This report is essential Uffe Engbergs thesis for the MSc degree from Department of Computer Science, Aarhus University--- except that all proofs of theorems have been left out. Should anyone have interest in particular proofs, they may be obtained by contacting one of the authors. 1 Introduction

) Davide Sangiorgi LFCS - Department of Computer Science Edinburgh University Edinburgh - EH9 3JZ - UK Abstract The use of lambda calculus in richer settings, possibly involving parallelism, is examined in terms of its effect on the equivalence between lambda terms. We concentrate here on Abramsky's lazy lambda calculus and we follow two directions. First, the lambda calculus is studied within a process calculus by examining the equivalence $ induced by Milner's encoding into the -calculus. We give exact operational and denotational characterizations for $. Secondly, we examine Abramsky's applicative bisimulation when the lambda calculus is augmented with (well-formed) operators, i.e. symbols equipped with reduction rules describing their behaviour. Then, maximal discrimination is obtained when all operators are considered; we show that this discrimination coincides with the one given by $ and that the adoption of certain non-deterministic operators is sufficient and necessary...

. This paper describes a general purpose program analysis that computes global control-flow and data-flow information for higher-order, call-by-value programs. This information can be used to drive global program optimizations such as inlining and run-time check elimination, as well as optimizations like constant folding and loop invariant code motion that are typically based on special-purpose local analyses. The analysis employs a novel approximation technique called polymorphic splitting that uses let-expressions as syntactic clues to gain precision. Polymorphic splitting borrows ideas from Hindley-Milner polymorphic type inference systems to create an analog to polymorphism for flow analysis. Experimental results derived from an implementation of the analysis for Scheme indicate that the analysis is extremely precise and has reasonable cost. In particular, it eliminates significantly more run-time checks than simple flow analyses (i.e. 0CFA) or analyses based on type ...

We investigate semantical normalization proofs for typed combinatory logic and weak -calculus. One builds a model and a function `quote' which inverts the interpretation function. A normalization function is then obtained by composing quote with the interpretation function. Our models are just like the intended model, except that the function space includes a syntactic component as well as a semantic one. We call this a `glued' model because of its similarity with the glueing construction in category theory. Other basic type constructors are interpreted as in the intended model. In this way we can also treat inductively defined types such as natural numbers and Brouwer ordinals. We also discuss how to formalize -terms, and show how one model construction can be used to yield normalization proofs for two different typed -calculi -- one with explicit and one with implicit substitution. The proofs are formalized using Martin-Lof's type theory as a meta language and mechanized using the A...

Machines Th. STREICHER Fachbereich 4 Mathematik, TU Darmstadt, Schlossgartenstr. 7, 64289 Darmstadt, streiche@mathematik.th-darmstadt.de B. REUS Institut fur Informatik, Ludwig-Maximilians-Universitat, Oettingenstr. 67, D-80538 Munchen, reus@informatik.uni-muenchen.de Abstract One of the goals of this paper is to demonstrate that denotational semantics is useful for operational issues like implementation of functional languages by abstract machines. This is exemplified in a tutorial way by studying the case of extensional untyped call-byname -calculus with Felleisen's control operator C. We derive the transition rules for an abstract machine from a continuation semantics which appears as a generalization of the ::-translation known from logic. The resulting abstract machine appears as an extension of Krivine's Machine implementing head reduction. Though the result, namely Krivine's Machine, is well known our method of deriving it from continuation semantics is new and applicable to other languages (as e.g. call-by-value variants).

A flow-directed inlining strategy uses information derived from control-flow analysis to specialize and inline procedures for functional and object-oriented languages. Since it uses control-flow analysis to identify candidate call sites, flowdirected inlining can inline procedures whose relationships to their call sites are not apparent. For instance, procedures defined in other modules, passed as arguments, returned as values, or extracted from data structures can all be inlined. Flow-directed inlining specializes procedures for particular call sites, and can selectively inline a particular procedure at some call sites but not at others. Finally, flow-directed inlining encourages modular implementations: control-flow analysis, inlining, and post-inlining optimizations are all orthogonal components. Results from a prototype implementation indicate that this strategy effectively reduces procedure call overhead and leads to significant reduction in execution time. 1 Introduction Functio...

Techniques for reasoning about extensional properties of functional programs are well understood, but methods for analysing the underlying intensional or operational properties have been much neglected. This paper begins with the development of a simple but useful calculus for time analysis of non-strict functional programs with lazy lists. One limitation of this basic calculus is that the ordinary equational reasoning on functional programs is not valid. In order to buy back some of these equational properties we develop a non-standard operational equivalence relation called cost equivalence, by considering the number of computation steps as an `observable' component of the evaluation process. We define this relation by analogy with Park's definition of bisimulation in CCS. This formulation allows us to show that cost equivalence is a contextual congruence (and thus is substitutive with respect to the basic calculus) and provides useful proof techniques for establishing cost-equivalen...

This article is intended to provide some new insights about concurrency theory using ideas from geometry, and more specifically from algebraic topology. The aim of the paper is two-fold: we justify applications of geometrical methods in concurrency through some chosen examples and we give the mathematical foundations needed to understand the geometric phenomenon that we identify. In particular we show that the usual notion of homotopy has to be refined to take into account some partial ordering describing the way time goes. This gives rise to some new interesting mathematical problems as well as give some common grounds to computer-scientific problems that have not been precisely related otherwise in the past. The organization of the paper is as follows. In Section 2 we explain to which extent we can use some geometrical ideas in computer science: we list a few of the potential or well known areas of application and try to exemplify some of the properties of concurrent (and distributed) systems we are interested in. We first explain the interest of using some geometric ideas for semantical reasons. Then we take the example of concurrent databases with the problem of finding deadlocks and with some aspects of serializability theory. More general questions about schedules can be asked as well and related to some geometric considerations, even for scheduling micro-instructions (and not only coarse-grained transactions as for databases). The final example is the one of fault-tolerant protocols for distributed systems, where subtle scheduling properties go into play. In Section 3 we give the first few definitions needed for modeling the topological spaces arising from Section 2. Basically, we need to define a topological space containing all traces of executions of the concu...

Bigraphs are graphs whose nodes may be nested, representing locality, independently of the edges connecting them. They may be equipped with reaction rules, forming a bigraphical reactive system (Brs) in which bigraphs can reconfigure themselves. Following an earlier paper describing link graphs, a constituent of bigraphs, this paper is a devoted to pure bigraphs, which in turn underlie various more refined forms. Elsewhere it is shown that behavioural analysis for Petri nets, π-calculus and mobile ambients can all be recovered in the uniform framework of bigraphs. The paper first develops the dynamic theory of an abstract structure, a wide reactive system (Wrs), of which a Brs is an instance. In this context, labelled transitions are defined in such a way that the induced bisimilarity is a congruence. This work is then specialised to Brss, whose graphical structure allows many refinements of the theory. The latter part of the paper emphasizes bigraphical theory that is relevant to the treatment of dynamics via labelled transitions. As a running example, the theory is applied to finite pure CCS, whose resulting transition system and bisimilarity are analysed in detail. The paper also mentions briefly the use of bigraphs to model pervasive computing and

this article we will not attempt to describe all the dierent possible choices of type theories. Instead we want to discuss the main underlying ideas, with a special focus on the use of type theory as the formalism for the description of theories including proofs