{"paper":{"title":"Cyclic Graphs and Memoization in Pure $\\lambda$-Calculus","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.PL","authors_text":"Bo Yang","submitted_at":"2026-06-22T06:46:37Z","abstract_excerpt":"$\\lambda$-calculus normally requires an added recursion construct, a \\texttt{letrec}, a $\\mu$-binder, or a built-in $Y$ for graph reduction, and sharing the repeated work of a memoized or dynamic-programming function normally requires an impure cache. We show that no extension is needed. We apply tabling, the standard method for solving a least-fixpoint equation, to weak-head reduction; this defines a new operational semantics for the pure $\\lambda$-calculus that keeps each term's standard lazy meaning. A term that reaches finitely many distinct states comes out as a finite graph, possibly cyc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22908","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.22908/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}