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Prototype Proofs in Type Theory
, 2000
"... The proofs of universally quantified statements, in mathematics, are given as "schemata" or as "prototypes" which may be applied to each specific instance of the quantified variable. Type Theory allows to turn into a rigorous notion this informal intuition described by many, i ..."
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The proofs of universally quantified statements, in mathematics, are given as "schemata" or as "prototypes" which may be applied to each specific instance of the quantified variable. Type Theory allows to turn into a rigorous notion this informal intuition described by many, including Herbrand. In this constructive approach where propositions are types, proofs are viewed as terms of \Gammacalculus and act as "proofschemata", as for universally quantified types. We examine here the critical case of Impredicative Type Theory, i.e. Girard's system F, where typequantification ranges over all types. Coherence and decidability properties are proved for prototype proofs in this impredicative context.
Parallel Haskell: The vectorisation monad
, 1993
"... It has long been known that some of the most common uses of for and whileloops in imperative programs can easily be expressed using the standard higherorder functions fold and map. With this correspondence as a starting point, we derive parallel implementations of various iterative constructs, ea ..."
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It has long been known that some of the most common uses of for and whileloops in imperative programs can easily be expressed using the standard higherorder functions fold and map. With this correspondence as a starting point, we derive parallel implementations of various iterative constructs, each having a better complexity than their sequential counterparts, and explore the use of monads to guarantee the soundness of the parallel implementation. As an aid to the presentation of the material, we use the proposed syntax for parallel Haskell [27] (figure 1) as a vehicle in which imperative functional programs will be expressed. Surprisingly, incorporating imperative features into a purely functional language has become an active area of research within the functional programming community [30, 24, 36, 20]. One of the techniques gaining widespread acceptance as a model for imperative functional programming is monads [38, 37, 26]. Typically monads are used to guarantee single threadedn...
Weak Relational Products
, 2006
"... Abstract. The existence of relational products in categories of relations is strongly connected with the representability of that category. In this paper we propose a canonical weakening of the notion of a relational product. Unlike the strong version any (small) category of relations can be embedde ..."
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Abstract. The existence of relational products in categories of relations is strongly connected with the representability of that category. In this paper we propose a canonical weakening of the notion of a relational product. Unlike the strong version any (small) category of relations can be embedded into a suitable category providing all weak relational products. Furthermore, we investigate the categorical properties of the new construction and proof several (weak) versions of propositions wellknown for relational products. 1
Handbook of the History of Logic. Volume 6
"... ABSTRACT: Here is a crude list, possibly summarizing the role of paradoxes within the framework of mathematical logic: 1. directly motivating important theories (e.g. type theory, axiomatic set theory, combinatory logic); 2. suggesting methods of proving fundamental metamathematical results (fixed p ..."
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ABSTRACT: Here is a crude list, possibly summarizing the role of paradoxes within the framework of mathematical logic: 1. directly motivating important theories (e.g. type theory, axiomatic set theory, combinatory logic); 2. suggesting methods of proving fundamental metamathematical results (fixed point theorems, incompleteness, undecidability, undefinability); 3. applying inductive definability and generalized recursion; 4. introducing new semantical methods (e. g. revision theory, semiinductive definitions, which require nontrivial set theoretic results); 5. (partly) enhancing new axioms in set theory: the case of antifoundation AFA and the mathematics of circular phenomena; 6. suggesting the investigation of nonclassical logical systems, from contractionfree and manyvalued logics to systems with generalized quantifiers; 7. suggesting frameworks with flexible typing for the foundations of Mathematics and Computer Science; 8. applying forms of selfreferential truth and in Artificial Intelligence, Theoretical Linguistics, etc. Below we attempt to shed some light on the genesis of the issues 1–8 through the history of the paradoxes in the twentieth century, with a special emphasis on semantical aspects.
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, 1997
"... An algebraic framework for the definition of compositional semantics of normal logic programs ..."
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An algebraic framework for the definition of compositional semantics of normal logic programs
Modified Realizability and Inductive Types
, 2006
"... PDF and gzipped PostScript formats via anonymous FTP from the areaftp.cs.unibo.it:/pub/TR/UBLCS or via WWW at ..."
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PDF and gzipped PostScript formats via anonymous FTP from the areaftp.cs.unibo.it:/pub/TR/UBLCS or via WWW at
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"... This paper reports a use of flexible bodies in Multi Body System (MBS) modeling. A combination of discrete and modal flexibility enables structural eigenfrequency investigation. The Voluntary Milking System ™ (VMS) is a product from Swedish agricultural company DeLaval AB [1]. The VMS introduces an ..."
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This paper reports a use of flexible bodies in Multi Body System (MBS) modeling. A combination of discrete and modal flexibility enables structural eigenfrequency investigation. The Voluntary Milking System ™ (VMS) is a product from Swedish agricultural company DeLaval AB [1]. The VMS introduces an entirely different way of milking cows. The cows themselves decide when its time to be milked and make their way to the milking unit (the VMS). The VMS model will consist of three major part models: the robot arm, the stall, and the control system. These systems can be seen as sub models when using a systematic approach [5]. The modeling this far has been concentrated on the first two sub models, i.e. the robot arm and the stall. Covered here will be the finite element (FE) modeling activity, to represent structural elasticity, and the connection of the stall part model to the robot arm part model. Emphasis is on modeling activities. Preliminary results from simulations regarding forced oscillation are presented.
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"... I wish to thank my parents for their continuing support, encouragement and understanding. Medda, Toto, Fiete, Anemone: Thanks for visiting me in the States! My friend Vidya was always on my side and helped me out on more than one occasion. Thanks for everything! Special thanks to Professor Karl H. H ..."
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I wish to thank my parents for their continuing support, encouragement and understanding. Medda, Toto, Fiete, Anemone: Thanks for visiting me in the States! My friend Vidya was always on my side and helped me out on more than one occasion. Thanks for everything! Special thanks to Professor Karl H. Hofmann, who taught my first course in mathematical analysis. He introduced me to mathematics, teaching with a rigour and style which motivated me throughout my career. I would like to express my thanks to all members of the department of mathematics at Tulane, most notably my fellow graduate students, for making my stay here such a pleasant one. Martin Laubinger gave me hints regarding the requirements of the Graduate School. I used a modified version of Dmitri Alexeev's Tulane University Thesis LATEX class; the diagrams were drawn using Paul Taylor's diagrams package [22].