Abstract

(in memory of Peter Landin (1930-2009) and Gerhard Gentzen (1909-1945))

Gentzen is at the origin of natural deduction and sequent calculus. Both had a deep echo in computer science, the first via the Curry- Howard correspondence linking lambda-calculus based programming languages with formal proofs written in natural deduction style, while the second led to the proof- search paradigm at the heart of logic programming. In this talk, we shall start from the backbone of Curry-Howard, which is simply typed lambda-calculus on one side, intuitionistic logic on the other side, and explain a few milestones:

• Griffin 1990: extending the picture to control operators on one side, classical logic on the other side
• Herbelin 1995: Curry-Howard in sequent calculus style
• Curien-Herbelin 2000: call-by-value is dual to call-by-name
• Munch, Curien-Munch 2008: focalised Curry-Howard, where the order of evaluation is reflected at the level of types/formulas (see also Zeilberger 2008)

In a nutshell, the sequent calculus offers symmetries between inputs and continuations, and between programs and program contexts, that make sequent calculus based syntaxes suitable for the formalisation of abstract machines.

(Supported by Leverhulme grant)