{"id":2581,"date":"2024-02-07T09:52:42","date_gmt":"2024-02-07T12:52:42","guid":{"rendered":"https:\/\/icc.fcen.uba.ar\/?p=2581"},"modified":"2024-02-07T09:52:42","modified_gmt":"2024-02-07T12:52:42","slug":"a-concrete-model-for-a-typed-linear-algebraic-lambda-calculus","status":"publish","type":"post","link":"https:\/\/icc.fcen.uba.ar\/en\/a-concrete-model-for-a-typed-linear-algebraic-lambda-calculus\/","title":{"rendered":"A concrete model for a typed linear algebraic lambda calculus"},"content":{"rendered":"<div class=\"fusion-fullwidth fullwidth-box fusion-builder-row-1 fusion-flex-container has-pattern-background has-mask-background nonhundred-percent-fullwidth non-hundred-percent-height-scrolling\" style=\"--awb-border-radius-top-left:0px;--awb-border-radius-top-right:0px;--awb-border-radius-bottom-right:0px;--awb-border-radius-bottom-left:0px;--awb-flex-wrap:wrap;\" ><div class=\"fusion-builder-row fusion-row fusion-flex-align-items-flex-start fusion-flex-content-wrap\" style=\"max-width:1144px;margin-left: calc(-4% \/ 2 );margin-right: calc(-4% \/ 2 );\"><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-0 fusion_builder_column_1_1 1_1 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:100%;--awb-margin-top-large:0px;--awb-spacing-right-large:1.92%;--awb-margin-bottom-large:20px;--awb-spacing-left-large:1.92%;--awb-width-medium:100%;--awb-order-medium:0;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-order-small:0;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-column-has-shadow fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div class=\"fusion-text fusion-text-1\"><p>Authors: Alejandro D\u00edaz-Caro and Octavio Malherbe.<\/p>\n<p>Abstract:<br \/>\nWe give an adequate, concrete, categorical-based model for Lambda-S, which is a typed version of a linear-algebraic lambda calculus, extended with measurements.\u00a0Lambda-S is an extension to first-order lambda calculus unifying two approaches of non-cloning in quantum lambda-calculi: to forbid duplication of variables, and to\u00a0consider all lambda-terms as algebraic linear functions. The type system of Lambda-S have a superposition constructor S such that a type A is considered as the base of\u00a0a vector space while SA is its span. Our model considers S as the composition of two functors in an adjunction relation between the category of sets and the category\u00a0of vector spaces over C. The right adjoint is a forgetful functor U, which is hidden in the language, and plays a central role in the computational reasoning.<\/p>\n<p>More information:<br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/1806.09236\" target=\"_blank\" rel=\"noopener\">https:\/\/arxiv.org\/abs\/1806.09236<\/a><\/p>\n<\/div><\/div><\/div><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":9,"featured_media":2582,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[98],"tags":[],"class_list":["post-2581","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-papers"],"_links":{"self":[{"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/posts\/2581","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/users\/9"}],"replies":[{"embeddable":true,"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/comments?post=2581"}],"version-history":[{"count":1,"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/posts\/2581\/revisions"}],"predecessor-version":[{"id":2583,"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/posts\/2581\/revisions\/2583"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/media\/2582"}],"wp:attachment":[{"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/media?parent=2581"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/categories?post=2581"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/tags?post=2581"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}