{"paper":{"title":"Logic as a distributive law","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Lucius Gregory Meredith, Mike Stay","submitted_at":"2016-10-07T12:26:03Z","abstract_excerpt":"We present an algorithm for deriving a spatial-behavioral type system from a formal presentation of a computational calculus. Given a 2-monad Calc: Catv$\\to$ Cat for the free calculus on a category of terms and rewrites and a 2-monad BoolAlg for the free Boolean algebra on a category, we get a 2-monad Form = BoolAlg + Calc for the free category of formulae and proofs. We also get the 2-monad BoolAlg $\\circ$ Calc for subsets of terms. The interpretation of formulae is a natural transformation $\\interp{-}$: Form $\\Rightarrow$ BoolAlg $\\circ$ Calc defined by the units and multiplications of the m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02247","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"}