A lambda-calculus schema is an expression of the lambda calculus augmented by uninterpreted constant and operator symbols. It is an abstraction of programming languages such as LISP which permit functions to be passed to and returned from other functions. When given an interpretation for its constant and operator symbols, certain schemata, called lambda abstractions, naturally define partial functions over the domain of interpretation. Two implementation strategies are considered: the retention strategy in which all variable bindings are retained until no longer needed (implying the use of some sort of garbage-collected store) and the deletion strategy, modeled after the usual stack implementation of ALGOL 60, in which variable bindings are destroyed when control leaves the procedure (or block) in which they were created. Not all lambda abstractions evaluate correctly under the deletion strategy. Nevertheless, both strategies are equally powerful in the sense that any lambda abstraction can be mechanically translated into another that evaluates correctly under the deletion strategy and defines the same partial function over the domain of interpretation as the original. Proof is by translation into continuation-passing style.

ion of Typed Contexts Olivier Danvy & Andrzej Filinski DIKU -- Computer Science Department, University of Copenhagen Universitetsparken 1, 2100 Copenhagen , Denmark uucp: danvy@diku.dk & andrzej@diku.dk Abstract This report investigates abstracting control with functions. This is achieved by defining continuations as functions abstracting lexically a delimited context [C[ ]] rather than dynamically an unlimited one C[ ], as it is usually the case. Because their co-domain is distinguished from the final domain of Answers, such continuations can be composed, and this contrasts with the simple exceptions of ML and Lisp and the unlimited first-class continuations of Scheme. Making these functional control abstractions first-class o#ers a new area in programming which this paper explores. The key points obtained here are: a denotational semantics for a simple, call-by-value, strongly typed expression language with higher-order functions and first-class continuations; its congruence with a ...

We propose a theoretical framework for adding assignments and dynamic data to functional languages without violating their semantic properties. This differs from semi-functional languages like Scheme and ML in that values of expressions remain static and side-effect-free. A new form of abstraction called observer is designed to encapsulate state-oriented computation from the remaining purely applicative computation. The type system ensures that observers are combined linearly, allowing an implementation in terms of a global store. The utility of this extension is in manipulating shared dynamic data embedded in data structures. Evaluation of well-typed programs is Church-Rosser. Thus, programs produce the same results whether an eager or lazy evaluation order is used (assuming termination). A simple, sound logic permits reasoning about well-typed programs. The benefits of this work include greater expressive power and efficiency (compared to applicative languages), while retaining simplicity of reasoning.

The construction of interactive server-side Web applications differs substantially from the construction of traditional interactive programs. In contrast, existing Web programming paradigms force programmers to save and restore control state between user interactions. We present an automated transformation that converts traditional interactive programs into standard CGI programs. This enables reuse of existing software development methodologies. Furthermore, an adaptation of existing programming environments supports the development of Web programs. 1 Designing Web Programs The need for generating Web information on demand is obvious. One page may need the current time and date; another page may include results from a database query; a third page may display the current status of the server. Since such programs compute small amounts of information and produce not much more than a single Web page, people call them scripts. Following a long-standing tradition in computing, Web scripti...

Traditional denotational semantics assigns radically different meanings to one and the same phrase depending on the rest of the programming language. If the language is purely functional, the denotation of a numeral is a function from environments to integers. But, in a functional language with imperative control operators, a numeral denotes a function from environments and continuations to integers. This paper introduces a new format for denotational language specifications, extended direct semantics, that accommodates orthogonal extensions of a language without changing the denotations of existing phrases. An extended direct semantics always maps a numeral to the same denotation: the injection of the corresponding number into the domain of values. In general, the denotation of a phrase in a functional language is always a projection of the denotation of the same phrase in the semantics of an extended language---no matter what the extension is. Based on extended direct semantics, i...

Programmers confront a minefield when they design interactive Web programs. Web interactions take place via Web browsers. With browsers, consumers can whimsically navigate among the various stages of a dialog and can thus confuse the most sophisticated corporate Web sites. In turn, Web services can fault in frustrating and inexplicable ways. The quickening transition from Web scripts to Web services lends these problems immediacy.

A fully abstract model of a programming language assigns the same meaning to two terms if and only if they have the same operational behavior. Such models are well-known for functional languages but little is known about extended functional languages with sophisticated control structures. We show that a direct model with error values and the conventional continuation model are adequate for functional languages augmented with first- and higher-order control facilities, respectively. Furthermore, both models become fully abstract on adding a control delimiter and a parallel conditional to the programming languages.

This thesis presents a formalism for reasoning about continuations in a categorical setting. It points out how values and continuations ca n be seen as categorically dual concepts, and that this symmetry extends to not only data types, but also control structures, evaluation strategies and higher-order constructs. The central idea is a view of continuations as a declarative concept, rather than an imperative one, and the implicat ions of this make up the spine of the presentation. A symmetrical extension of the typed *-calculus is introduced, where values and continuations are treated as opposites, permitting a mirror-image syntax for dual categorical concepts like products and coproducts. An implementable semantic description and a static type system for this calculus are given. A purely categorical description of the language is also obtained, through a correspondence with a system of combinatory logic, similar to a cartesian closed category, but with a completely symmetrical set of axioms. Finally, a number of possible practical applications and directions for further research are suggested.

Abstract. Landin’s SECD machine was the first abstract machine for applicative expressions, i.e., functional programs. Landin’s J operator was the first control operator for functional languages, and was specified by an extension of the SECD machine. We present a family of evaluation functions corresponding to this extension of the SECD machine, using a series of elementary transformations (transformation into continuation-passing style (CPS) and defunctionalization, chiefly) and their left inverses (transformation into direct style and refunctionalization). To this end, we modernize the SECD machine into a bisimilar one that operates in lockstep with the original one but that (1) does not use a data stack and (2) uses the caller-save rather than the callee-save convention for environments. We also identify that the dump component of the SECD machine is managed in a callee-save way. The caller-save counterpart of the modernized SECD machine precisely corresponds to Thielecke’s doublebarrelled continuations and to Felleisen’s encoding of J in terms of call/cc. We then variously characterize the J operator in terms of CPS and in terms of delimited-control operators in the CPS hierarchy. As a byproduct, we also present several reduction semantics for applicative expressions

Plotkin, in his seminal article Call-by-name, call-by-value and the λ-calculus, formalized evaluation strategies and simulations using operational semantics and continuations. In particular, he showed how call-by-name evaluation could be simulated under call-by-value evaluation and vice versa. Since Algol 60, however, call-by-name is both implemented and simulated with thunks rather than with continuations. We recast