Results 1  10
of
14
Equations and rewrite rules: a survey
 In Formal Language Theory: Perspectives and Open Problems
, 1980
"... bY ..."
Game Theoretic Analysis Of CallByValue Computation
, 1997
"... . We present a general semantic universe of callbyvalue computation based on elements of game semantics, and validate its appropriateness as a semantic universe by the full abstraction result for callbyvalue PCF, a generic typed programming language with callbyvalue evaluation. The key idea is ..."
Abstract

Cited by 59 (20 self)
 Add to MetaCart
. We present a general semantic universe of callbyvalue computation based on elements of game semantics, and validate its appropriateness as a semantic universe by the full abstraction result for callbyvalue PCF, a generic typed programming language with callbyvalue evaluation. The key idea is to consider the distinction between callbyname and callbyvalue as that of the structure of information flow, which determines the basic form of games. In this way the callbyname computation and callbyvalue computation arise as two independent instances of sequential functional computation with distinct algebraic structures. We elucidate the type structures of the universe following the standard categorical framework developed in the context of domain theory. Mutual relationship between the presented category of games and the corresponding callbyname universe is also clarified. 1. Introduction The callbyvalue is a mode of calling procedures widely used in imperative and function...
Games and full abstraction for nondeterministic languages
, 1999
"... Abstract Nondeterminism is a pervasive phenomenon in computation. Often it arises as an emergent property of a complex system, typically as the result of contention for access to shared resources. In such circumstances, we cannot always know, in advance, exactly what will happen. In other circumstan ..."
Abstract

Cited by 29 (3 self)
 Add to MetaCart
Abstract Nondeterminism is a pervasive phenomenon in computation. Often it arises as an emergent property of a complex system, typically as the result of contention for access to shared resources. In such circumstances, we cannot always know, in advance, exactly what will happen. In other circumstances, nondeterminism is explicitly introduced as a means of abstracting away from implementation details such as precise command scheduling and control flow. However, the kind of behaviours exhibited by nondeterministic computations can be extremely subtle in comparison to those of their deterministic counterparts and reasoning about such programs is notoriously tricky as a result. It is therefore important to develop semantic tools to improve our understanding of, and aid our reasoning about, such nondeterministic programs. In this thesis, we extend the framework of game semantics to encompass nondeterministic computation. Game semantics is a relatively recent development in denotational semantics; its main novelty is that it views a computation not as a static entity, but rather as a dynamic process of interaction. This perspective makes the theory wellsuited to modelling many aspects of computational processes: the original use of game semantics in modelling the simple functional language PCF has subsequently been extended to handle more complex control structures such as references and continuations.
Continuous Functions and Parallel Algorithms on Concrete Data Structures
 IN MFPS'91, L.N.C.S
, 1991
"... We report progress in two closely related lines of research: the semantic study of sequentiality and parallelism, and the development of a theory of intensional semantics. We generalize Kahn and Plotkin's concrete data structures to obtain a cartesian closed category of generalized concrete dat ..."
Abstract

Cited by 12 (2 self)
 Add to MetaCart
We report progress in two closely related lines of research: the semantic study of sequentiality and parallelism, and the development of a theory of intensional semantics. We generalize Kahn and Plotkin's concrete data structures to obtain a cartesian closed category of generalized concrete data structures and continuous functions. The generalized framework continues to support a definition of sequential functions. Using this ccc as an extensional framework, we define an intensional framework  a ccc of generalized concrete data structures and parallel algorithms. This construction is an instance of a more general and more widely applicable categorytheoretic approach to intensional semantics, encapsulating a notion of intensional behavior as a computational comonad, and employing the coKleisli category as an intensional framework. We discuss the relationship between parallel algorithms and continuous functions, and supply some operational intuition for the parallel algorithms. We s...
Compiling Lazy Pattern Matching
 In Proc. of the 1992 conference on Lisp and Functional Programming
, 1992
"... this paper we take a more direct approach: we compile pattern matching on overlapping patterns. We first recall the semantics of lazy pattern matching, as given by A. Laville [5]. Then, we explain our compilation technique as a source to source transformation. Given a set of patterns, several compil ..."
Abstract

Cited by 11 (4 self)
 Add to MetaCart
this paper we take a more direct approach: we compile pattern matching on overlapping patterns. We first recall the semantics of lazy pattern matching, as given by A. Laville [5]. Then, we explain our compilation technique as a source to source transformation. Given a set of patterns, several compilations are possible, we prove that they all satisfy a partial correctness
Two Techniques for Compiling Lazy Pattern Matching
, 1994
"... In ML style pattern matching, pattern size is not constrained and ambiguous patterns are allowed. This generality leads to a clear and concise programming style but is challenging in the context of lazy evaluation. A first challenge concerns language designers: in lazy ML, the evaluation order of ex ..."
Abstract

