## About

12

Publications

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41

Citations

Citations since 2016

## Publications

Publications (12)

We investigate cut elimination in multi-focused sequent calculi and the impact on the cut elimination proof of design choices in such calculi. The particular design we advocate is illustrated by a multi-focused calculus for full linear logic using an explicitly polarised syntax and incremental focus handling, for which we provide a syntactic cut el...

Linear logic enjoys strong symmetries inherited from classical logic while providing a constructive framework comparable to intuitionistic logic. However, the computational interpretation of sequent calculus presentations of linear logic remains problematic, mostly because of the many rule permutations allowed in the sequent calculus. We address th...

Proof assistants and programming languages based on type theories usually
come in two flavours: one is based on the standard natural deduction
presentation of type theory and involves eliminators, while the other provides
a syntax in equational style. We show here that the equational approach
corresponds to the use of a focused presentation of a ty...

We investigate the control of evaluation strategies in a variant of the Λ-calculus derived through the Curry-Howard correspondence from LJF, a sequent calculus for intuitionistic logic implementing the focusing technique. The proof theory of focused intuitionistic logic yields a single calculus in which a number of known Λ-calculi appear as subsyst...

We study cut elimination for a multifocused variant of full linear logic in
the sequent calculus. The multifocused normal form of proofs yields problems
that do not appear in a standard focused system, related to the constraints in
grouping rule instances in focusing phases. We show that cut elimination can be
performed in a sensible way even thoug...

We discuss the extension of the LF logical framework with operators for manipulating worlds, as found in hybrid logics or in the HLF framework. To overcome the restrictions of HLF, we present a more general approach to worlds in LF, where the structure of worlds can be described in an explicit way. We give a canonical presentation for this system a...

We present two proof systems for implication-only intuitionistic logic in the calculus of structures. The first is a direct adaptation of the standard sequent calculus to the deep inference setting, and we describe a procedure for cut elimination, similar to the one from the sequent calculus, but using a non-local rewriting. The second system is th...

The standard proof theory for logics with equality and fixpoints suffers from limitations of the sequent calculus, where reasoning is separated from computational tasks such as unification or rewriting. We propose in this paper an extension of the calculus of structures, a deep inference formalism, that supports incremental and contextual reasoning...

This thesis investigates the use of deep inference formalisms as basis for a computational interpretation of proof systems, following the two main approaches: proofs-as-programs and proof-search-as-computation. The first contribution is the development of a family of proof systems for intuitionistic logic in the calculus of structures and in nested...

The focusing theorem identifies a complete class of sequent proofs that have no inessential nondeterministic choices and restrict the essential choices to a particular normal form. Focused proofs are therefore well suited both for the search and for the representation of sequent proofs. The calculus of structures is a proof formalism that allows ru...

We present a system for propositional implicative intuitionistic logic in the calculus of structures, which is a generalisation of the sequent calculus to the deep inference methodology. We show that it is sound and complete with respect to the usual sequent calculus, and consider a restricted system for a smaller class of formulas. Then, we encode...

The proof-theoretic approach to logic programming has benefited from the introduction of focused proof systems through the non-determinism reduction and control they provide when searching for proofs in the sequent calculus. However, this technique was not available in the calculus of structures, known for inducing even more non-determinism than ot...