Delia Kesner

Proof nets and explicit substitutions

We refine the simulation technique introduced in Di Cosmo and Kesner (1997) to show strong normalisation of

The theory of calculi with explicit substitutions revisited

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Simulating expansions without expansions

-calculi with explicit substitutions via termination of cut elimination in proof nets (Girard 1987). We first propose a notion of equivalence relation for proof nets that extends the one in Di Cosmo and Guerrini (1999), and show that cut elimination modulo this equivalence relation is terminating. We then show strong normalisation of the typed version of the

A Typed Pattern Calculus

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A Confluent Reduction for the Extensional Typed lambda-Calculus with Pairs, Sums, Recursion and terminal Object

-calculus with de Bruijn indices (a calculus with full composition defined in David and Guillaume (1999)) using a translation from typed

Pattern matching as cut elimination

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Confluence of extensional and non-extensional l-calculi with explicit substitutions

to proof nets. Finally, we propose a version of typed

Extending the explicit substitution paradigm

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Quantitative Types for the Linear Substitution Calculus

with named variables, which helps to give a better understanding of the complex mechanism of the explicit weakening notation introduced in the

Combining First Order Algebraic Rewriting Systems, Recursion and Extensional Lambda Calculi

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