On properties of $B$-terms
| Autor: | Ikebuchi, Mirai, Nakano, Keisuke |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Logical Methods in Computer Science, Volume 16, Issue 2 (June 2, 2020) lmcs:5156 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.23638/LMCS-16(2:8)2020 |
| Popis: | $B$-terms are built from the $B$ combinator alone defined by $B\equiv\lambda fgx. f(g~x)$, which is well known as a function composition operator. This paper investigates an interesting property of $B$-terms, that is, whether repetitive right applications of a $B$-term cycles or not. We discuss conditions for $B$-terms to have and not to have the property through a sound and complete equational axiomatization. Specifically, we give examples of $B$-terms which have the cyclic property and show that there are infinitely many $B$-terms which do not have the property. Also, we introduce another interesting property about a canonical representation of $B$-terms that is useful to detect cycles, or equivalently, to prove the cyclic property, with an efficient algorithm. Comment: Journal version in Logical Methods in Computer Science. arXiv admin note: substantial text overlap with arXiv:1703.10938 |
| Databáze: | arXiv |
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