{"paper":{"title":"A Coinductive Framework for Infinitary Rewriting and Equational Reasoning (Extended Version)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Alexandra Silva, Andrew Polonsky, Dimitri Hendriks, Helle Hvid Hansen, J\\\"org Endrullis","submitted_at":"2015-05-05T19:11:54Z","abstract_excerpt":"We present a coinductive framework for defining infinitary analogues of equational reasoning and rewriting in a uniform way. We define the relation =^infty, notion of infinitary equational reasoning, and ->^infty, the standard notion of infinitary rewriting as follows:\n  =^infty := nu R. ( <-_root + ->_root + lift(R) )^*\n  ->^infty := mu R. nu S. ( ->_root + lift(R) )^* ; lift(S)\n  where\n  lift(R) := { (f(s_1,...,s_n), f(t_1,...,t_n)) | s_1 R t_1,...,s_n R t_n } + id ,\n  and where mu is the least fixed point operator and nu is the greatest fixed point operator.\n  The setup captures rewrite seq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.01128","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":""},"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"}