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However, its\n                    <jats:italic>quantitative<\/jats:italic>\n                    aspects are not reflected in the preorders and equational theories induced by these models. Indeed, they can be characterized in terms of (in)equalities between B\u00f6hm trees up to extensionality, which are\n                    <jats:italic>qualitative<\/jats:italic>\n                    in nature. We employ the recently introduced checkers calculus to define a quantitative contextual preorder on\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\lambda $$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mi>\u03bb<\/mml:mi>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    -terms, and demonstrate that it coincides with the preorder associated to the relational semantics.\n                  <\/jats:p>","DOI":"10.1007\/978-3-032-22730-0_18","type":"book-chapter","created":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T16:24:24Z","timestamp":1776270264000},"page":"372-395","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Interaction Improvement"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-5481-5719","authenticated-orcid":false,"given":"Adrienne","family":"Lancelot","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1448-9014","authenticated-orcid":false,"given":"Giulio","family":"Manzonetto","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0305-6398","authenticated-orcid":false,"given":"Guy","family":"McCusker","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8762-8674","authenticated-orcid":false,"given":"Gabriele","family":"Vanoni","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,4,15]]},"reference":[{"key":"18_CR1","doi-asserted-by":"publisher","unstructured":"Abramsky, S., Jagadeesan, R., Malacaria, P.: Full abstraction for PCF. 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