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In this paper we introduce M-LISP, a simple new dialect of LISP which is designed with an eye toward reconciling LISP's metalinguistic power with the structural style of operational semantics advocated by Plotkin [Plo75]. We begin by reviewing the original denition of LISP [McC61] in an attempt to clarify the source of its metalinguistic power. We nd that it arises from a problematic clause in this denition. We then dene the abstract syntax and operational semantics of M-LISP, essentially a hybrid of M-expression LISP and Scheme. Next, we tie the operational semantics to the corresponding equational logic. As usual, provable equality in the logic implies operational equality. Having established this framework we then extend M-LISP with the metalinguistic eval and reify operators (the latter is a non-strict operator which converts its argument to its metalanguage representation.) These operators encapsulate the metalinguistic representation conversions that occur globall...

We describe a programming language called Symmetric Lisp that treats environments as first­class objects. Symmetric Lisp allows programmers to write expressions that evaluate to environments, and to create and denote variables and constants of type environment as well. One consequence is that the roles filled in other languages by a variety of limited, special purpose environment forms like records, structures, closures, modules, classes and abstract data types are filled instead by a single versatile and powerful structure. In addition to being its fundamental structuring tool, environments also serve as the basic functional object in the language. Because the elements of an environment are evaluated in parallel, Symmetric Lisp is a parallel programming language; because they may be assembled dyamically as well as statically, Symmetric Lisp accomodates an unusually flexible and simple (parallel) interpreter as well as other history­sensitive applications requiring dynamic environments. We show that first­class environments bring about fundamental changes in a language's structure: conventional distinctions between declarations and expressions, data structures and program structures, passive modules and active processes disappear. We argue that the resulting language is clean, simple and powerful.

Compilers for higher-order programming languages like Scheme, ML, and Lisp can be broadly characterized as either "direct compilers" or "continuation-passing style (CPS) compilers", depending on their main intermediate representation. Our central result is a precise correspondence between the two compilation strategies. Starting from

While Game Semantics has been remarkably successful at modelling, often in a fully abstract manner, a wide range of features of programming languages, there has to date been no attempt at applying it to subtyping. We show how the simple device of explicitly introducing error values in the syntax of the calculus leads to a notion of subtyping for game semantics. We construct an interpretation of a simple -calculus with subtyping and show how the range of the interpretation of types is a complete lattice thus yielding an interpretation of bounded quantification.

. In a simply-typed, call-by-value (CBV) language with first-class continuations, the usual CBV fixpoint operator can be defined in terms of a simple, infinitelylooping iteration primitive. We first consider a natural but flawed definition, based on exceptions and "iterative deepening" of finite unfoldings, and point out some of its shortcomings. Then we present the proper construction using full first-class continuations, with both an informal derivation and a proof that the behavior of the defined operator faithfully mimics a "built-in" recursion primitive. In fact, given an additional uniformity assumption, the construction is a two-sided inverse of the usual definition of iteration from recursion. Continuing, we show that the CBV looping primitive is in fact the direct-style equivalent of a continuation-passing-style fixpoint, and that this correspondence extends all the way to traditional definitions of these operators in terms of reflexive types. 1. Introduction 1.1. Background ...

In this paper, we take an abstract view of search by describing search procedures via particular kinds of proofs in type theory. We rely on the proofs-as-programs interpretation to extract programs from our proofs. Using these techniques we explore, in depth, a large family of search problems by parameterizing the speci cation of the problem. A constructive proof is presented which has as its computational content a correct search procedure for these problems. We show how a classical extension to an otherwise constructive system can be used to describe a typical use of the nonlocal control operator call/cc. Using the classical typing of nonlocal control we extend our purely constructive proof to incorporate a sophisticated backtracking technique known as ‘con ict-directed backjumping’ (CBJ). A variant of this proof is formalized in Nuprl yielding a correct-by-construction implementation of CBJ. The extracted program has been translated into Scheme and serves as the basis for an implementation of a new solution to the Hamiltonian circuit problem. This paper demonstrates a nontrivial application of the proofs-as-programs paradigm by applying the technique to the derivation of a sophisticated search algorithm; also, it shows the generality of the resulting implementation by demonstrating its application in a new problem

There is a middle ground between parametric and ad-hoc polymorphism in which a computation can depend upon a type parameter but is restricted to being defined at all types in an inductive fashion. We call such polymorphism non-parametric. We show how nonparametric polymorphism can be used to implement a variety of useful language mechanisms including overloading, unboxed data representations in the presence of ML-style polymorphism, and canonical representations of equivalent types. We show that, by using a second-order, explicitly typed language extended with non-parametric operations, these mechanisms can be implemented without having to tag data with type information at runtime. Furthermore, this approach retains a "phase distinction" and permits static type checking and separate compilation. Our aim is to provide a unifying language, translation, and proof framework in which a variety of non-parametric mechanisms can be expressed and verified. 1 Introduction Polymorphism is the ...

We consider the natural combinations of algebraic computational effects such as side-effects, exceptions, interactive input/output, and nondeterminism with continuations. Continuations are not an algebraic effect, but previously developed combinations of algebraic effects given by sum and tensor extend, with effort, to include commonly used combinations of the various algebraic effects with continuations. Continuations also give rise to a third sort of combination, that given by applying the continuations monad transformer to an algebraic effect. We investigate the extent to which sum and tensor extend from algebraic effects to arbitrary monads, and the extent to which Felleisen et al.’s C operator extends from continuations to its combination with algebraic effects. To do all this, we use Dubuc’s characterisation of strong monads in terms of enriched large Lawvere theories.

Observationally equivalent programs are programs which are indistinguishable in all contexts, as far as their termination property is concerned. In this paper, we present rules preserving observational equivalence, for the parallel evaluation of programs using call/cc. These rules allow the capture of continuations in any applicative context and they prevent from aborting the whole computation when a continuation is applied in the extent of the call/cc by which it was reied. As a consequence, these results prove that one can design a functional language with rst-class continuations which has transparent constructs for parallelism. 1 Introduction Some programming languages, like Scheme and Standard ML of New Jersey, provide a control operator call/cc which gives the programmer the possibility to reify the current continuation as a rst-class object. When such a reied continuation is applied to a value v, the current computation is aborted and the execution resumes at the point wher...