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Elements of Basic Category Theory
, 1996
"... Category theory provides an elegant and powerful means of expressing relationships across a wide area of mathematics. But further than this it has had a considerable impact on the conceptual basis both of mathematics and many parts of theoretical computer science. Important connections in computer s ..."
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Category theory provides an elegant and powerful means of expressing relationships across a wide area of mathematics. But further than this it has had a considerable impact on the conceptual basis both of mathematics and many parts of theoretical computer science. Important connections in computer science include the design of both functional and imperative programming languages, semantic models of programming languages, semantics of concurrency, specification and development of algorithms, type theory and polymorphism, specification languages, algebraic semantics, constructive logic and automata theory. The purpose of this text is to provide a soft stairway to this infectious and attractive field of mathematics. We provide here a careful and detailed explanation of "basic elements", or more precisely, from the elementary definitions to adjoint situations. The general approach used here is to provide a careful motivation for the majority of constructions as well as a detailed presentat...
Introduction to Functional Programming using Gofer
, 1990
"... ing out and studying those patterns of computation as useful objects in their own right leads to further insights into the nature of computation. The list operators studied later in these notes follow this approach. ffl Functional programs are usually an order of magnitude more concise than their i ..."
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ing out and studying those patterns of computation as useful objects in their own right leads to further insights into the nature of computation. The list operators studied later in these notes follow this approach. ffl Functional programs are usually an order of magnitude more concise than their imperative counterparts. Besides being shorter, they can be much more readable. The functional community like to cite studies that show the number of bugs per line is more or less constant, independent of the level of the language in use. Higherlevel languages encode more concept per line, and therefore have relatively fewer bugs. ffl Functional programs are often more akin to formal specifications than their conventional counterparts. A good notation goes a long way towards solving the problem[47]. ffl Lazy evaluation permits a new approach to some algorithms. It is a simple but powerful idea that can remove the need for explicit backtracking, and can allow the programmer to manipulate in...
Title: Quantum Theory of Computation and Relativistic Physics
, 1997
"... Reportno: ALP271264306DRELCOMALEXNEWPHYSCOMP96LATEX2EXXXvay11230197 In the eprint is discussed a few steps to introducing of "vocabulary " of relativistic physics in quantum theory of information and computation (QTI&C). The behavior of a few simple quantum systems those are used as model ..."
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Reportno: ALP271264306DRELCOMALEXNEWPHYSCOMP96LATEX2EXXXvay11230197 In the eprint is discussed a few steps to introducing of "vocabulary " of relativistic physics in quantum theory of information and computation (QTI&C). The behavior of a few simple quantum systems those are used as models in QTI&C is tested by usual relativistic tools (transformation properties of wave vectors, etc.). Massless and charged massive particles with spin 1/2 is considered. Field theory is also discussed briefly. In the paper is described some steps for merger between relativistic quantum theory and theory of computation. The first step is consideration of transformation of qubit state due to rotation of coordinate system. The Lorentz transformation is considered after that. The some new properties of this transformation change usual model of qubit. The system of q 2 bit seems more fundamental relativistic model. It is shown also that such model as electron is really such q 2 bit systems and for modelling of qubit is necessary to use massless particle like electron neutrino. The quantum field theory (QFT) is briefly discussed further. The wave vectors of interacted particle now described by some operator and it can produce some multiparticle (â€˜nonlinearâ€™) effects.