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P.L. Curien

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3 papers

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I&C Journal 1994 Journal Article

Decidability and Confluence of βη top≤ Reduction in F≤

P.L. Curien
G. Ghelli

We contribute to the syntactic study of F ≤, a variant of second-order λ-calculus F which appears as a paradigmatic kernel language for polymorphism and subtyping. The type system of F ≤ has a maximum type Top and bounded quantification. We endow this language with the β-rules (for terms and types), to which we add η-rules (for terms and types) and a rule which equates all terms of type Top. These rules are suggested by the axiomatization of cartesian closed categories. We exhibit a weakly normalizing and confluent reduction system for this theory βη top≤, and show that it is decidable. It is also confluent, but decidability does not follow from confluence, since reduction is not effective. Our proofs rely on the confluence and decidability of a corresponding system on F 1 (the extension of F with a terminal type).

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I&C Journal 1994 Journal Article

Fully Abstract Semantics for Observably Sequential Languages

R. Cartwright
P.L. Curien
M. Felleisen

One of the major challenges in denotational semantics is the construction of a fully abstract semantics for a higher-order sequential programming language. For the past fifteen years, research on this problem has focused on developing a semantics for PCF, an idealized functional programming language based on the typed λ-calculus. Unlike most practical languages, PCF has no facilities for observing and exploiting the evaluation order of arguments to procedures. Since we believe that these facilities play a crucial role in sequential computation, this paper focuses on a sequential extension of PCF, called SPCF, that includes two classes of control operators: a possibly empty set of error generators and a collection of catch and throw constructs. For each set of error generators, the paper presents a fully abstract semantics for SPCF. If the set of error generators is empty, the semantics interprets all procedures-including catch and throw-as Berry-Curien sequential algorithms. If the language contains error generators, procedures denote manifestly sequential functions. The manifestly sequential functions form a Scott domain that is isomorphic to a domain of decision trees, which is the natural extension of the Berry-Curien domain of sequential algorithms in the presence of errors.

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TCS Journal 1982 Journal Article

Sequential algorithms on concrete data structures

G. Berry
P.L. Curien

We provide a sequential denotational semantics for sequential programming languages, based on a new notion of sequential algorithm on the Kahn-Plotkin concrete data structures. Intuitively an algorithm may be seen either as a concrete object—a “program” in a simple output-driven language — or as an abstract object — the pair of a sequential function and of a computation strategy for it. The concrete and abstract presentations are equivalent, as shown by a representation theorem. The algorithms form a cartesian closed category with straightforward solutions to recursive domain equations. Hence they may replace functions in the denotational semantics of any sequential language. An applicative programming language based on sequential algorithms is presented in a companion paper.

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