{"paper":{"title":"A Coinductive Approach to Proof Search","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Braga, C.N.R.S., France), Jos\\'e Esp\\'irito Santo (Centro de Matem\\'atica, Lu\\'is Pinto (Centro de Matem\\'atica, Portugal), Ralph Matthes (Institut de Recherche en Informatique de Toulouse (IRIT), Universidade do Minho, University of Toulouse","submitted_at":"2013-09-04T02:13:15Z","abstract_excerpt":"We propose to study proof search from a coinductive point of view. In this paper, we consider intuitionistic logic and a focused system based on Herbelin's LJT for the implicational fragment. We introduce a variant of lambda calculus with potentially infinitely deep terms and a means of expressing alternatives for the description of the \"solution spaces\" (called B\\\"ohm forests), which are a representation of all (not necessarily well-founded but still locally well-formed) proofs of a given formula (more generally: of a given sequent).\n  As main result we obtain, for each given formula, the red"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0892","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"}