This paper describes the construction of categorical models for the nu-calculus, a language that combines higher-order functions with dynamically created names. Names are created with local scope, they can be compared with each other and passed around through function application, but that is all. The intent behind this language is to examine one aspect of the imperative character of Standard ML: the use of local state by dynamic creation of references. The nu-calculus is equivalent to a certain fragment of ML, omitting side effects, exceptions, datatypes and recursion. Even without all these features, the interaction of name creation with higher-order functions can be complex and subtle; it is particularly difficult to characterise the observable behaviour of expressions. Categorical monads, in the style of Moggi, are used to build denotational models for the nu-calculus. An intermediate stage is the use of a computational metalanguage, which distinguishes in the type system between values and computations. The general requirements for a categorical model are presented, and two specific examples described in detail. These provide a sound denotational semantics for the nu-calculus, and can be used to reason about observable equivalence in the language. In particular a model using logical relations is fully abstract for first-order expressions.

Pure functional programming languages have been proposed as a vehicle to describe, simulate and manipulate circuit specifications. We propose an extension to Haskell to solve a standard problem when manipulating data types representing circuits in a lazy functional language. The problem is that circuits are finite graphs -- but viewing them as an algebraic (lazy) datatype makes them indistinguishable from potentially infinite regular trees. However, implementations of Haskell do indeed represent cyclic structures by graphs. The problem is that the sharing of nodes that creates such cycles is not observable by any function which traverses such a structure. In this paper we propose an extension to call-by-need languages which makes graph sharing observable. The extension is based on non updatable reference cells and an equality test (sharing detection) on this type. We show that this simple and practical extension has well-behaved semantic properties, which means that many typical source-to-source program transformations, such as might be performed by a compiler, are still valid in the presence of this extension.

Abstract. We propose a simple compositional program logic for an imperative extension of call-by-value PCF, built on Hoare logic and our preceding work on program logics for pure higher-order functions. A systematic use of names and operations on them allows precise and general description of complex higher-order imperative behaviour. The proof rules of the logic exactly follow the syntax of the language and can cleanly embed, justify and extend the standard proof rules for total correctness of Hoare logic. The logic offers a foundation for general treatment of aliasing and local state on its basis, with minimal extensions. After establishing soundness, we prove that valid assertions for programs completely characterise their behaviour up to observational congruence, which is proved using a variant of finite canonical forms. The use of the logic is illustrated through reasoning examples which are hard to assert and infer using existing program logics.

We adopt the untyped imperative object calculus of Abadi and Cardelli as a minimal setting in which to study problems of compilation and program equivalence that arise when compiling objectoriented languages. We present both a big-step and a small-step substitution-based operational semantics for the calculus. Our rst two results are theorems asserting the equivalence of our substitutionbased semantics with a closure-based semantics like that given by Abadi and Cardelli. Our third result is a direct proof of the correctness of compilation to a stack-based abstract machine via a small-step decompilation algorithm. Our fourth result is that contextual equivalence of objects coincides with a form of Mason and Talcott's CIU equivalence; the latter provides a tractable means of establishing operational equivalences. Finally, we prove correct an algorithm, used in our prototype compiler, for statically resolving method osets. This is the rst study of correctness of an object-oriented abstract machine, and of operational equivalence for the imperative object calculus.

Plotkin has advocated the combination of linear lambda calculus, polymorphism and fixed point recursion as an expressive semantic metalanguage. We study its expressive power from an operational point of view. We show that the naturally call-by-value operators of linear lambda calculus can be given a call-by-name semantics without affecting termination at exponential types and hence without affecting ground contextual equivalence. This result is used to prove properties of a logical relation that provides a new extensional characterisation of ground contextual equivalence and relational parametricity properties of polymorphic types.

