{"id":"https://openalex.org/W1498482969","doi":"https://doi.org/10.1007/bfb0049339","title":"Program transformation and proof transformation","display_name":"Program transformation and proof transformation","publication_year":2006,"publication_date":"2006-03-06","ids":{"openalex":"https://openalex.org/W1498482969","doi":"https://doi.org/10.1007/bfb0049339","mag":"1498482969"},"language":"en","primary_location":{"id":"doi:10.1007/bfb0049339","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bfb0049339","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023409888","display_name":"Wilfried Sieg","orcid":"https://orcid.org/0000-0002-7130-0524"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Wilfried Sieg","raw_affiliation_strings":["Carnegie Mellon University, Pittsburgh, USA","Carnegie Mellon University"],"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, USA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113891766","display_name":"Stanley S. Wainer","orcid":null},"institutions":[{"id":"https://openalex.org/I130828816","display_name":"University of Leeds","ror":"https://ror.org/024mrxd33","country_code":"GB","type":"education","lineage":["https://openalex.org/I130828816"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Stanley S. Wainer","raw_affiliation_strings":["University of Leeds, UK","(University of Leeds"],"affiliations":[{"raw_affiliation_string":"University of Leeds, UK","institution_ids":["https://openalex.org/I130828816"]},{"raw_affiliation_string":"(University of Leeds","institution_ids":["https://openalex.org/I130828816"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5023409888"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.06528284,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"305","last_page":"317"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.8521960973739624},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.6295057535171509},{"id":"https://openalex.org/keywords/sequent-calculus","display_name":"Sequent calculus","score":0.5901463627815247},{"id":"https://openalex.org/keywords/sequent","display_name":"Sequent","score":0.5712721943855286},{"id":"https://openalex.org/keywords/cut-elimination-theorem","display_name":"Cut-elimination theorem","score":0.559750497341156},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.5402061939239502},{"id":"https://openalex.org/keywords/constructive-proof","display_name":"Constructive proof","score":0.5043169260025024},{"id":"https://openalex.org/keywords/proof-complexity","display_name":"Proof complexity","score":0.47336193919181824},{"id":"https://openalex.org/keywords/direct-proof","display_name":"Direct proof","score":0.46439129114151},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44970202445983887},{"id":"https://openalex.org/keywords/structural-proof-theory","display_name":"Structural proof theory","score":0.44012168049812317},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.43439874053001404},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.43190309405326843},{"id":"https://openalex.org/keywords/proof-theory","display_name":"Proof theory","score":0.42645037174224854},{"id":"https://openalex.org/keywords/analytic-proof","display_name":"Analytic proof","score":0.41651153564453125},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4037594795227051},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.29983824491500854},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19829845428466797}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.8521960973739624},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.6295057535171509},{"id":"https://openalex.org/C65880906","wikidata":"https://www.wikidata.org/wiki/Q1771121","display_name":"Sequent calculus","level":3,"score":0.5901463627815247},{"id":"https://openalex.org/C89421646","wikidata":"https://www.wikidata.org/wiki/Q843632","display_name":"Sequent","level":2,"score":0.5712721943855286},{"id":"https://openalex.org/C111404639","wikidata":"https://www.wikidata.org/wiki/Q376166","display_name":"Cut-elimination theorem","level":4,"score":0.559750497341156},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.5402061939239502},{"id":"https://openalex.org/C202854965","wikidata":"https://www.wikidata.org/wiki/Q3044470","display_name":"Constructive proof","level":2,"score":0.5043169260025024},{"id":"https://openalex.org/C105605280","wikidata":"https://www.wikidata.org/wiki/Q7249999","display_name":"Proof complexity","level":3,"score":0.47336193919181824},{"id":"https://openalex.org/C161505775","wikidata":"https://www.wikidata.org/wiki/Q3240280","display_name":"Direct proof","level":2,"score":0.46439129114151},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44970202445983887},{"id":"https://openalex.org/C195653647","wikidata":"https://www.wikidata.org/wiki/Q7625047","display_name":"Structural proof theory","level":4,"score":0.44012168049812317},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.43439874053001404},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.43190309405326843},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.42645037174224854},{"id":"https://openalex.org/C135754263","wikidata":"https://www.wikidata.org/wiki/Q4751136","display_name":"Analytic proof","level":3,"score":0.41651153564453125},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4037594795227051},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29983824491500854},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19829845428466797},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/bfb0049339","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bfb0049339","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:repository.cmu.edu:philosophy-1214","is_oa":false,"landing_page_url":"http://repository.cmu.edu/philosophy/219","pdf_url":null,"source":{"id":"https://openalex.org/S4306400668","display_name":"Research Showcase @ Carnegie Mellon University (Carnegie Mellon University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I74973139","host_organization_name":"Carnegie Mellon University","host_organization_lineage":["https://openalex.org/I74973139"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Department of Philosophy","raw_type":"text"},{"id":"pmh:doi:10.1184/r1/6492473","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal contribution"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W47204537","https://openalex.org/W105943185","https://openalex.org/W172035187","https://openalex.org/W193737235","https://openalex.org/W1515444786","https://openalex.org/W1523525039","https://openalex.org/W1573627012","https://openalex.org/W1715062909","https://openalex.org/W1897683944","https://openalex.org/W1966181449","https://openalex.org/W1980915530","https://openalex.org/W2911865844","https://openalex.org/W3039529476","https://openalex.org/W4232626105","https://openalex.org/W4239618235","https://openalex.org/W4249319495"],"related_works":["https://openalex.org/W171706349","https://openalex.org/W2922318846","https://openalex.org/W4234403895","https://openalex.org/W2461509449","https://openalex.org/W2626436722","https://openalex.org/W2722497084","https://openalex.org/W153148314","https://openalex.org/W187835144","https://openalex.org/W2119682046","https://openalex.org/W1961313574"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}