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Relating Operational and Denotational Semantics for Input/Output Effects
, 1999
"... We study the longstanding problem of semantics for input/output (I/O) expressed using sideeffects. Our vehicle is a small higherorder imperative language, with operations for interactive character I/O and based on ML syntax. Unlike previous theories, we present both operational and denotational se ..."
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We study the longstanding problem of semantics for input/output (I/O) expressed using sideeffects. Our vehicle is a small higherorder imperative language, with operations for interactive character I/O and based on ML syntax. Unlike previous theories, we present both operational and denotational semantics for I/O effects. We use a novel labelled transition system that uniformly expresses both applicative and imperative computation. We make a standard definition of bisimilarity. We prove bisimilarity is a congruence using Howe's method. Next, we define a metalanguage M in which we may give a denotational semantics to O. M generalises Crole and Pitts' FIXlogic by adding in a parameterised recursive datatype, which is used to model I/O. M comes equipped both with an operational semantics and a domaintheoretic semantics in the category CPPO of cppos (bottompointed posets with joins of !chains) and Scott continuous functions. We use the CPPO semantics to prove that M is computationally...
Enrichment and Representation Theorems for Categories of Domains and Continuous Functions
, 1996
"... This paper studies the notions of approximation and passage to the limit in an axiomatic setting. Our axiomatisation is subject to the following criteria: the axioms should be natural (so that they are available in as many contexts as possible) and nonordertheoretic (so that Research supported b ..."
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This paper studies the notions of approximation and passage to the limit in an axiomatic setting. Our axiomatisation is subject to the following criteria: the axioms should be natural (so that they are available in as many contexts as possible) and nonordertheoretic (so that Research supported by SERC grant RR30735 and EC project Programming Language Semantics and Program Logics grant SC1000 795 they explain the ordertheoretic structure). Our aim is 1. to provide a justification of Scott's original consideration of ordered structures, and 2. to deepen our understanding of the notion of passage to the limit
Traced Premonoidal Categories
, 1999
"... Motivated by some examples from functional programming, we propose a generalization of the notion of trace to symmetric premonoidal categories and of Conway operators to Freyd categories. We show that in a Freyd category, these notions are equivalent, generalizing a wellknown theorem relating trace ..."
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Motivated by some examples from functional programming, we propose a generalization of the notion of trace to symmetric premonoidal categories and of Conway operators to Freyd categories. We show that in a Freyd category, these notions are equivalent, generalizing a wellknown theorem relating traces and Conway operators in cartesian categories.
Hybrid PartialTotal Type Theory
, 1995
"... In this paper a hybrid type theory HTT is defined which combines the programming language notion of partial type with the logical notion of total type into a single theory. A new partial type constructor A is added to the type theory: objects in A may diverge, but if they converge, they must be memb ..."
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In this paper a hybrid type theory HTT is defined which combines the programming language notion of partial type with the logical notion of total type into a single theory. A new partial type constructor A is added to the type theory: objects in A may diverge, but if they converge, they must be members of A. A fixed point typing rule is given to allow for typing of fixed points. The underlying theory is based on ideas from Feferman's Class Theory and Martin Lof's Intuitionistic Type Theory. The extraction paradigm of constructive type theory is extended to allow direct extraction of arbitrary fixed points. Important features of general programming logics such as LCF are preserved, including the typing of all partial functions, a partial ordering ! ¸ on computations, and a fixed point induction principle. The resulting theory is thus intended as a generalpurpose programming logic. Rules are presented and soundness of the theory established. Keywords: Constructive Type Theory, Logics...
An Enrichment Theorem for an Axiomatisation of Categories of Domains and Continuous Functions
, 1996
"... This paper studies the notions of approximation and passage to the limit in an axiomatic setting. Our axiomatisation is subject to the following criteria: the axioms should be natural (so that they are available in as many contexts as possible) and nonordertheoretic (so that they explain the order ..."
