文章基本信息

标题：Modal Embeddings and Calling Paradigms
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作者：Jos Esp{'i}rito Santo ; Lu{'i}s Pinto ; Tarmo Uustalu 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2019
卷号：131
页码：1-20
DOI：10.4230/LIPIcs.FSCD.2019.18
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We study the computational interpretation of the two standard modal embeddings, usually named after Girard and Gödel, of intuitionistic logic into IS4. As source system we take either the call-by-name (cbn) or the call-by-value (cbv) lambda-calculus with simple types. The target system can be taken to be the, arguably, simplest fragment of IS4, here recast as a very simple lambda-calculus equipped with an indeterminate lax monoidal comonad. A slight refinement of the target and of the embeddings shows that: the target is a calculus indifferent to the calling paradigms cbn/cbv, obeying a new paradigm that we baptize call-by-box (cbb), and enjoying standardization; and that Girard's (resp. Gödel's) embbedding is a translation of cbn (resp. cbv) lambda-calculus into this calculus, using a compilation technique we call protecting-by-a-box, enjoying the preservation and reflection properties known for cps translations - but in a stronger form that allows the extraction of standardization for cbn or cbv as consequence of standardization for cbb. The modal target and embeddings achieve thus an unification of call-by-name and call-by-value as call-by-box.
关键词：intuitionistic S4; call-by-name; call-by-value; comonadic lambda-calculus; standardization; indifference property