An interpretation of Abadi and Cardelli's first-order Imperative Object Calculus into a typed pi-calculus is presented. The interpretation validates the subtyping relation and the typing judgements of the Object Calculus, and is computationally adequate. The proof of computational adequacy makes use of (a pi-calculus version) of ready simulation, and of a factorisation of the interpretation into a functional part and a very simple imperative part. The interpretation can be used to compare and contrast the Imperative and the Functional Object Calculi, and to prove properties about them, within a unified framework.

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.

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...

A region calculus is a polymorphically typed lambda calculus with explicit memory management primitives. Every value is annotated with a region in which it is stored. Regions are allocated and deallocated in a stack-like fashion. The annotations can be statically inferred by a type and eect system, making a region calculus suitable as an intermediate language for a compiler of statically typed programming languages.