{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T07:49:50Z","timestamp":1776325790435,"version":"3.50.1"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,12,13]]},"abstract":"<jats:p>We introduce a calculus of extensional resource terms. These are resource terms \u00e0 la Ehrhard-Regnier, but in infinitely eta-long form. The calculus still retains a finite syntax and dynamics: in particular, we prove strong confluence and normalization.   Then we define an extensional version of Taylor expansion, mapping ordinary lambda-terms to (possibly infinite) linear combinations of extensional resource terms: like in the ordinary case, the dynamics of our resource calculus allows us to simulate the beta-reduction of lambda-terms; the extensional nature of this expansion shows in the fact that we are also able to simulate eta-reduction.   In a sense, extensional resource terms contain a language of finite approximants of Nakajima trees, much like ordinary resource terms can be seen as a richer version of finite B\u00f6hm trees. We show that the equivalence induced on lambda-terms by the normalization of extensional Taylor-expansion is nothing but H*, the greatest consistent sensible lambda-theory -- which is also the theory induced by Nakajima trees. This characterization provides a new, simple way to exhibit models of H*: it becomes sufficient to model the extensional resource calculus and its dynamics.   The extensional resource calculus moreover allows us to recover, in an untyped setting, a connection between Taylor expansion and game semantics that was previously limited to the typed setting. Indeed, simply typed, eta-long, beta-normal resource terms are known to be in bijective correspondence with plays in the sense of Hyland-Ong game semantics, up to Melli\u00e8s' homotopy equivalence. Extensional resource terms are the appropriate counterpart of eta-long resource terms in an untyped setting: we spell out the bijection between normal extensional resource terms and isomorphism classes of augmentations (a canonical presentation of plays up to homotopy) in the universal arena.<\/jats:p>\n                  <jats:p>90 pages. This is the TheoretiCS journal version<\/jats:p>","DOI":"10.46298\/theoretics.26.7","type":"journal-article","created":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T07:05:12Z","timestamp":1776323112000},"source":"Crossref","is-referenced-by-count":0,"title":["Extensional Taylor Expansion"],"prefix":"10.46298","volume":"Volume 5","author":[{"given":"Lison","family":"Blondeau-Patissier","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3285-6028","authenticated-orcid":false,"given":"Pierre","family":"Clairambault","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9466-418X","authenticated-orcid":false,"given":"Lionel Vaux","family":"Auclair","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2026,4,16]]},"container-title":["TheoretiCS"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/2305.08489v6","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/2305.08489v6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T07:05:13Z","timestamp":1776323113000},"score":1,"resource":{"primary":{"URL":"https:\/\/theoretics.episciences.org\/14269"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,16]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/theoretics.26.7","relation":{"has-preprint":[{"id-type":"arxiv","id":"2305.08489v3","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2305.08489","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2305.08489","asserted-by":"subject"}]},"ISSN":["2751-4838"],"issn-type":[{"value":"2751-4838","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,16]]},"article-number":"14269"}}