... set **theory** is provided with a specific type system, expressed using set constructs, resulting in a lack of separation in a B formula between typing and set ...B **proof** system, we can translate Zenon proofs ...

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... some **proof**-theoretical properties of indexed nested ...indirect **proof** [23]. However, only an internal cut-elimination **proof** makes a **proof** formalism a first-class citizen for structural ...

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... (µMALL **sequent** **calculus**). The **sequent** **calculus** for the propositional fragment of µMALL is a finitary **sequent** **calculus** whose rules are the same as those of µMALL ∞ , except that ...

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... a **proof** **theory** perspective, two lines of inquiry seem ...our **sequent** **calculus**; by completeness of the **calculus**, the (cut) rule is admissible, but this is a semantic **proof** rather ...

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... formal **proof** can be subdivided into its abstract deductive structure, often called skeleton, and a way of instantiating it with formulas which renders it a valid ...For **proof**-search, the separation of these ...

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... Kleene algebra In our **sequent** system, called LKA, proofs are finitely branching, but possibly infinitely deep (i.e. not wellfounded). To prevent fallacious reasoning, we give a simple validity criterion for proofs ...

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... intuitionistic **sequent** **calculus** G4ii of [Hud89, Hud92, ...higher-order **calculus** for it —decorating proofs with **proof**-terms, which uses constructors cor- responding to admissible rules such as ...

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... structured **proof**-**theory** is needed in order to apply such logics to the study of programming languages with (co)inductive data types and au- tomated (co)inductive theorem ...traditional **proof** system ...

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... of **proof** terms for statements like the full axiom of ...the **calculus** of inductive constructions for Coq [ 6 ], and Martin-Löf’s type **theory** for Agda [ 24 ...

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... of **proof** terms for statements like the full axiom of ...the **calculus** of inductive constructions for Coq [ 6 ], and Martin-Löf’s type **theory** for Agda [ 24 ...

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... considering proofs as preexisting objects that can be seen as winning strategies in the interaction, we see each step of the interaction as a step in two simultaneous exhaustive searches for the proofs of two dual ...

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... complete **proof** of some **sequent** ∆ ` and no previous entry ∆ 0 ` exists with ∆ 0 ⊆ ∆, or whenever it concludes that some **sequent** ∆ ` is not provable and no previous entry ∆ 0 ` exists with ∆ ⊆ ∆ 0 ...a ...

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... in **proof** **theory**, it is now well-established that continuation- passing style (CPS) translations in call by name and call by value correspond to different polarisations of formulae ( Girard , 1991 ; Danos, ...

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... original **sequent** **calculus** has major defects for **proof**-search: the freedom with which rules can be applied leads to a very broad and redundant search ...reasonable **proof**-search procedures. ...

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... the **sequent** **calculus**. Whereas in the **sequent** **calculus** we can allow or forbid the rules on the left and/or on the right of the turnstile, in deep inference we have other ...

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... L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignemen[r] ...

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... a **proof** system that is geared towards SMT solvers and follows their conceptually modular ...Our **proof** system makes a clear distinction between propositional and **theory** ...specific **proof** ...

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... L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignemen[r] ...

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... 3 Another approach consists in twisting the definition of group to make it fit the previous model : defining “groups” — or at least what will figure in the statement of a property at the position where a group can be ...

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... Unité de recherche INRIA Sophia Antipolis 2004, route des Lucioles - BP 93 - 06902 Sophia Antipolis Cedex France Unité de recherche INRIA Futurs : Parc Club Orsay Université - ZAC des Vi[r] ...

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