A Generalization of the Curry-Howard Correspondence

The Essence of Event-Driven Programming

Event-driven programming is based on a natural abstraction: an event is a computation that can eventually return a value. This paper exploits the intuition relating events and time by drawing a Curry-Howard correspondence between a functional event-driven programming language and a linear-time temporal logic. In this logic, the eventually proposition ♦A describes the type of events, and Girard’...

Classical Logic and the Curry–Howard Correspondence

We present the Curry–Howard correspondence for constructive logic via natural deduction, typed λ-calculus and cartesian closed categories. We then examine how the correspondence may be extended to classical logic and non-constructive proofs, and discuss some of the problems and questions that then arise.

Extended Curry-Howard Correspondence for a Basic Constructive Modal Logic

Putting Curry-Howard to work

It is a well known fact that there is a correspondence between propositions and type, and similarly a correspondence between a proof of a proposition and a program of a type; this is the Curry-Howard correspondence. In this talk I will describe a program, Djinn, which takes a Haskell type and produces a program of that type, using the Curry-Howard correspondence. For the subset of Haskell types...

Substructural Proofs as Automata

We present subsingleton logic as a very small fragment of linear logic containing only , 1, least fixed points and allowing circular proofs. We show that cut-free proofs in this logic are in a Curry– Howard correspondence with subsequential finite state transducers. Constructions on finite state automata and transducers such as composition, complement, and inverse homomorphism can then be reali...