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Modal embeddings and calling paradigms

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Resumo: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-byname (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.
Autores principais:Espírito Santo, José
Outros Autores:Pinto, Luís F.; Uustalu, Tarmo
Assunto:Intuitionistic S4 Call-by-name Call-by-value Comonadic lambda-calculus Standardization Indifference property
Ano:2019
País:Portugal
Tipo de documento:comunicação em conferência
Tipo de acesso:acesso aberto
Instituição associada:Universidade do Minho
Idioma:inglês
Origem:RepositóriUM - Universidade do Minho

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