J. Longley. Realizability Toposes and Language Semantics. PhD thesis, University of Edinburgh, 1995. Available as ECS-LFCS-95-332. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Notions of computability at higher types II - Longley (2001) Self-citation (Longley) (Correct)
....We will not explicitly define the call by value and lazy variants here, since the only purpose in doing so would be to point out that they are equivalent for our present purposes. In the case of PCF, the relationship between the three variants has been studied in [Sie90, Rie93] and more fully in [Lon95, Chapter 6], where a syntactic equivalence result comparable with Theorem 1.8 is proved in detail. The view we are advocating here is that, for any notion of computable functional, the corresponding standard category is the real underlying object of interest, and di#erent definitions of type structure ....
.... algebra A, the category PER(A) is defined as follows: objects are PERs on A, and morphisms E # E # are functions f : A E # A E # that are tracked by some element r # A (that is, for all x with xEx we have f ( x] E ) rx] E # ) The category PER(A) enjoys many good properties (see e.g. [Lon95, Chapter 1]) In particular it is cartesian closed: the exponential E #E is defined by r(E #E )r # i# r, r # both track the same morphism f : E # E # . Clearly, given any PER # on A, the type structure over # in PER(A) is precisely the extensional collapse of A (viewed as a PTS) w.r.t. #. It follows ....
[Article contains additional citation context not shown here]
J.R. Longley. Realizability Toposes and Language Semantics. PhD thesis, University of Edinburgh, 1995. Available as ECS-LFCS-95-332.
Notions of computability at higher types III - John Longley April (2001) Self-citation (Longley) (Correct)
.... A typed PCA over 1 is just a PCA in the usual sense (with a mild relaxation of the usual condition for s) Note that in this special case it does not matter whether we include the product types in the definition or not, since suitable combinators pair, fst, snd are definable from k, s (see e.g. [Lon95, Chapter 1]) Example 1.5 A large class of syntactic typed PCAs may be obtained from typed programming languages as follows. Let L be a simply typed # calculus (including product types) over a signature # consisting of a set of ground types # (including the special type #) and a set of typed constants ....
....A, it does and we can model disjunction. In the case of term models for typed programming languages, the interpretation of firstorder logic in these categories is exactly the typed realizability interpretation discussed in [Lon99a] Expand this ] 1. 1 Applicative morphisms between typed PCAs In [Lon95, Chapter 2] we introduced and studied the notion of applicative morphism between PCAs, and the corresponding functors between realizability categories. We now show that all this theory lifts in a straightforward way to the typed setting. Definition 1.9 Let A be a typed PCA over T , and B a typed PCA over U ....
[Article contains additional citation context not shown here]
J.R. Longley. Realizability Toposes and Language Semantics. PhD thesis, University of Edinburgh, 1995. Available as ECS-LFCS-95-332.
Notions of Computability for General Datatypes - Fourman, Plotkin, Longley (2001) Self-citation (Longley Language) (Correct)
....end of [Lon98a] Shortly thereafter, in May 1999, we discovered a much more general framework which embraces both extensional and non extensional notions of computability. This framework is based around a typed generalization of standard realizability and of material in Longley s Ph.D. thesis [Lon95]. This new framework remains in the spirit of our inquiry into notions of computability (what can be computed) as distinguished from particular models of computation (how it is computed) but it massively broadens the scope of our investigation from notions of computable function to much more ....
J.R. Longley. Realizability Toposes and Language Semantics. PhD thesis, University of Edinburgh, 1995. Available as ECS-LFCS-95-332.
A Proof System for Correct Program Development - Fourman, Fleuriot, Longley (2000) Self-citation (Longley Language) (Correct)
....long term motivation has been that a deeper mathematical understanding should shed light on the kinds of logic required for reasoning about programs. The problem of finding clean and expressive program logics has been a major motivation behind our theoretical work to date (see e.g. PF92, FT95, Lon95, LP97] Recently we realized that in terms of the underlying theory, we now have all the pieces we need in order to achieve this goal for a very substantial language, including the full power of a higher order functional language, plus (we believe) most everyday uses of exceptions, references ....
