Putting Curry-Howard to work

Continuation Semantics Values, Contexts and Computations

A promising line of research in the interaction between syntax and semantics has been open by the work on Continuation Semantics started by [1] and [5] and further explored by [8]. Work done within Curry Howard Correspondence to Classical Logic has brought to the attention the duality distinction holding between terms and contexts (or co-terms), and can help further shaping the syntax-semantics...

A Computational Interpretation of the -calculus

This paper proposes a simple computational interpretation of Parigot’s -calculus. The -calculus is an extension of the typed -calculus which corresponds via the Curry-Howard correspondence to classical logic. Whereas other work has given computational interpretations by translating the -calculus into other calculi, I wish to propose here a direct computational interpretation. This interpretatio...

Investigations into the Duality of Computation

The work presented here is an extension of a previous work realised jointly with Pierre-Louis Curien [CH00]. The current work focuses on the pure calculus of variables and binders that operates at the core of the duality between call-by-name and call-by-value evaluations. A Curry-Howard-de Bruijn correspondence is given that shed light on some aspects of Gentzen’s sequent calculus. This include...

Curry-Howard Terms for Linear Logic

In this paper we 1. provide a natural deduction system for full rst-order linear logic, 2. introduce Curry{Howard{style terms for this version of linear logic, 3. extend the notion of substitution of Curry-Howard terms for term variables, 4. deene the reduction rules for the Curry{Howard terms and 5. outline a proof of the strong normalization for the full system of linear logic using a develop...

Extended Curry-Howard Correspondence for a Basic Constructive Modal Logic