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# Proof theory Sequent calculus

### Soundly Proving B Method Formulae Using Typed Sequent Calculus

... 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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### Proof theory for indexed nested sequents

... 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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### Infinitary proof theory : the multiplicative additive case

... (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 Sequent Calculus for a Modal Logic on Finite Data Trees

... 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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### A Sequent Calculus with Implicit Term Representation

... 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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### Non-wellfounded proof theory for (Kleene+action)(algebras+lattices)

... 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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### Normalisation & Equivalence in Proof Theory & Type Theory

... 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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### Infinets: The parallel syntax for non-wellfounded proof-theory

... 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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### A Classical Sequent Calculus with Dependent Types

... 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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### A Classical Sequent Calculus with Dependent Types

... 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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### Symmetric dialogue games in the proof theory of linear logic

... 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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### A bisimulation between DPLL(T) and a proof-search strategy for the focused sequent calculus

... 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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### Dependent Type Theory in Polarised Sequent Calculus (abstract)

... 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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### Automated Reasoning Techniques as Proof-search in Sequent Calculus

... 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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### Towards a Combinatorial Proof Theory

... 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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### Residual theory in lambda-calculus : a formal development

... 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 Nelson-Oppen based Proof System using Theory Specific Proof Systems

... 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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### A Proof of Weak Termination of the Simply-Typed {$\lambda\sigma$}-Calculus

... 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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### Generic Proof Tools and Finite Group Theory

... 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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### A Fault Tolerance protocol for ASP calculus: Design and Proof

... 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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