data types embody uniformity in the form of information hiding. Information hiding enforces the uniform treatment of those entities that dier only on hidden information.

Compilers for ML and Haskell typically go to a good deal of trouble to arrange that multiple arguments can be passed eciently to a procedure. For some reason, less effort seems to be invested in ensuring that multiple results can also be returned efficiently. In the context

We present here a large family of concrete models for Girard and Reynolds polymorphism (System F ), in a non categorical setting. The family generalizes the construction of the model of Barbanera and Berardi [2], hence it contains complete models for F [5] and we conjecture that it contains models which are complete for F . It also contains simpler models, the simplest of them, E 2 ; being a second order variant of the Engeler-Plotkin model E . All the models here belong to the continuous semantics and have underlying prime algebraic domains, all have the maximum number of polymorphic maps. The class contains models which can be viewed as two intertwined compatible webbed models of untyped -calculus (in the sense of [8]), but it is much larger than this. Finally many of its models might be read as two intertwined strict intersection type systems. Contents 1

We introduce a new type system called \System ST" (ST stands for SubTyping), based on subtyping, and prove the basic property of the system. We show the extraordinary expressive power of the system which leads us to think that it could be a good candidate for doing both proof and extraction of programs.

In this paper, we extend the non-uniform denotational semantics de ned by Bucciarelli and Ehrhard in [BuEh,00] to second-order linear logic.

Map theory, or MT for short, has been designed as an \integrated" foundation for mathematics, logic and computer science. By this we mean that most primitives and tools are designed from the beginning to bear the three intended meanings: logical, computational, and set-theoretic. MT was originally introduced in [17]. It is based on -calculus instead of logic and sets, and it fullls Church's original aim of introducing -calculus. In particular, it embodies all of ZFC set theory, including classical propositional and classical rst order predicate calculus. MT also embodies the unrestricted, untyped lambda calculus including unrestricted abstraction and unrestricted use of the xed point operator. MT is an equational theory. We present here a semantic proof of the consistency of map theory within ZFC + SI, where SI asserts the existence of an inaccessible cardinal. The proof is in the spirit of denotational semantics and relies on mathematical tools which reect faithful...

The main contribution of this paper is a partial type-checking algorithm for the system F and its use in a programming language like ML. We dene this system as an extension of the second-order -calculus (system F) verifying the preservation of type during computation (subject-reduction) for -reduction (this result fails for -reduction in system F). Our presentation is based on an original notion of sub-typing which includes all the handling of quantication rules. 1 Introduction. Motivation. Type systems have proved to be useful for many modern functional programming languages such as ML, Miranda, Haskell, . . . . In most cases, the basis of the type system is Milner's algorithm [12]. The main characteristic of these type systems is polymorphism which allows the programmer to write generic functions that can work on arguments of dierent types. However it is often insucient: polymorphic recursion, existential types or the state monad of Haskell are treated using specic exte...