{"id":151004,"date":"1996-01-01T00:00:00","date_gmt":"1996-01-01T00:00:00","guid":{"rendered":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/msr-research-item\/five-axioms-of-alpha-conversion\/"},"modified":"2018-10-16T20:16:16","modified_gmt":"2018-10-17T03:16:16","slug":"five-axioms-of-alpha-conversion","status":"publish","type":"msr-research-item","link":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/publication\/five-axioms-of-alpha-conversion\/","title":{"rendered":"Five Axioms of Alpha-Conversion"},"content":{"rendered":"<div class=\"asset-content\">\n<p>We present five axioms of name-carrying lambda-terms identified up to alpha-conversion, that is, up to renaming of bound variables. We assume constructors for constants, variables, application and lambda abstraction. Other constants represent a function Fv that returns the set of free variables in a term and a function that substitutes a term for a variable free in another term. Our axioms are: (1) equations relating Fv and each constructor; (2) equations relating substitution and each constructor; (3) alpha-conversion itself; (4) unique existence of functions on lambda-terms defined by structural iteration; and (5) construction of lambda-abstractions given certain functions from variables to terms. By building a model from de Bruijn&#8217;s nameless lambda-terms, we show that our five axioms are a conservative extension of HOL. Theorems provable from the axioms include distinctness, injectivity and an exhaustion principle for the constructors, principles of structural induction and primitive recursion on lambda-terms, Hindley and Seldin&#8217;s substitution lemmas, and the existence of their length function. These theorems and the model have been mechanically checked in the Cambridge HOL system.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We present five axioms of name-carrying lambda-terms identified up to alpha-conversion, that is, up to renaming of bound variables. We assume constructors for constants, variables, application and lambda abstraction. Other constants represent a function Fv that returns the set of free variables in a term and a function that substitutes a term for a variable [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"Springer Berlin Heidelberg","msr_publisher_other":"","msr_booktitle":"Lecture Notes in Computer Science (LNCS)","msr_chapter":"","msr_edition":"9th International Conference, TPHOLs\u201996","msr_editors":"","msr_how_published":"","msr_isbn":"978-3-540-61587-3 (Print) 978-3-540-70641-0 (Online)","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"173-190","msr_page_range_start":"173","msr_page_range_end":"190","msr_series":"","msr_volume":"1125","msr_copyright":"","msr_conference_name":"9th International Conference, TPHOLs'96","msr_doi":"10.1007\/BFb0105404","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"Andrew D. 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