Eugenio Moggi

Notions of computation and monads

Abstract The λ-calculus is considered a useful mathematical tool in the study of programming languages, since programs can be identified with λ-terms. However, if one goes further and uses βη-conversion to prove equivalence of programs, then a gross simplification is introduced (programs are identified with total functions from values to values ) that may jeopardise the applicability of theoretical results. In this paper we introduce calculi, based on a categorical semantics for computations , that provide a correct basis for proving equivalence of programs for a wide range of notions of computation .

Computational lambda-calculus and monads

The lambda -calculus is considered a useful mathematical tool in the study of programming languages. However, if one uses beta eta -conversion to prove equivalence of programs, then a gross simplification is introduced. The author gives a calculus based on a categorical semantics for computations, which provides a correct basis for proving equivalence of programs, independent from any specific computational model.<<ETX>>

Higher-order modules and the phase distinction

In earlier work, we used a typed function calculus, XML, with dependent types to analyze several aspects of the Standard ML type system. In this paper, we introduce a refinement of XML with a clear compile-time/run-time phase distinction, and a direct compile-time type checking algorithm. The calculus uses a finer separation of types into universes than XML and enforces the phase distinction using a nonstandard equational theory for module and signature expressions. While unusual from a type-theoretic point of view, the nonstandard equational theory arises naturally from the well-known Grothendieck construction on an indexed category.

A fully-abstract model for the /spl pi/-calculus

This paper provides both a fully abstract (domain-theoretic) model for the /spl pi/-calculus and a universal (set-theoretic) model for the finite /spl pi/-calculus with respect to strong late bisimulation and congruence. This is done by: considering categorical models, defining a metalanguage for these models, and translating the /spl pi/-calculus into the metalanguage. A technical novelty of our approach is an abstract proof of full abstraction: The result on full abstraction for the finite /spl pi/-calculus in the set-theoretic model is axiomatically extended to the whole /spl pi/-calculus with respect to the domain-theoretic interpretation. In this proof, a central role is played by the description of non-determinism as a free construction and by the equational theory of the metalanguage.

The Klaim Project: Theory and Practice

Klaim (Kernel Language for Agents Interaction and Mobility) is an experimental language specifically designed to program distributed systems consisting of several mobile components that interact through multiple distributed tuple spaces. Klaim primitives allow programmers to distribute and retrieve data and processes to and from the nodes of a net. Moreover, localities are first-class citizens that can be dynamically created and communicated over the network. Components, both stationary and mobile, can explicitly refer and control the spatial structures of the network. This paper reports the experiences in the design and development of Klaim. Its main purpose is to outline the theoretical foundations of the main features of Klaim and its programming model. We also present a modal logic that permits reasoning about behavioural properties of systems and various type systems that help in controlling agents movements and actions. Extensions of the language in the direction of object oriented programming are also discussed together with the description of the implementation efforts which have lead to the current prototypes.

Monads and Effects

A tension in language design has been between simple semantics on the one hand, and rich possibilities for side-effects, exception handling and so on on the other. The introduction of monads has made a large step towards reconciling these alternatives. First proposed by Moggi as a way of structuring semantic descriptions, they were adopted by Wadler to structure Haskell programs. Monads have been used to solve long-standing problems such as adding pointers and assignment, inter-language working, and exception handling to Haskell, without compromising its purely functional semantics. The course introduces monads, effects, and exemplifies their applications in programming (Haskell) and in compilation (MLj). The course presents typed metalanguages for monads and related categorical notions, and then describes how they can be further refined by introducing effects.

An Idealized MetaML: Simpler, and More Expressive

MetaML is a multi-stage functional programming language featuring three constructs that can be viewed as statically-typed refinements of the back-quote, comma, and eval of Scheme. Thus it provides special support for writing code generators and serves as a semantically-sound basis for systems involving multiple interdependent computational stages. In previous work, we reported on an implementation of MetaML, and on a reduction semantics and type-system for MetaML. In this paper, we present An Idealized MetaML (AIM) that is the result of our study of a categorical model for MetaML. An important outstanding problem is finding a type system that provides the user with a means for manipulating both open and closed code. This problem has eluded efforts by us and other researchers for over three years. AIM solves the issue by providing two type constructors, one classifies closed code and the other open code, and exploiting the way they interact. We point out that AIM can be verbose, and outline a possible remedy relating to the strictness of the closed code type.

ML-Like Inference for Classifiers

Environment classifiers were proposed as a new approach to typing multi-stage languages. Safety was established in the simply-typed and let-polymorphic settings. While the motivation for classifiers was the feasibility of inference, this was in fact not established. This paper starts with the observation that inference for the full classifier-based system fails. We then identify a subset of the original system for which inference is possible. This subset, which uses implicit classifiers, retains significant expressivity (e.g. it can embed the calculi of Davies and Pfenning) and eliminates the need for classifier names in terms. Implicit classifiers were implemented in MetaOCaml, and no changes were needed to make an existing test suite acceptable by the new type checker.

Functorial ML

We present an extension of the Hindley–Milner type system that supports a generous class of type constructors called functors, and provide a parametrically polymorphic algorithm for their mapping, i.e. for applying a function to each datum appearing in a value of constructed type. The algorithm comes from shape theory, which provides a uniform method for locating data within a shape. The resulting system is Church–Rosser and strongly normalizing, and supports type inference. Several different semantics are possible, which affects the choice of constants in the language, and are used to illustrate the relationship to polytypic programming.

Closed types for a safe imperative MetaML

This paper addresses the issue of safely combining computational effects and multi-stage programming. We propose a type system which exploits a notion of closed type, to check statically that an imperative multi-stage program does not cause run-time errors. Our approach is demonstrated formally for a core language called