The Russell-Prawitz embedding and the atomization of universal instantiation

• Autor(a) principal: Espírito Santo, José
• Data de Publicação: 2021
• Outros Autores: Ferreira, Gilda
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/1822/75419
• topic: Intuitionistic propositional calculus; System F; Predicative polymorphism; Russell-Prawitz translation; Proof reduction; Ciências Naturais::Matemáticas; Science & Technology

Given the recent interest in the fragment of system F where universal instantiation is restricted to atomic formulas, a fragment nowadays named system Fat, we study directly in system F new conversions whose purpose is to enforce that restriction. We show some benefits of these new atomization conversions: (i) they help achieving strict simulation of proof reduction by means of the Russell–Prawitz embedding of IPC into system F, (ii) they are not stronger than a certain ‘dinaturality’ conversion known to generate a consistent equality of proofs, (iii) they provide the bridge between the Russell–Prawitz embedding and another translation, due to the authors, of IPC directly into system Fat and (iv) they give means for explaining why the Russell–Prawitz translation achieves strict simulation whereas the translation into Fat does not.