{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,28]],"date-time":"2023-09-28T05:40:15Z","timestamp":1695879615722},"reference-count":10,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":5430,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1992,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We give a formal interpretation of Martin\u2010L\u00f6f's Constructive Theory of Types in Elementary Topos Theory which is presented as a formalised theory with intensional equality of objects. Types are interpreted as arrows and variables as sections of their types. This is necessary to model correctly the working of the assumption <jats:italic>x<\/jats:italic> \u2208 <jats:italic>A.<\/jats:italic> Then intensional equality interprets equality of types. The normal form theorem which asserts that the interpretation of a type is intensional equal to the pullback of its \u201calignment\u201d along some \u201cbase\u201d arrow relates this interpretation to categorical semantic of types.<\/jats:p>","DOI":"10.1002\/malq.19920380118","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T05:44:46Z","timestamp":1180417486000},"page":"213-240","source":"Crossref","is-referenced-by-count":1,"title":["AN INTERPRETATION OF MARTIN\u2010L\u00d6F'S CONSTRUCTIVE THEORY OF TYPES IN ELEMENTARY TOPOS THEORY"],"prefix":"10.1002","volume":"38","author":[{"given":"Anne","family":"Preller","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(86)90053-9"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00375896"},{"key":"e_1_2_1_4_2","unstructured":"Ehrhard T. A categorical semantics of constructions. In: Logic in Computer Science1988."},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/092\/1003199"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(09)70189-2"},{"key":"e_1_2_1_7_2","volume-title":"Intuitionistic Type Theory","author":"Martin\u2010L\u00f6f P.","year":"1984"},{"key":"e_1_2_1_8_2","unstructured":"Preller A. Langages \u00e0 graphes et schema de s\u00e9paration. In: Colloques Internationaux du CNRS No. 249 1976 pp.183\u2013190."},{"key":"e_1_2_1_9_2","first-page":"421","article-title":"Intensional equality in categories with structure and coherence problems","volume":"34","author":"Preller A.","year":"1988","journal-title":"This Zeitschrift"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100061284"},{"key":"e_1_2_1_11_2","unstructured":"Streicher T. Correctness and completeness of a categorical semantics of the calculus of constructions. Thesis Universit\u00e4t Passau 1989."}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19920380118","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19920380118","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,27]],"date-time":"2023-09-27T20:36:04Z","timestamp":1695846964000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19920380118"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,1]]},"references-count":10,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1992,1]]}},"alternative-id":["10.1002\/malq.19920380118"],"URL":"https:\/\/doi.org\/10.1002\/malq.19920380118","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,1]]}}}