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Our goal is to understand Variable Elimination as an algorithm acting <jats:italic>on programs<\/jats:italic> in an idealized probabilistic functional language\u2014a linear simply-typed <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>-calculus suffices for our purpose. Precisely, we express <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\textsf{VE}$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>VE<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> as <jats:italic>a term rewriting process<\/jats:italic>, which transforms a global definition of a variable into a\u00a0local definition, by swapping and nesting let-in expressions. We exploit in an essential way linear types.<\/jats:p>","DOI":"10.1007\/978-3-031-91118-7_12","type":"book-chapter","created":{"date-parts":[[2025,4,30]],"date-time":"2025-04-30T08:17:09Z","timestamp":1746001029000},"page":"292-321","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Variable Elimination as Rewriting in a Linear Lambda Calculus"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5231-5504","authenticated-orcid":false,"given":"Thomas","family":"Ehrhard","sequence":"first","affiliation":[]},{"given":"Claudia","family":"Faggian","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6271-3557","authenticated-orcid":false,"given":"Michele","family":"Pagani","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,5,1]]},"reference":[{"key":"12_CR1","doi-asserted-by":"publisher","unstructured":"Benton, P.N., Wadler, P.: Linear logic, monads and the lambda calculus. 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