{"id":"https://openalex.org/W2969720931","doi":"https://doi.org/10.1007/978-3-030-29436-6_20","title":"Composing Proof Terms","display_name":"Composing Proof Terms","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2969720931","doi":"https://doi.org/10.1007/978-3-030-29436-6_20","mag":"2969720931"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-030-29436-6_20","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-29436-6_20","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-030-29436-6_20.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-030-29436-6_20.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008310386","display_name":"Christina Kohl","orcid":null},"institutions":[{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Christina Kohl","raw_affiliation_strings":["Department of Computer Science, University of Innsbruck, Innsbruck, Austria"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Innsbruck, Innsbruck, Austria","institution_ids":["https://openalex.org/I190249584"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049118633","display_name":"Aart Middeldorp","orcid":"https://orcid.org/0000-0001-7366-8464"},"institutions":[{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Aart Middeldorp","raw_affiliation_strings":["Department of Computer Science, University of Innsbruck, Innsbruck, Austria"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Innsbruck, Innsbruck, Austria","institution_ids":["https://openalex.org/I190249584"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5008310386"],"corresponding_institution_ids":["https://openalex.org/I190249584"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.15362302,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"337","last_page":"353"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9965999722480774,"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":0.9954000115394592,"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/computer-science","display_name":"Computer science","score":0.7466175556182861},{"id":"https://openalex.org/keywords/rewriting","display_name":"Rewriting","score":0.7396808862686157},{"id":"https://openalex.org/keywords/structural-proof-theory","display_name":"Structural proof theory","score":0.706031322479248},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.6436371207237244},{"id":"https://openalex.org/keywords/proof-theory","display_name":"Proof theory","score":0.565177321434021},{"id":"https://openalex.org/keywords/proof-of-concept","display_name":"Proof of concept","score":0.534491240978241},{"id":"https://openalex.org/keywords/direct-proof","display_name":"Direct proof","score":0.5133420825004578},{"id":"https://openalex.org/keywords/constructive-proof","display_name":"Constructive proof","score":0.5128512382507324},{"id":"https://openalex.org/keywords/computer-assisted-proof","display_name":"Computer-assisted proof","score":0.47834154963493347},{"id":"https://openalex.org/keywords/analytic-proof","display_name":"Analytic proof","score":0.4506549537181854},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.43967193365097046},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.4151086211204529},{"id":"https://openalex.org/keywords/automated-proof-checking","display_name":"Automated proof checking","score":0.4107292890548706},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.32942771911621094},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.23407462239265442},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.21630769968032837},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.21218803524971008},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.2029193937778473}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7466175556182861},{"id":"https://openalex.org/C154690210","wikidata":"https://www.wikidata.org/wiki/Q1668499","display_name":"Rewriting","level":2,"score":0.7396808862686157},{"id":"https://openalex.org/C195653647","wikidata":"https://www.wikidata.org/wiki/Q7625047","display_name":"Structural proof theory","level":4,"score":0.706031322479248},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.6436371207237244},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.565177321434021},{"id":"https://openalex.org/C124978682","wikidata":"https://www.wikidata.org/wiki/Q1201019","display_name":"Proof of concept","level":2,"score":0.534491240978241},{"id":"https://openalex.org/C161505775","wikidata":"https://www.wikidata.org/wiki/Q3240280","display_name":"Direct proof","level":2,"score":0.5133420825004578},{"id":"https://openalex.org/C202854965","wikidata":"https://www.wikidata.org/wiki/Q3044470","display_name":"Constructive proof","level":2,"score":0.5128512382507324},{"id":"https://openalex.org/C173613240","wikidata":"https://www.wikidata.org/wiki/Q1150675","display_name":"Computer-assisted proof","level":3,"score":0.47834154963493347},{"id":"https://openalex.org/C135754263","wikidata":"https://www.wikidata.org/wiki/Q4751136","display_name":"Analytic proof","level":3,"score":0.4506549537181854},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.43967193365097046},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.4151086211204529},{"id":"https://openalex.org/C13766981","wikidata":"https://www.wikidata.org/wiki/Q11387554","display_name":"Automated proof checking","level":3,"score":0.4107292890548706},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.32942771911621094},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.23407462239265442},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.21630769968032837},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.21218803524971008},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.2029193937778473},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-030-29436-6_20","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-29436-6_20","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-030-29436-6_20.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":{"id":"doi:10.1007/978-3-030-29436-6_20","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-29436-6_20","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-030-29436-6_20.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2969720931.pdf","grobid_xml":"https://content.openalex.org/works/W2969720931.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W1583295953","https://openalex.org/W1976195354","https://openalex.org/W1997678912","https://openalex.org/W2007343091","https://openalex.org/W2091567516","https://openalex.org/W2170550263","https://openalex.org/W2885703247","https://openalex.org/W4230919050"],"related_works":["https://openalex.org/W4234403895","https://openalex.org/W171706349","https://openalex.org/W1601404805","https://openalex.org/W2119682046","https://openalex.org/W2162495973","https://openalex.org/W1852954869","https://openalex.org/W187835144","https://openalex.org/W1614097270","https://openalex.org/W2263677784","https://openalex.org/W2599938050"],"abstract_inverted_index":{"Abstract":[0],"Proof":[1],"terms":[2,16,45],"are":[3],"a":[4,50],"useful":[5],"concept":[6],"for":[7,52],"comparing":[8],"computations":[9],"in":[10,35],"term":[11],"rewriting.":[12],"We":[13,24,38],"analyze":[14],"proof":[15,44,54],"with":[17,19,46],"composition,":[18],"an":[20],"eye":[21],"towards":[22],"automation.":[23],"revisit":[25],"permutation":[26],"equivalence":[27],"and":[28],"projection":[29],"equivalence,":[30],"two":[31],"key":[32],"notions":[33],"presented":[34],"the":[36,41],"literature.":[37],"report":[39],"on":[40],"integration":[42],"of":[43],"composition":[47],"into":[48],"ProTeM,":[49],"tool":[51],"manipulating":[53],"terms.":[55]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}