# Unboundedness for Recursion Schemes: A Simpler Type System ``` release_rev_cc605265-494a-4b1f-9da9-6bd8b8920291 ```

by David Barozzini, Paweł Parys, Jan Wróblewski

 `abstracts[]` ``` {'sha1': 'bd853c8163fca8ce3c0d823b49359c6a58f2b3ee', 'content': 'Decidability of the problems of unboundedness and simultaneous unboundedness\n(aka. the diagonal problem) for higher-order recursion schemes was established\nby Clemente, Parys, Salvati, and Walukiewicz (2016). Then a procedure of\noptimal complexity was presented by Parys (2017); this procedure used a\ncomplicated type system, involving multiple flags and markers. We present here\na simpler and much more intuitive type system serving the same purpose. We\nprove that this type system allows to solve the unboundedness problem for a\nwidely considered subclass of recursion schemes, called safe schemes. For\nunsafe recursion schemes we only have soundness of the type system: if one can\nestablish a type derivation claiming that a recursion scheme is unbounded then\nit is indeed unbounded. Completeness of the type system for unsafe recursion\nschemes is left as an open question. Going further, we discuss an extension of\nthe type system that allows to handle the simultaneous unboundedness problem.\n We also design and implement an algorithm that fully automatically checks\nunboundedness of a given recursion scheme, completing in a short time for a\nwide variety of inputs.', 'mimetype': 'text/plain', 'lang': 'en'} ``` `container` `container_id` `contribs[]` ``` {'index': 0, 'creator_id': None, 'creator': None, 'raw_name': 'David Barozzini', 'given_name': None, 'surname': None, 'role': 'author', 'raw_affiliation': None, 'extra': None} {'index': 1, 'creator_id': None, 'creator': None, 'raw_name': 'Paweł Parys', 'given_name': None, 'surname': None, 'role': 'author', 'raw_affiliation': None, 'extra': None} {'index': 2, 'creator_id': None, 'creator': None, 'raw_name': 'Jan Wróblewski', 'given_name': None, 'surname': None, 'role': 'author', 'raw_affiliation': None, 'extra': None} ``` `ext_ids` `{'doi': None, 'wikidata_qid': None, 'isbn13': None, 'pmid': None, 'pmcid': None, 'core': None, 'arxiv': '2204.11023v1', 'jstor': None, 'ark': None, 'mag': None, 'doaj': None, 'dblp': None, 'oai': None, 'hdl': None}` `files` `filesets` `issue` `language` `en` `license_slug` `CC-BY` `number` `original_title` `pages` `publisher` `refs` `[]` `release_date` `2022-04-23` `release_stage` `submitted` `release_type` `article` `release_year` `2022` `subtitle` `title` `Unboundedness for Recursion Schemes: A Simpler Type System` `version` `v1` `volume` `webcaptures` `withdrawn_date` `withdrawn_status` `withdrawn_year` `work_id` `46tr6dofwncsllph76rx5vmu74`
 `arxiv.base_id` `2204.11023` `arxiv.categories` `['cs.LO', 'cs.FL']`