{"paper":{"title":"On Jumps, Interactions, and Intersection Types","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Gabriele Vanoni, Stefano Catozi, Ugo Dal Lago","submitted_at":"2026-06-25T14:07:22Z","abstract_excerpt":"The Jumping Abstract Machine (JAM), an evaluation mechanism for the $\\lambda$-calculus, was introduced by Danos and Regnier as an optimization of the Interaction Abstract Machine (IAM), itself an operational counterpart to Girard's Geometry of Interaction and Abramsky $\\textit{et al}$. game semantics. Moreover, the JAM is isomorphic to the Pointer Abstract Machine (PAM), the syntactical counterpart of Hyland and Ong's game semantics. We study a generalization of the JAM, that we call the Parametric Jumping Abstract Machine (PaJAM) and show that there is a tight correspondence between the PaJAM"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27062","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/2606.27062/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"}