{"paper":{"title":"Lineal: A linear-algebraic Lambda-calculus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO","cs.PL"],"primary_cat":"quant-ph","authors_text":"Gilles Dowek, Pablo Arrighi","submitted_at":"2006-12-22T17:25:56Z","abstract_excerpt":"We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus with the possibility to make arbitrary linear combinations of terms alpha.t + beta.u. We describe how to \"execute\" this language in terms of a few rewrite rules, and justify them through the two fundamental requirements that the language be a language of linear operators, and that it be higher-order. We mention the perspectives of this work in the field of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0612199","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}