Results 1  10
of
32
Secrets of the Glasgow Haskell Compiler inliner
 UNDER CONSIDERATION FOR PUBLICATION IN J. FUNCTIONAL PROGRAMMING
"... Higherorder languages, such as Haskell, encourage the programmer to build abstractions by composing functions. A good compiler must inline many of these calls to recover an eciently executable program. In principle, ..."
Abstract

Cited by 55 (6 self)
 Add to MetaCart
Higherorder languages, such as Haskell, encourage the programmer to build abstractions by composing functions. A good compiler must inline many of these calls to recover an eciently executable program. In principle,
A complete, coinductive syntactic theory of sequential control and state
 In POPL
, 2007
"... We present a new coinductive syntactic theory, eager normal form bisimilarity, for the untyped callbyvalue lambda calculus extended with continuations and mutable references. We demonstrate that the associated bisimulation proof principle is easy to use and that it is a powerful tool for proving ..."
Abstract

Cited by 23 (2 self)
 Add to MetaCart
(Show Context)
We present a new coinductive syntactic theory, eager normal form bisimilarity, for the untyped callbyvalue lambda calculus extended with continuations and mutable references. We demonstrate that the associated bisimulation proof principle is easy to use and that it is a powerful tool for proving equivalences between recursive imperative higherorder programs. The theory is modular in the sense that eager normal form bisimilarity for each of the calculi extended with continuations and/or mutable references is a fully abstract extension of eager normal form bisimilarity for its subcalculi. For each calculus, we prove that eager normal form bisimilarity is a congruence and is sound with respect to contextual equivalence. Furthermore, for the calculus with both continuations and mutable references, we show that eager normal form bisimilarity is complete: it coincides with contextual equivalence.
On the Insufficiency of Ontologies: Problems in Knowledge Sharing and Alternative Solutions
"... One of the benefits of formally represented knowledge lies in its potential to be shared. Ontologies have been proposed as the ultimate solution to problems in knowledge sharing. However even when an agreed correspondence between ontologies is reached that is not the end of the problems in knowledge ..."
Abstract

Cited by 21 (2 self)
 Add to MetaCart
One of the benefits of formally represented knowledge lies in its potential to be shared. Ontologies have been proposed as the ultimate solution to problems in knowledge sharing. However even when an agreed correspondence between ontologies is reached that is not the end of the problems in knowledge sharing. In this paper we explore a number of realistic knowledgesharing situations and their related problems for which ontologies fall short in providing a solution. For each situation we propose and analyse alternative solutions.
Eager normal form bisimulation
 In Proc. 20th Annual IEEE Symposium on Logic in Computer Science
, 2005
"... Abstract. Normal form bisimulation is a powerful theory of program equivalence, originally developed to characterize LévyLongo tree equivalence and Boehm tree equivalence. It has been adapted to a range of untyped, higherorder calculi, but types have presented a difficulty. In this paper, we prese ..."
Abstract

Cited by 20 (8 self)
 Add to MetaCart
Abstract. Normal form bisimulation is a powerful theory of program equivalence, originally developed to characterize LévyLongo tree equivalence and Boehm tree equivalence. It has been adapted to a range of untyped, higherorder calculi, but types have presented a difficulty. In this paper, we present an account of normal form bisimulation for types, including recursive types. We develop our theory for a continuationpassing style calculus, JumpWithArgument (JWA), where normal form bisimilarity takes a very simple form. We give a novel congruence proof, based on insights from game semantics. A notable feature is the seamless treatment of etaexpansion. We demonstrate the normal form bisimulation proof principle by using it to establish a syntactic minimal invariance result and the uniqueness of the fixed point operator at each type.
A lambda calculus for real analysis
, 2005
"... Abstract Stone Duality is a revolutionary theory that works directly with computable continuous functions, without using set theory, infinitary lattice theory or a prior theory of discrete computation. Every expression in the calculus denotes both a continuous function and a program, but the reasoni ..."
Abstract

Cited by 14 (0 self)
 Add to MetaCart
(Show Context)
Abstract Stone Duality is a revolutionary theory that works directly with computable continuous functions, without using set theory, infinitary lattice theory or a prior theory of discrete computation. Every expression in the calculus denotes both a continuous function and a program, but the reasoning looks remarkably like a sanitised form of that in classical topology. This paper is an introduction to ASD for the general mathematician, and applies it to elementary real analysis. It culminates in the Intermediate Value Theorem, i.e. the solution of equations fx = 0 for continuous f: R → R. As is well known from both numerical and constructive considerations, the equation cannot be solved if f “hovers ” near 0, whilst tangential solutions will never be found. In ASD, both of these failures and the general method of finding solutions of the equation when they exist are explained by the new concept of “overtness”. The zeroes are captured, not as a set, but by highertype operators � and ♦ that remain (Scott) continuous across singularities of a parametric equation. Expressing topology in terms of continuous functions rather than sets of points leads to
Computably based locally compact spaces
, 2003
"... ASD (Abstract Stone Duality) is a reaxiomatisation of general topology in which the topology on a space is treated, not as an infinitary lattice, but as an exponential object of the same category as the original space, with an associated lambdacalculus. In this paper, this is shown to be equivalen ..."
Abstract

Cited by 10 (6 self)
 Add to MetaCart
(Show Context)
ASD (Abstract Stone Duality) is a reaxiomatisation of general topology in which the topology on a space is treated, not as an infinitary lattice, but as an exponential object of the same category as the original space, with an associated lambdacalculus. In this paper, this is shown to be equivalent to a notion of computable basis for locally compact sober spaces or locales, involving a family of open subspaces and accompanying family of compact ones. This generalises Smyth’s effectively given domains and Jung’s Strong proximity lattices. Part of the data for a basis is the inclusion relation of compact subspaces within open ones, which is formulated in locale theory as the waybelow relation on a continuous lattice. The finitary properties of this relation are characterised here, including the Wilker condition for the cover of a compact space by two open ones. The real line is used as a running example, being closely related to Scott’s domain of intervals. ASD does not use the category of sets, but the full subcategory of overt discrete objects plays this role; it is an arithmetic universe (pretopos with lists). In particular, we use this subcategory to translate computable bases for classical spaces into objects in the ASD calculus.
Extensional rewriting with sums
 In TLCA
, 2007
"... Abstract. Inspired by recent work on normalisation by evaluation for sums, we propose a normalising and confluent extensional rewriting theory for the simplytyped λcalculus extended with sum types. As a corollary of confluence we obtain decidability for the extensional equational theory of simply ..."
Abstract

Cited by 10 (5 self)
 Add to MetaCart
Abstract. Inspired by recent work on normalisation by evaluation for sums, we propose a normalising and confluent extensional rewriting theory for the simplytyped λcalculus extended with sum types. As a corollary of confluence we obtain decidability for the extensional equational theory of simplytyped λcalculus extended with sum types. Unlike previous decidability results, which rely on advanced rewriting techniques or advanced category theory, we only use standard techniques. 1
A formalism for higherorder composition languages that satisfies the churchrosser property
, 2006
"... personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires pri ..."
Abstract

Cited by 8 (6 self)
 Add to MetaCart
(Show Context)
personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission.