{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T03:26:18Z","timestamp":1767929178843,"version":"3.49.0"},"reference-count":20,"publisher":"Elsevier BV","issue":"1","license":[{"start":{"date-parts":[[1979,7,1]],"date-time":"1979-07-01T00:00:00Z","timestamp":299635200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,7,17]],"date-time":"2013-07-17T00:00:00Z","timestamp":1374019200000},"content-version":"vor","delay-in-days":12435,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Theoretical Computer Science"],"published-print":{"date-parts":[[1979,7]]},"DOI":"10.1016\/0304-3975(79)90007-0","type":"journal-article","created":{"date-parts":[[2002,7,25]],"date-time":"2002-07-25T23:48:55Z","timestamp":1027640935000},"page":"73-81","source":"Crossref","is-referenced-by-count":117,"title":["The typed \u03bb-calculus is not elementary recursive"],"prefix":"10.1016","volume":"9","author":[{"given":"Richard","family":"Statman","sequence":"first","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/0304-3975(79)90007-0_BIB1","series-title":"The Design and Analysis of Computer Algorithms","author":"Aho","year":"1974"},{"key":"10.1016\/0304-3975(79)90007-0_BIB2","article-title":"The Calculi of Lambda-Conversion","author":"Church","year":"1941","journal-title":"Annals of Math. Studies No. 6"},{"key":"10.1016\/0304-3975(79)90007-0_BIB3","article-title":"Equality between functionals","volume":"453","author":"Friedman","year":"1974"},{"key":"10.1016\/0304-3975(79)90007-0_BIB4","article-title":"On an extension of finitary mathematics which has not yet been used","volume":"12","author":"G\u00f6del","year":"1958","journal-title":"Dialectica"},{"key":"10.1016\/0304-3975(79)90007-0_BIB5","first-page":"46","article-title":"Some classes of recursive functions","volume":"4","author":"Grzegorczyk","year":"1953","journal-title":"Rozprawy Mat."},{"key":"10.1016\/0304-3975(79)90007-0_BIB6","doi-asserted-by":"crossref","first-page":"323","DOI":"10.4064\/fm-52-3-323-344","article-title":"A theory of propositional types","volume":"52","author":"Henkin","year":"1963","journal-title":"Fund. Math."},{"key":"10.1016\/0304-3975(79)90007-0_BIB7","series-title":"London Math. Soc.","article-title":"Introduction to Combinatory Logic","author":"Hindley","year":"1972"},{"key":"10.1016\/0304-3975(79)90007-0_BIB8","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/0304-3975(75)90011-0","article-title":"A unification algorithm for typed \u03bb-calculus","volume":"1","author":"Huet","year":"1975","journal-title":"Theoret. Comput. Sci."},{"key":"10.1016\/0304-3975(79)90007-0_BIB9","series-title":"Introduction to Mathematics","author":"Kleene","year":"1952"},{"key":"10.1016\/0304-3975(79)90007-0_BIB10","series-title":"Intuitionism and Proof Theory","article-title":"An abstract notion of realizability for which the intuitionistic predicate calculus is complete","author":"Lauchli","year":"1968"},{"issue":"3","key":"10.1016\/0304-3975(79)90007-0_BIB11","doi-asserted-by":"crossref","DOI":"10.1112\/plms\/s3-31.3.289","article-title":"The connection between equivalence of proofs and cartesian closed categories","volume":"31","author":"Mann","year":"1975","journal-title":"Proc. London Math. Soc. (3)"},{"key":"10.1016\/0304-3975(79)90007-0_BIB12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0304-3975(77)90053-6","article-title":"Fully abstract models of typed \u03bb-calculi","volume":"4","author":"Milner","year":"1977","journal-title":"Theoret. Comput. Sci."},{"key":"10.1016\/0304-3975(79)90007-0_BIB13","series-title":"Proc. Int. Congr. of Math.","article-title":"The inherent computational complexity of theories of ordered sets","author":"Meyer","year":"1974"},{"key":"10.1016\/0304-3975(79)90007-0_BIB14","series-title":"Approaches to Natural Language","article-title":"The proper treatment of quantification in ordinary English","author":"Montague","year":"1973"},{"key":"10.1016\/0304-3975(79)90007-0_BIB15","series-title":"Natural Deduction","author":"Prawitz","year":"1965"},{"key":"10.1016\/0304-3975(79)90007-0_BIB16","first-page":"3","article-title":"Definierbare Functionem im \u03bb-Kalkul mit Typen","volume":"17","author":"Schwichtenberg","year":"1975","journal-title":"Arch. Math. Logic"},{"key":"10.1016\/0304-3975(79)90007-0_BIB17","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/0304-3975(79)90006-9","article-title":"Intuitionistic propositional logic is polynomial-space complete","volume":"9","author":"Statman","year":"1979","journal-title":"Theoret. Comput. Sci."},{"key":"10.1016\/0304-3975(79)90007-0_BIB18","doi-asserted-by":"crossref","unstructured":"R. Statman, Completeness, invariance and \u03bb-definability, J. Symbolic Logic, to appear.","DOI":"10.2307\/2273377"},{"key":"10.1016\/0304-3975(79)90007-0_BIB19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0304-3975(76)90061-X","article-title":"The polynomial-time hierarchy","volume":"3","author":"Stockmeyer","year":"1976","journal-title":"Theoret. Comput. Sci."},{"key":"10.1016\/0304-3975(79)90007-0_BIB20","article-title":"A realizability interpretation of the theory of species","volume":"453","author":"Tait","year":"1974"}],"container-title":["Theoretical Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:0304397579900070?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:0304397579900070?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2020,2,5]],"date-time":"2020-02-05T06:32:19Z","timestamp":1580884339000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/0304397579900070"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1979,7]]},"references-count":20,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1979,7]]}},"alternative-id":["0304397579900070"],"URL":"https:\/\/doi.org\/10.1016\/0304-3975(79)90007-0","relation":{},"ISSN":["0304-3975"],"issn-type":[{"value":"0304-3975","type":"print"}],"subject":[],"published":{"date-parts":[[1979,7]]}}}