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25
Comprehensions, a Query Notation for DBPLs
 Proceedings of the 3rd International Workshop on Database Programming Languages
, 1991
"... This paper argues that comprehensions, a construct found in some programming languages, are a good query notation for DBPLs. It is shown that, like many other query notations, comprehensions can be smoothly integrated into DBPLs and allow queries to be expressed clearly, concisely and efficiently. M ..."
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Cited by 62 (4 self)
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This paper argues that comprehensions, a construct found in some programming languages, are a good query notation for DBPLs. It is shown that, like many other query notations, comprehensions can be smoothly integrated into DBPLs and allow queries to be expressed clearly, concisely and efficiently. More significantly, two advantages of comprehensions are demonstrated. The first advantage is that, unlike conventional notations, comprehension queries combine computational power with ease of optimisation. That is, not only can comprehension queries express both recursion and computation, but equivalent comprehension transformations exist for all of the major conventional optimisations. The second advantage is that comprehensions provide a uniform notation for expressing and performing some optimisation on queries over several bulk data types. The bulk types that comprehensions can be defined over include sets, relations, bags and lists. A DBPL can also be automatically extended to provide and partially optimise comprehension queries over new bulk types constructed by the application programmer, providing that the new type has some welldefined properties. 1
MONAD COMPOSITIONS I: GENERAL CONSTRUCTIONS AND RECURSIVE DISTRIBUTIVE LAWS
"... ABSTRACT. New techniques for constructing a distributive law of a monad over another are studied using submonads, quotient monads, product monads, recursivelydefined distributive laws, and linear equations. Sequel papers will consider distributive laws in closed categories and will construct monad ..."
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Cited by 6 (0 self)
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ABSTRACT. New techniques for constructing a distributive law of a monad over another are studied using submonads, quotient monads, product monads, recursivelydefined distributive laws, and linear equations. Sequel papers will consider distributive laws in closed categories and will construct monad approximations for compositions which fail to be a monad. 1.
Deep Inference Proof Theory Equals Categorical Proof Theory Minus Coherence
, 2004
"... This paper links deep inference proof theory, as studied by Guglielmi et al., to categorical proof theory in the sense of Lambek et al.. It observes how deep inference proof theory is categorical proof theory, minus the coherence diagrams/laws. Coherence yields a readymade and well studied notion o ..."
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Cited by 4 (1 self)
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This paper links deep inference proof theory, as studied by Guglielmi et al., to categorical proof theory in the sense of Lambek et al.. It observes how deep inference proof theory is categorical proof theory, minus the coherence diagrams/laws. Coherence yields a readymade and well studied notion of equality on deep inference proofs. The paper notes a precise correspondence between the symmetric deep inference system for multiplicative linear logic (the linear fragment of SKSg) and the presentation of #autonomous categories as symmetric linearly distributive categories with negation. Contraction and weakening in SKSg corresponds precisely to the presence of (co)monoids.
Locally convex approach spaces
 Applied General Topology
"... Dedicated to Professor S. Naimpally on the occasion of his 70 th birthday. We continue the investigation of suitable structures for quantified functional analysis, by looking at the notion of local convexity in the setting of approach vector spaces as introduced in [6]. We prove that the locally co ..."
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Cited by 4 (4 self)
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Dedicated to Professor S. Naimpally on the occasion of his 70 th birthday. We continue the investigation of suitable structures for quantified functional analysis, by looking at the notion of local convexity in the setting of approach vector spaces as introduced in [6]. We prove that the locally convex objects are exactly the ones generated (in the usual approach sense) by collections of seminorms. Furthermore, we construct a quantified version of the projective tensor product and show that the locally convex objects admitting a decent exponential law with respect to it are precisely the seminormed spaces.
A Criterion for the Existence of Subobject Classifiers
, 1998
"... We give a criterion for the existence of subobject classifiers of cocomplete categories with a small, dense subcategory. (key word: subobject classifier, cocomplete, dense, topos, AMS Classification:18B25, 18A40, 68Q55) 1 Introduction It often occurs that a cocomplete category E has a small and den ..."