J.R. Longley. Realizability Toposes and Language Semantics. PhD thesis, University of Edinburgh, 1995. Available as ECS-LFCS-95-332.
Notions of Computability for General Datatypes - Case.. - Fourman, Plotkin.. Self-citation (Longley) (Correct)
....research, however, is that for us it is the notions of computability, rather than the models of computation, which will be the primary objects of study. Thus, for example, we will be interested in knowing which intensional settings give rise to the same extensional notion of computability (see [Lon95, Chapter 7] for some results of this nature) we will also be interested in properties of the extensional notions that are not dependent on any particular intensional model (see e.g. Loa96] Along a different axis, the proposed research has affinities with work in the algebraic specification tradition by ....
....emphasis on the ideas and methods of denotational semantics; indeed, we believe that our programme will furnish a broader, more conceptual framework within which much of their work may be placed. Our interest in general notions of computability has arisen from our study of realizability models [Lon95, LS97]. These have already given us a good handle on computability at higher types over the natural numbers, and we expect that the ideas of realizability will continue to play a major role in our research. B. Programme and methodology The proposed research will investigate classes of computable ....
[Article contains additional citation context not shown here]
J.R. Longley. Realizability Toposes and Language Semantics. PhD thesis, University of Edinburgh, 1995. Available as ECS-LFCS-95-332.
Notions of Computability for General Datatypes - Fourman, Plotkin, Longley Self-citation (Longley Edinburgh) (Correct)
....papers with each of them [FFL97, LP97] His main area of research has been the semantics and logic of programming languages. He has focused in particular on realizability models considered as embodiments of abstract notions of computability, and as settings for semantics and program logics [Lon95, LS97, LP97]. His Ph.D. thesis [Lon95] written under Fourman s supervision) contained major new contributions in these areas, and was nominated for the 1996 BCS Distinguished Dissertation Award scheme. In particular, his work has highlighted the existence of distinct notions of computability corresponding to ....
....LP97] His main area of research has been the semantics and logic of programming languages. He has focused in particular on realizability models considered as embodiments of abstract notions of computability, and as settings for semantics and program logics [Lon95, LS97, LP97] His Ph.D. thesis [Lon95] (written under Fourman s supervision) contained major new contributions in these areas, and was nominated for the 1996 BCS Distinguished Dissertation Award scheme. In particular, his work has highlighted the existence of distinct notions of computability corresponding to different programming ....
J.R. Longley. Realizability Toposes and Language Semantics. PhD thesis, University of Edinburgh, 1995. Available as ECS-LFCS-95-332.
Realizability Models for Sequential Computation - Longley (1998) (2 citations) Self-citation (Longley) (Correct)
....Thomas Streicher for suggesting that I give the talk on which this note is based. 1 Introduction to realizability models I will start with a crash course in realizability models for programming languages and some of the motivations for studying them. Fuller details may be found in my thesis [19] or that of Wesley Phoa [25] The vague idea behind realizability semantics for programming languages is as follows. We start by choosing some model of data and computations on it which we think of as primitive. If we like, we can think of this primitive layer as a model for low level or machine ....
.... the above examples, and many others, are discussed in detail in the book by Barendregt [4] Experts will recognize that our notion of a CA is somewhat less general than the notion more often considered, namely that of a partial combinatory algebra equipped with an arbitrary divergence (see e.g. [19, 20]) However, the definition given above is slightly simpler to present, and will suffice for all the examples I will consider in this paper. Any combinatory algebra can be seen as a model of untyped computation, in which application is taken to be the primitive operation. One can think of a ....
[Article contains additional citation context not shown here]
J.R. Longley. Realizability Toposes and Language Semantics. PhD thesis, University of Edinburgh, 1995. Available as ECS-LFCS-95-332.
Comparing Hierarchies of Types in Models of Linear Logic - Mellies (2003) (1 citation) (Correct)
No context found.
J. Longley. Realizability Toposes and Language Semantics. PhD thesis, University of Edinburgh, 1995. Available as ECS-LFCS-95-332.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC