{"paper":{"title":"Definitional Inversion, Without Normalisation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.PL"],"primary_cat":"cs.LO","authors_text":"Adrien Frabetti Mathieu, Mario Carneiro, Meven Lennon-Bertrand, Paul-Andr\\'e Melli\\`es, Stephanie Weirich, Thierry Coquand","submitted_at":"2026-07-15T10:06:45Z","abstract_excerpt":"We contribute a new proof technique, based on domain theory, to prove key meta-theoretic properties of dependent type systems: definitional inversion properties, i.e. injectivity and no-confusion of type constructors. This proof technique is independent of normalisation, and indeed applies even for the \"type-in-type\" rule of Martin-L\\\"of's original type theory. Our proof is the first to establish injectivity of type constructors for such a system in the presence of $\\eta$ laws. More generally, the technique is motivated by, and intended for, the metatheory of systems such as Idris, Lean, or de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13662","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/2607.13662/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"}