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Cited by 2 (2 self)
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We give a criterion for the existence of subobject classifiers of cocomplete categories with a small, dense subcategory. (key word: subobject classifier, cocomplete, dense, topos, AMS Classification:18B25, 18A40, 68Q55) 1 Introduction It often occurs that a cocomplete category E has a small and dense subcategory C. In this case, there is an adjunction between the category E and the category Set C op of presheaves over C, which enables us to construct E objects from presheaves over C. In this paper, we give a criterion for the existence of a subobject classifier in E expressed as a condition in the presheaf category. Moreover we give the subobject classifier concretely by using the presheaves if there exists a subobject classifier. This criterion is used heavily in the proof of the existence of subobject classifier in the category of functional bisimulations[6]. We expect this applicable to other similar problems. 3 This work was done when the author was in Department of Mathem...
DuoInternal Labeled Graphs with Distinguished Nodes: a Categorial Framework for Graph Based Anticipatory Systems
 CASYS'99  Third International Conference on Computing Anticipatory Systems, International Journal of Computing Anticipatory Systems
, 2000
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Naïve Synthetic Domain Theory: A Logical Approach
"... We present two dioeerent approaches to Synthetic Domains. First we give a synthetic, axiomatic version of extensional PERs which [Freyd et al. 92] introduced model theoretically. Second we rephrase the theory of replete objects (cf. [Hyland 91], [Taylor 91]). If the category of predomains is small a ..."
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Cited by 1 (1 self)
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We present two dioeerent approaches to Synthetic Domains. First we give a synthetic, axiomatic version of extensional PERs which [Freyd et al. 92] introduced model theoretically. Second we rephrase the theory of replete objects (cf. [Hyland 91], [Taylor 91]). If the category of predomains is small and internally complete two logical characterizations of repletion are possible. Closure properties of the corresponding predomains and domains are stated and finally the most important proofs of traditional domain theory are sketched in the synthetic setting. So this paper might serve as an introduction into Synthetic Domain Theory also for readers unfamiliar with topos or category theory.
CAUCHY CHARACTERIZATION OF ENRICHED CATEGORIES
 REPRINTS IN THEORY AND APPLICATIONS OF CATEGORIES, NO. 4, 2004, PP. 1–16.
, 2004
"... Soon after the appearance of enriched category theory in the sense of EilenbergKelly1, I wondered whether Vcategories could be the same as Wcategories for nonequivalent monoidal categories V and W. It was not until my fourmonth sabbatical in Milan at the end of 1981 that I made a serious attemp ..."
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Soon after the appearance of enriched category theory in the sense of EilenbergKelly1, I wondered whether Vcategories could be the same as Wcategories for nonequivalent monoidal categories V and W. It was not until my fourmonth sabbatical in Milan at the end of 1981 that I made a serious attempt to properly formulate this question and try to solve it. By this time I was very impressed by the work of Bob Walters [28] showing that sheaves on a site were enriched categories. On sabbatical at Wesleyan University (Middletown) in 197677, I had looked at a preprint of Denis Higgs showing that sheaves on a Heyting algebra H couldbeviewedassomekindofHvalued sets. The latter seemed to be understandable as enriched categories without identities. Walters ’ deeper explanation was that they were enriched categories (with identities) except that the base was not H but rather a bicategory built from H. A stream of research was initiated in which the base monoidal category for enrichment was replaced, more generally, by a base bicategory. In analysis, Cauchy complete metric spaces are often studied as completions of more readily defined metric spaces. Bill Lawvere [15] had found that Cauchy completeness could be expressed for general enriched categories with metric spaces as a special case. Cauchy sequences became left adjoint modules2 and convergence became representability. In Walters ’ work it was the Cauchy complete enriched categories that were the sheaves. It was natural then to ask, rather than my original question, whether Cauchy complete Vcategories were the same as Cauchy complete Wcategories for appropriate base bicategories V and W. I knew already [20] that the bicategory VMod whose morphisms were modules between Vcategories could be constructed from the bicategory whose morphisms were Vfunctors. So the question became: given a base bicategory V, for which
Abstract Diagrams
"... Abstract: The awkwardnes of ‘up to isomorphism ’ diagrammatic constructions is recalled, and one repost, via skeleton categories and standard isomorphisms, is reviewed. An alternative approach is introduced, which defines abstract diagrams as natural isomorphism classes of concrete diagrams, and is ..."
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Abstract: The awkwardnes of ‘up to isomorphism ’ diagrammatic constructions is recalled, and one repost, via skeleton categories and standard isomorphisms, is reviewed. An alternative approach is introduced, which defines abstract diagrams as natural isomorphism classes of concrete diagrams, and is related to the previous one. Maximal abstract diagrams yield canonical diagrammatic constructions, where only ‘up to isomorphism ’ constructions were available previously. 1