{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T17:12:13Z","timestamp":1760202733005,"version":"3.41.2"},"reference-count":1,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2015,6,10]],"date-time":"2015-06-10T00:00:00Z","timestamp":1433894400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"funder":[{"DOI":"10.13039\/501100001665","name":"French National Research Agency","doi-asserted-by":"crossref","award":["ANR-14-CE25-0005"],"award-info":[{"award-number":["ANR-14-CE25-0005"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>In this paper, we study the complexity of execution in higher-order\nprogramming languages. Our study has two facets: on the one hand we give an\nupper bound to the length of interactions between bounded P-visible strategies\nin Hyland-Ong game semantics. This result covers models of programming\nlanguages with access to computational effects like non-determinism, state or\ncontrol operators, but its semantic formulation causes a loose connection to\nsyntax. On the other hand we give a syntactic counterpart of our semantic\nstudy: a non-elementary upper bound to the length of the linear head reduction\nsequence (a low-level notion of reduction, close to the actual implementation\nof the reduction of higher-order programs by abstract machines) of simply-typed\nlambda-terms. In both cases our upper bounds are proved optimal by giving\nmatching lower bounds. These two results, although different in scope, are\nproved using the same method: we introduce a simple reduction on finite trees\nof natural numbers, hereby called interaction skeletons. We study this\nreduction and give upper bounds to its complexity. We then apply this study by\ngiving two simulation results: a semantic one measuring progress in\ngame-theoretic interaction via interaction skeletons, and a syntactic one\nestablishing a correspondence between linear head reduction of terms satisfying\na locality condition called local scope and the reduction of interaction\nskeletons. This result is then generalized to arbitrary terms by a local\nscopization transformation.<\/jats:p>","DOI":"10.2168\/lmcs-11(2:6)2015","type":"journal-article","created":{"date-parts":[[2016,11,21]],"date-time":"2016-11-21T13:13:12Z","timestamp":1479733992000},"source":"Crossref","is-referenced-by-count":3,"title":["Bounding linear head reduction and visible interaction through skeletons"],"prefix":"10.46298","volume":"Volume 11, Issue 2","author":[{"given":"Pierre","family":"Clairambault","sequence":"first","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2015,6,10]]},"reference":[{"key":"967:not-found"}],"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/1566\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/1566\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T20:06:36Z","timestamp":1681243596000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/1566"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,6,10]]},"references-count":1,"URL":"https:\/\/doi.org\/10.2168\/lmcs-11(2:6)2015","relation":{"is-same-as":[{"id-type":"arxiv","id":"1503.04034","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1503.04034","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2015,6,10]]},"article-number":"1566"}}