{"id":5030,"date":"2015-09-17T07:59:19","date_gmt":"2015-09-17T05:59:19","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=5030"},"modified":"2015-09-17T07:59:19","modified_gmt":"2015-09-17T05:59:19","slug":"resena-formalisation-in-constructive-type-theory-of-stoughtons-substitution-for-the-lambda-calculus","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/resena-formalisation-in-constructive-type-theory-of-stoughtons-substitution-for-the-lambda-calculus\/","title":{"rendered":"Rese\u00f1a: Formalisation in constructive type theory of Stoughton’s substitution for the lambda calculus"},"content":{"rendered":"

Se ha publicado un art\u00edculo de razonamiento formalizado en Agda<\/a> sobre metal\u00f3gica titulado Formalisation in constructive type theory of Stoughton’s substitution for the lambda calculus<\/a>.<\/p>\n

Sus autores son \u00c1lvaro Tasistro<\/a>, Ernesto Copello<\/a> y Nora Szasz<\/a> (del Grupo de Computaci\u00f3n Te\u00f3rica (Compute)<\/a> en la Universidad ORT<\/a>, Uruguay).<\/p>\n

Su resumen es<\/p>\n

\n In Substitution revisited<\/a>, Alley Stoughton proposed a notion of (simultaneous) substitution for the Lambda calculus as formulated in its original syntax \u2013 i.e. with only one sort of symbols (names) for variables \u2013 and without identifying \u03b1-convertible terms. According to such formulation, the action of substitution on terms is defined by simple structural recursion and an interesting theory arises concerning the connection to \u03b1-conversion.<\/p>\n

In this paper we present a formalisation of Stoughton’s work in Constructive Type Theory using the language Agda, which reaches up to the Substitution Lemma for \u03b1-conversion. The development has been quite inexpensive e.g. in labour cost, and we are able to formulate some improvements over the original presentation. For instance, our definition of \u03b1-conversion is just syntax directed and we prove it to be an equivalence relation in an easy way, whereas in Substitution revisited<\/a> the latter was included as part of the definition and then proven to be equivalent to an only nearly structural definition as corollary of a lengthier development. As a result of this work we are inclined to assert that Stoughton’s is the right way to formulate the Lambda calculus in its original, conventional syntax and that it is a formulation amenable to fully formal treatment.\n<\/p><\/blockquote>\n

El trabajo se ha publicado en Electronic Notes in Theoretical Computer Science<\/a>.<\/p>\n

El c\u00f3digo de las correspondientes teor\u00edas en Agda literario se encuentra aqu\u00ed<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"

Se ha publicado un art\u00edculo de razonamiento formalizado en Agda sobre metal\u00f3gica titulado Formalisation in constructive type theory of Stoughton’s substitution for the lambda calculus. Sus autores son \u00c1lvaro Tasistro, Ernesto Copello y Nora Szasz (del Grupo de Computaci\u00f3n Te\u00f3rica (Compute) en la Universidad ORT, Uruguay). Su resumen es In Substitution revisited, Alley Stoughton proposed…<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"footnotes":"","_jetpack_memberships_contains_paid_content":false},"categories":[100],"tags":[195,285],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_likes_enabled":false,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/5030"}],"collection":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/comments?post=5030"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/5030\/revisions"}],"predecessor-version":[{"id":5031,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/5030\/revisions\/5031"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=5030"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=5030"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=5030"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}