Software executing on distributed systems consists of many asynchronous, autonomous components which interact in order to coordinate local activity. The need for such coordination, as well as requirements such as heterogeneity, scalability, security and availability, considerably increase the complexity of code in distributed applications. Moreover, changing requirements, as well as changes in hardware platforms, lead to software that is constantly evolving and complicates reuse. To support development and evolution of distributed applications requires techniques which allow coordination code to be specified, customized, and maintained independently of application components; goals which cannot be realized solely through object-oriented techniques. This thesis demonstrates that meta-level specification of interaction policies enables modular description of component interaction policies, as well as customization of policy implementations. We present the high-level language Dil for spec...

Machine The semantics presented in this section is essentially Sestoft's \mark 1" abstract machine for laziness [Sestoft 1997]. In that paper, he proves his abstract machine 6 A. K. Moran and D. Sands h fx = Mg; x; S i ! h ; M; #x : S i (Lookup) h ; V; #x : S i ! h fx = V g; V; S i (Update) h ; M x; S i ! h ; M; x : S i (Unwind) h ; x:M; y : S i ! h ; M [ y = x ]; S i (Subst) h ; case M of alts ; S i ! h ; M; alts : S i (Case) h ; c j ~y; fc i ~x i N i g : S i ! h ; N j [ ~y = ~x j ]; S i (Branch) h ; let f~x = ~ Mg in N; S i ! h f~x = ~ Mg; N; S i ~x dom(;S) (Letrec) Fig. 1. The abstract machine semantics for call-by-need. semantics sound and complete with respect to Launchbury's natural semantics, and we will not repeat those proofs here. Transitions are over congurations consisting of a heap, containing bindings, the expression currently being evaluated, and a stack. The heap is a partial function from variables to terms, and denoted in an identical manner to a coll...

this paper we regard the following as synonyms: references, program variables, pointers, locations, and unary cells) to a programming language complicates life. Adding them to the simply typed lambda calculus causes the failure of most of the nice mathematical properties and some of the more basic rules (such as j). For example strong normalization fails since it is possible, for each provably non--empty function type, to construct a Y --combinator for that type. References also interact unpleasantly with polymorphism [34, 35]. They are also troublesome from a denotational point of view as illustrated by the lack of fully abstract models. For example, in [22] Meyer and Sieber give a series of examples of programs that are operationally equivalent (according to the intended semantics of block-structured Algol-like programs) but which are not given equivalent denotations in traditional denotational semantics. They propose various modifications to the denotational semantics which solve some of these discrepancies, but not all. In [27, 26] a denotational semantics that overcomes some of these problems is presented. However variations on the seventh example remain problematic. Since numerous proof systems for Algol are sound for the denotational models in question, [8, 7, 32, 28, 16, 27, 26], these equivalences, if expressible, must be independent of these systems. The problem which motivated Meyer and Sieber's paper, [22], was to provide mathematical justification for the informal but convincing proofs of the operational equivalence of their examples. In this paper we approach the same problem, but from an operational rather than denotational perspective. This paper accomplishes two goals. Firstly, we present the first-order part of a new logic for reasoning about programs....

Inter-language interoperability is big business, as the success of Microsoft’s.NET and COM and Sun’s JVM show. Programming language designers are designing programming languages that reflect that fact — SML#, Mondrian, and Scala, to name just a few examples, all treat interoperability with other languages as a central design feature. Still, current multi-language research tends not to focus on the semantics of interoperation features, but only on how to implement them efficiently. In this paper, we take first steps toward higher-level models of interoperating systems. Our technique abstracts away the low-level details of interoperability like garbage collection and representation coherence, and lets us focus on semantic properties like type-safety and observable equivalence. Beyond giving simple expressive models that are natural compositions of single-language models, our studies have uncovered several interesting facts about interoperability. For example, higherorder contracts naturally emerge as the glue to ensure that interoperating languages respect each other’s type systems. While we present our results in an abstract setting, they shed light on real multi-language systems and tools such as the JNI, SWIG, and Haskell’s stable pointers.

We present a compositional program logic for call-by-value imperative higherorder functions with general forms of aliasing, which can arise from the use of reference names as function parameters, return values, content of references and part of data structures. The program logic