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| − | ''Computer Science is no more about computers than astronomy is about telescopes''.
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| − | -- E. W. Dijkstra
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| − | __TOC__
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| − | == Introduction ==
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| − | Wikipedia's [http://en.wikipedia.org/wiki/Computer_science Computer science].
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| − | [http://www.cs.bham.ac.uk/~mhe/ Martín Escardó] maintains a [http://www.math.niu.edu/~rusin/known-math/index/68-XX.html Computer science] page, being both detailed and comprehensive. The Dijkstra-quotation cited above comes from this page.
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| − | [http://mitpress.mit.edu/sicp/full-text/book/book.html Structure and Interpretation of Computer Programs] (by Harold Abelson and Gerald Jay Sussman
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| − | with Julie Sussman, foreword by Alan J. Perlis).
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| − | == Computability theory ==
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| − | Wikipedia's [http://en.wikipedia.org/wiki/Computability_theory Computability theory].
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| − | An interesting area related to computabilty theory: [[Exact real arithmetic]]. For me, it was surprising, how it connected problems in mathematical analysis, arithmetic and computability theory.
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| − | == To do ==
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| − | There are several (equivalent) definitions to the concept of ''algorithm'':
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| − | * [[Turing machine]]
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| − | * [[Combinatory logic]]
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| − | * [http://en.wikipedia.org/wiki/Markov_algorithm Markov algorithm]
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| − | * [http://en.wikipedia.org/wiki/Post_system Post system]
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| − | * [[Recursive function theory]]
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| − | * ...
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| − | These can be conceived also as computer programming languages -- there should be implemented as many of them as possible.
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| − | And some of them can be very good for making such jokes as
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| − | * [[Combinatory logic#Self-replication.2C_quines.2C_reflective_programming|self replication programs or self-representing formulas]]
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| − | * metacircular interpreters.
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| − | At least
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| − | * to write a combinatory logic expression which is equivalent to its own quotation (term representation)
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| − | * to specify and implement a programming language, which could be seen as an experimentable, playable incarnation of [[recursive function theory]] -- it could yield a playground for learning concepts like [http://www.madore.org/~david/computers/quine.html iteration theorem, recursion theorem, fixed point theorem]
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| − | Although there are many differences between [[Combinatory logic]] and recursive function theory, I suspect they have some important common features
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| − | * both of them allow us to avoid the concept of variable
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| − | * both of them can be used well for metaprogramming
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| − | [[Algorithmic information theory]] may exemplify relatedness of computer science to [http://en.wikipedia.org/wiki/Philosophy_of_mathematics philosophical] and [http://en.wikipedia.org/wiki/Foundations_of_mathematics foundational] questions of [[mathematics]].
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| − | [[Category:Theoretical foundations]]
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