Cited by 10 (1 self)
 Add to MetaCart
In ML style pattern matching, pattern size is not constrained and ambiguous patterns are allowed. This generality leads to a clear and concise programming style but is challenging in the context of lazy evaluation. A first challenge concerns language designers: in lazy ML, the evaluation order of expressions follows actual data dependencies. That is, only the computations that are needed to produce the final result are performed. Once given a proper (that is, nonambiguous) semantics, pattern matching should be compiled in a similar spirit: any value matching a given pattern should be recognized by performing only the minimal number of elementary tests needed to do so. This challenge was first met by A. Laville. A second challenge concerns compiler designers. As it stands, Laville's compilation algorithm cannot be incorporated in an actual lazy ML compiler for efficiency and completeness reasons. As a matter of fact, Laville's original algorithm did not fully treat the case of intege...
A Cartesian Closed Category of Parallel Algorithms between Scott Domains
, 1991
"... We present a categorytheoretic framework for providing intensional semantics of programming languages and establishing connections between semantics given at different levels of intensional detail. We use a comonad to model an abstract notion of computation, and we obtain an intensional category fr ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
We present a categorytheoretic framework for providing intensional semantics of programming languages and establishing connections between semantics given at different levels of intensional detail. We use a comonad to model an abstract notion of computation, and we obtain an intensional category from an extensional category by the coKleisli construction; thus, while an extensional morphism can be viewed as a function from values to values, an intensional morphism is akin to a function from computations to values. We state a simple categorytheoretic result about cartesian closure. We then explore the particular example obtained by taking the extensional category to be Cont, the category of Scott domains with continuous functions as morphisms, with a computation represented as a nondecreasing sequence of values. We refer to morphisms in the resulting intensional category as algorithms. We show that the category Alg of Scott domains with algorithms as morphisms is cartesian closed. We...
Nonexpressibility of Fairness and Signaling
 in &quot;Proceedings, IEEE Foundations of Computer Science&quot;, Panangaden
, 1990
"... In this paper we establish new expressiveness results for indeterminate dataflow primitives. We consider split primitives with three differing fairness assumptions and show that they are strictly inequivalent in expressive power. We also show that the ability to announce internal choices enhances th ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
In this paper we establish new expressiveness results for indeterminate dataflow primitives. We consider split primitives with three differing fairness assumptions and show that they are strictly inequivalent in expressive power. We also show that the ability to announce internal choices enhances the expressive power of two of the primitives. These results are proved using a very crude notion of observation and thus apply in any reasonable theory of process equivalence. 1 Introduction Fairness is regarded as an important property of real systems and there is considerable interest in semantic theories and proof systems for reasoning about fairness [12]. In the present paper we examine the relative expressive power of a variety of fairness primitives and prove new inexpressibility results in the context of asynchronous systems. We prove that three different "split" primitives have different expressive power. We also consider the effect of adding signaling to each primitive. By "signalin...
Stable and Sequential Functions on Scott Domains
, 1992
"... The search for a general semantic characterization of sequential functions is motivated by the full abstraction problem for sequential programming languages such as PCF. We present here some new developments towards such a theory of sequentiality. We give a general definition of sequential functions ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
The search for a general semantic characterization of sequential functions is motivated by the full abstraction problem for sequential programming languages such as PCF. We present here some new developments towards such a theory of sequentiality. We give a general definition of sequential functions on Scott domains, characterized by means of a generalized form of topology, based on sequential open sets. Our notion of sequential function coincides with the KahnPlotkin notion of sequential function when restricted to distributive concrete domains, and considerably expands the class of domains for which sequential functions may be defined. We show that the sequential functions between two dIdomains, ordered stably, form a dIdomain. The analogous property fails for KahnPlotkin sequential functions. Our category of dIdomains and sequential functions is not cartesian closed, because application is not sequential. We attribute this to certain operational assumptions underlying our notio...
A Theory of Types for πCalculus
, 1998
"... We introduce a theory of behavioural types as a semantic foundation of typed πcalculi. The basic idea is that a type is a set of behaviours, represented by name passing synchronisation trees, which conform to a certain behavioural constraint. Operations on typed processes are derived from typed var ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
We introduce a theory of behavioural types as a semantic foundation of typed πcalculi. The basic idea is that a type is a set of behaviours, represented by name passing synchronisation trees, which conform to a certain behavioural constraint. Operations on typed processes are derived from typed variants of wellknown processtheoretic operations for mobile processes, and each model of typed ßcalculi in a typed universe induces a compositional theory of typed bisimilarities. The construction is simple and intuitive, yet offers a rich class of typed universes of name passing interactive behaviours, which contain, among others, models of known typed πcalculi and universes of game semantics. After introducing the basic theory, which includes the general notion of behavioural subtyping and a theory of typed bisimulations, we show how the basic sorting by Milner and the IOsubsorting by Pierce and Sangiorgi can be soundly modelled in the corresponding typed universes, giving a new insig...