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Relational parametricity for control considered as a computational effect
 Electr. Notes Theor. Comput. Sci
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Replace this file with prentcsmacro.sty for your meeting, or with entcsmacro.sty for your meeting. Both can be
Relational Limits in General Polymorphism
, 1993
"... Parametric models of polymorphic lambda calculus have the structure of enriched categories with cotensors and ends in some generalized sense, and thus have many categorical data types induced by them. The !order minimum model is a parametric model. ..."
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Parametric models of polymorphic lambda calculus have the structure of enriched categories with cotensors and ends in some generalized sense, and thus have many categorical data types induced by them. The !order minimum model is a parametric model.
Two Probabilistic Powerdomains in Topological Domain Theory
"... We present two probabilistic powerdomain constructions in topological domain theory. The first is given by a free ”convex space” construction, fitting into the theory of modelling computational effects via free algebras for equational theories, as proposed by Plotkin and Power. The second is given b ..."
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We present two probabilistic powerdomain constructions in topological domain theory. The first is given by a free ”convex space” construction, fitting into the theory of modelling computational effects via free algebras for equational theories, as proposed by Plotkin and Power. The second is given by an observationally induced approach, following Schröder and Simpson. We show the two constructions coincide when restricted to ωcontinuous dcppos, in which case they yield the space of (continuous) probability valuations equipped with the Scott topology. Thus either construction generalises the classical domaintheoretic probabilistic powerdomain. On more general spaces, the constructions differ, and the second seems preferable. Indeed, for countablybased spaces, we characterise the observationally induced powerdomain as the space of probability valuations with weak topology. However, we show that such a characterisation does not extend to non countablybased spaces.
Categorical Properties of Logical Frameworks
, 1993
"... In this paper we give a new presentation of ELF which is wellsuited for semantic analysis. We introduce the notions of internal codability, internal definability, internal typed calculi and frame languages. These notions are central to our perspective of logical frameworks. We will argue that a ..."
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In this paper we give a new presentation of ELF which is wellsuited for semantic analysis. We introduce the notions of internal codability, internal definability, internal typed calculi and frame languages. These notions are central to our perspective of logical frameworks. We will argue that a logical framework is a typed calculus which formalizes the relationship between internal typed languages and frame languages. In the second half of the paper, we demonstrate the advantage of our logical framework by showing some categorical properties of it and of encodings in it. By doing so we hope to indicate a sensible model theory of encodings. Copyright c fl1993. All rights reserved. Reproduction of all or part of this work is permitted for educational or research purposes on condition that (1) this copyright notice is included, (2) proper attribution to the author or authors is made and (3) no commercial gain is involved. Technical Reports issued by the Department of Computer Sc...
Parametricity as Isomorphism
 Theoretical Computer Science
, 1993
"... . We investigate a simple form of parametricity, based on adding "abstract" copies of preexisting types. Connections are made with the ReynoldsMa theory of parametricity by logical relations, with the theory of parametricity via dinaturality, and with the categorical notion of equivalenc ..."
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. We investigate a simple form of parametricity, based on adding "abstract" copies of preexisting types. Connections are made with the ReynoldsMa theory of parametricity by logical relations, with the theory of parametricity via dinaturality, and with the categorical notion of equivalence. Introduction In his fundamental paper on the notion of parametricity in connection with type theories [Rey83], John Reynolds links the notion of parametricity firmly to the notion of data abstraction. This, unlike Strachey's earlier characterization via algorithm reuse, is a needdriven analysis. We need things to be parametric because otherwise our data abstractions will no longer be abstract. In his subsequent paper with Ma [MR91], two further points are made. One is that the problems reside more at the level of parametrized types than at the level of the quantified polymorphic types, and the other is that the notion of parametricity is not absolute, but relative. The MaReynolds work produces ...
Variations on Realizability: Realizing the Propositional Axiom of Choice
 Math. Structures Comput. Sci
, 2000
"... Introduction 1.1 Historical background Early investigators of realizability were interested in metamathematical questions. In keeping with the traditions of the time they concentrated on interpretations of one formal system in another. They considered an ad hoc collection of increasingly ingenious ..."
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Introduction 1.1 Historical background Early investigators of realizability were interested in metamathematical questions. In keeping with the traditions of the time they concentrated on interpretations of one formal system in another. They considered an ad hoc collection of increasingly ingenious interpretations mainly to establish consistency, independence and conservativity results. van Oosten's contribution to the Workshop (see van Oosten [56] and the extended account van Oosten [57]) gave inter alia an account of these concerns from a modern perspective. (One should also draw attention to realizability used to provide interpretations of Brouwer's theory of Choice Sequences. An early approach is in Kleene Vesley [28]; for modern work in the area consult Moschovakis [35], [36], [37].) In the early days of categorical logic one considered realizability as providing models for constructive mathematics; while the metamathematics could be retrieved by `coding' the mod
On the Failure of FixedPoint Theorems for Chaincomplete Lattices in the Effective Topos
, 2009
"... In the effective topos there exists a chaincomplete distributive lattice with a monotone and progressive endomap which does not have a fixed point. Consequently, the BourbakiWitt theorem and Tarski’s fixedpoint theorem for chaincomplete lattices do not have constructive (toposvalid) proofs. 1 ..."
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In the effective topos there exists a chaincomplete distributive lattice with a monotone and progressive endomap which does not have a fixed point. Consequently, the BourbakiWitt theorem and Tarski’s fixedpoint theorem for chaincomplete lattices do not have constructive (toposvalid) proofs. 1
A Notion of Homotopy for the Effective Topos
, 2010
"... We define a notion of homotopy in the effective topos. AMS Subject Classification (2000): 18B25 (Topos Theory),55U35 (Abstract and axiomatic homotopy theory) ..."
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We define a notion of homotopy in the effective topos. AMS Subject Classification (2000): 18B25 (Topos Theory),55U35 (Abstract and axiomatic homotopy theory)