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Cited by 4 (4 self)
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This paper studies the notions of approximation and passage to the limit in an axiomatic setting. Our axiomatisation is subject to the following criteria: the axioms should be natural (so that they are available in as many contexts as possible) and nonordertheoretic (so that they explain the ordertheoretic structure). Our aim is y
A Computational Formalization for Partial Evaluation (Extended Version)
, 1996
"... We formalize a partial evaluator for Eugenio Moggi's computational metalanguage. This formalization gives an evaluationorder independent view of bindingtime analysis and program specialization, including a proper treatment of call unfolding, and enables us to express the essence of "controlba ..."
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We formalize a partial evaluator for Eugenio Moggi's computational metalanguage. This formalization gives an evaluationorder independent view of bindingtime analysis and program specialization, including a proper treatment of call unfolding, and enables us to express the essence of "controlbased bindingtime improvements" for let expressions. Specifically,
Inductive Reasoning About Effectful Data Types
 In Proceedings of the ACM SIGPLAN International Conference on Functional Programming
, 2007
"... We present a pair of reasoning principles, definition and proof by rigid induction, which can be seen as proper generalizations of lazydatatype induction to monadic effects other than partiality. We further show how these principles can be integrated into logicalrelations arguments, and obtain as ..."
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We present a pair of reasoning principles, definition and proof by rigid induction, which can be seen as proper generalizations of lazydatatype induction to monadic effects other than partiality. We further show how these principles can be integrated into logicalrelations arguments, and obtain as a particular instance a general and principled proof that the successstream and failurecontinuation models of backtracking are equivalent. As another application, we present a monadic model of general search trees, not necessarily traversed depthfirst. The results are applicable to both lazy and eager languages, and we emphasize this by presenting most examples in both Haskell and SML.
On Fixpoint Objects and Gluing Constructions
, 1997
"... This article 1 has two parts: In the first part, we present some general results about fixpoint objects. The minimal categorical structure required to model soundly the equational type theory which combines higher order recursion and computation types (introduced by [4]) is shown to be precisely a ..."
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This article 1 has two parts: In the first part, we present some general results about fixpoint objects. The minimal categorical structure required to model soundly the equational type theory which combines higher order recursion and computation types (introduced by [4]) is shown to be precisely a letcategory possessing a fixpoint object. Functional completeness for such categories is developed. We also prove that categories with fixpoint operators do not necessarily have a fixpoint object. In the second part, we extend Freyd's gluing construction for cartesian closed categories to cartesian closed letcategories, and observe that this extension does not obviously apply to categories possessing fixpoint objects. We solve this problem by giving a new gluing construction for a limited class of categories with fixpoint objects; this is the main result of the paper. We use this categorytheoretic construction to prove a typetheoretic conservative extension result. A version of this pap...
Categorical Logic
, 2001
"... This document provides an introduction to the interaction between category theory and mathematical logic which is slanted towards computer scientists. ..."
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This document provides an introduction to the interaction between category theory and mathematical logic which is slanted towards computer scientists.
A semantical approach to equilibria and rationality
, 905
"... ”An equilibrium does not appear because agents are rational, but rather agents appear to be rational because an equilibrium has been reached.[...] The task for game theory is to formulate a notion of rationality.” Larry Samuelson [20, p. 3] Abstract. Game theoretic equilibria are mathematical expres ..."
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”An equilibrium does not appear because agents are rational, but rather agents appear to be rational because an equilibrium has been reached.[...] The task for game theory is to formulate a notion of rationality.” Larry Samuelson [20, p. 3] Abstract. Game theoretic equilibria are mathematical expressions of rationality. Rational agents are used to model not only humans and their software representatives, but also organisms, populations, species and genes, interacting with each other and with the environment. Rational behaviors are achieved not only through conscious reasoning, but also through spontaneous stabilization at equilibrium points. Formal theories of rationality are usually guided by informal intuitions, which are acquired by observing some concrete economic, biological, or network processes. Treating such processes as instances of computation, we reconstruct and refine some basic notions of equilibrium and rationality from the some basic structures of computation. It is, of course, well known that equilibria arise as fixed points; the point is that semantics of computation of fixed points seems to be providing novel methods, algebraic and coalgebraic, for reasoning about them. 1