{"paper":{"title":"Deciding equivalence with sums and the empty type","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.PL","authors_text":"Gabriel Scherer","submitted_at":"2016-10-04T21:37:45Z","abstract_excerpt":"The logical technique of focusing can be applied to the $\\lambda$-calculus; in a simple type system with atomic types and negative type formers (functions, products, the unit type), its normal forms coincide with $\\beta\\eta$-normal forms. Introducing a saturation phase gives a notion of quasi-normal forms in presence of positive types (sum types and the empty type). This rich structure let us prove the decidability of $\\beta\\eta$-equivalence in presence of the empty type, the fact that it coincides with contextual equivalence, and a finite model property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01213","kind":"arxiv","version":3},"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"}