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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 60 (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
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 5 (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.
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
"... A categorial framework for structured graph based systems with or without distinguished nodes or labeling on both arcs and nodes is proposed. Requirements for the existence of limits and colimits in the resulting categories are set. In this context, unrestricted and bicomplete categories of graph ba ..."
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Cited by 2 (2 self)
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A categorial framework for structured graph based systems with or without distinguished nodes or labeling on both arcs and nodes is proposed. Requirements for the existence of limits and colimits in the resulting categories are set. In this context, unrestricted and bicomplete categories of graph based systems such as Petri Nets, Labeled Transition Systems, Nonsequential Automata, etc., are easily defined. Then it is shown how limits and colimits can be interpreted as structuring and anticipatory properties of systems. The proposed framework called duointernalization generalizes the notion of internal graphs allowing that nodes and arc may be objects from different categories. The results about limits and colimits of (reflexive) duointernal (labeled) graphs (with distinguished nodes) are, for our knowledge, new.
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...
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 2 (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.
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.
BlockFactor Fields Of Bernoulli Shifts
, 1998
"... . The distributions of the random arrays (a j i ;j j ; i; j ? 1) where (a i;j ; i; j 6 n) is a matrix and j = (j i ; i ? 1) is an i.i.d. sequence are completely characterized. They must be jointly exchangeable, dissociated and satisfy a new reducibility condition. Probabilities of conøgurations ..."
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. The distributions of the random arrays (a j i ;j j ; i; j ? 1) where (a i;j ; i; j 6 n) is a matrix and j = (j i ; i ? 1) is an i.i.d. sequence are completely characterized. They must be jointly exchangeable, dissociated and satisfy a new reducibility condition. Probabilities of conøgurations in these arrays are computed using combinatorial ideas motivated by category theory. The used methods are mainly algebraic and rely on the structure of ring homomorphisms. AMS 1991 Subject Classiøcation: Primary: 60G09, secondary: 62H05, 12E10, 13F20, 05A15. Key words : Partial exchangeability, dissociatedness, invariant polynomials, ring homomorphisms. 1. INTRODUCTION Let j = (j i ; i ? 1) be an i.i.d. sequence, a Bernoulli shift, each j i taking values in b n = f1; 2; : : : ng, n ? 1, with probabilities p 1 ; : : : ; pn . Where A = (a i;j ; 1 6 i; j 6 n) is a matrix with entries in a ønite nonempty set S, the inønite random array (a j i ;j j ; i; j ? 1) will be denoted by A j;j and ...
Journal of the Brazilian Computer Society
"... Inspired by Meseguer and Montanari's "Petri Nets are Monoids", we propose that a reification of a Petri net is a special kind of net morphism were the target object is enriched with all conceivable sequential and concurrent computations. Then it is proven that while reification of nets satisfies t ..."
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Inspired by Meseguer and Montanari's "Petri Nets are Monoids", we propose that a reification of a Petri net is a special kind of net morphism were the target object is enriched with all conceivable sequential and concurrent computations. Then it is proven that while reification of nets satisfies the vertical compositionality requirement (i.e., reifications compose), it lacks the horizontal compositionality requirement (i.e., reification does not distribute over parallel composition). To achieve both requirements, a new categorial semantic domain based on labeled transition systems with full concurrency, called nonsequential automata, is constructed. Again, a class of morphisms stands for reification and, in this framework, the diagonal compositionality requirement (i.e., both vertical and horizontal) is achieved. Adjunctions between both models are provided extending the approach of Winskel and Nielsen. The steps of abstraction involved in moving between models show that nonsequential automata are more concrete than Petri nets. Moreover, categories of Petri Nets are isomorphic to subcategories of nonsequential automata.
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