Section: Research Program
Around and beyond the Curry-Howard correspondence
For two decades, the Curry-Howard correspondence has been limited to the intuitionistic case but since 1990, an important stimulus spurred on the community following Griffin's discovery that this correspondence was extensible to classical logic. The community then started to investigate unexplored potential connections between computer science and logic. One of these fields is the computational understanding of Gentzen's sequent calculus while another one is the computational content of the axiom of choice.
Control operators and classical logic
Indeed, a significant extension of the Curry-Howard correspondence has been
obtained at the beginning of the 90's thanks to the seminal
observation by Griffin [63] that some operators known as
control operators were typable by the principle of double negation
elimination (
Control operators are used to jump from one location of a
program to another. They were first considered in the 60's by
Landin [70] and Reynolds [73] and started to
be studied in an abstract way in the 80's by Felleisen et
al [59] , leading to Parigot's
Sequent calculus
The Curry-Howard interpretation of sequent calculus started to be investigated at the beginning of the 90's. The main technicality of sequent calculus is the presence of left introduction inference rules, for which two kinds of interpretations are applicable. The first approach interprets left introduction rules as construction rules for a language of patterns but it does not really address the problem of the interpretation of the implication connective. The second approach, started in 1994, interprets left introduction rules as evaluation context formation rules. This line of work led in 2000 to the design by Hugo Herbelin and Pierre-Louis Curien of a symmetric calculus exhibiting deep dualities between the notion of programs and evaluation contexts and between the standard notions of call-by-name and call-by-value evaluation semantics.
Abstract machines
Abstract machines came as an intermediate evaluation device, between
high-level programming languages and the computer microprocessor. The
typical reference for call-by-value evaluation of
Delimited control
Delimited control extends the expressiveness of control operators with
effects: the fundamental result here is a completeness result by
Filinski [60] : any side-effect expressible in monadic
style (and this covers references, exceptions, states, dynamic
bindings, ...) can be simulated in