Abstract. For use in earlier approaches to automated module interface adaptation, we seek a restricted form of program synthesis. Given some typing assumptions and a desired result type, we wish to automatically build a number of program fragments of this chosen typing, using functions and values available in the given typing environment. We call this problem term enumeration. To solve the problem, we use the CurryHoward correspondence (propositions-as-types, proofs-as-programs) to transform it into a proof enumeration problem for an intuitionistic logic calculus. We formally study proof enumeration and counting in this calculus. We prove that proof counting is solvable and give an algorithm to solve it. This in turn yields a proof enumeration algorithm.

ML F is a type system that seamlessly merges ML-style type inference with System-F polymorphism. We propose a system of graphic (type) constraints that can be used to perform type inference in both ML or ML F . We show that this constraint system is a small extension of the formalism of graphic types, originally introduced to represent ML F types. We give a few semantic preserving transformations on constraints and propose a strategy for applying them to solve constraints. We show that the resulting algorithm has optimal complexity for ML F type inference, and argue that, as for ML, this complexity is linear under reasonable assumptions.

The evolution of Web sites towards very dynamic applications makes it necessary to reconsider current Web programming technologies. We believe that Web development would benefit greatly from more abstract paradigms and that a more semantical approach would result in huge gains in expressiveness. In particular, functional programming provides a really elegant solution to some important Web interaction problems, but few frameworks take advantage of it.The Ocsigen project is an attempt to provide global solutions to these needs. We present our experience in designing this general framework for Web programming, written in Objective Caml. It provides a fully featured Web server and a framework for programming Web applications, with the aim of improving expressiveness and safety. This is done by taking advantage of functional programming and static typing as much as possible.

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ML F is a type system that seamlessly merges ML-style implicit but second-class polymorphism with System-F explicit first-class polymorphism. We present x ML F , a Church-style version of ML F with full type information that can easily be maintained during reduction. All parameters of functions are explicitly typed and both type abstraction and type instantiation are explicit. However, type instantiation in x ML F is more general than type application in System F. We equip x ML F with a small-step reduction semantics that allows reduction in any context, and show that this relation is confluent and type preserving. We also show that both subject reduction and progress hold for weak-reduction strategies, including call-by-value with the value-restriction. We exhibit a type preserving encoding of ML F into x ML F , which shows that x ML F can be used as the internal language for ML F after type inference, and also ensures type soundness for the most expressive variant of ML F .