introduced by Ehrhard and Regnier, expresses a lambda-term as a series of multi-linear terms, called simple terms, which capture bounded computations. Normal forms of Taylor expansions give a notion of infinitary normal forms, refining the notion of Böhm trees in a quantitative setting.
We give the algebraic conditions over a set of normal simple terms which characterize the property of being the normal form of the Taylor expansion of a lambda-term. From this full completeness result, we give further conditions which semantically describe normalizable and total lambda-terms.
Keywords
- Lambda-Calculus
- Böhm trees
- Differential Lambda-Calculus
- Linear Logic
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