{"paper":{"title":"Modules over relative monads for syntax and semantics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.PL"],"primary_cat":"cs.LO","authors_text":"Benedikt Ahrens","submitted_at":"2011-07-26T16:06:20Z","abstract_excerpt":"We give an algebraic characterization of the syntax and semantics of a class of languages with variable binding.\n  We introduce a notion of 2-signature: such a signature specifies not only the terms of a language, but also reduction rules on those terms. To any 2-signature $S$ we associate a category of \"models\" of $S$. This category has an initial object, which integrates the terms freely generated by $S$, and which is equipped with reductions according to the inequations given in $S$. We call this initial object the language generated by $S$. Models of a 2--signature are built from relative "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5252","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"}