# Computer science

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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. |
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]] |
[[Category:Theoretical foundations]] |

## Latest revision as of 18:35, 5 August 2006

*Computer Science is no more about computers than astronomy is about telescopes*.

-- E. W. Dijkstra

## Contents |

## [edit] 1 Introduction

Wikipedia's Computer science.

Martín Escardó maintains a Computer science page, being both detailed and comprehensive. The Dijkstra-quotation cited above comes from this page.

Structure and Interpretation of Computer Programs (by Harold Abelson and Gerald Jay Sussman with Julie Sussman, foreword by Alan J. Perlis).

## [edit] 2 Computability theory

Wikipedia's Computability theory.

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.

## [edit] 3 To do

There are several (equivalent) definitions to the concept of *algorithm*:

These can be conceived also as computer programming languages -- there should be implemented as many of them as possible. And some of them can be very good for making such jokes as

- self replication programs or self-representing formulas
- metacircular interpreters.

At least

- to write a combinatory logic expression which is equivalent to its own quotation (term representation)
- 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 iteration theorem, recursion theorem, fixed point theorem

Although there are many differences between Combinatory logic and recursive function theory, I suspect they have some important common features

- both of them allow us to avoid the concept of variable
- both of them can be used well for metaprogramming

Algorithmic information theory may exemplify relatedness of computer science to philosophical and foundational questions of mathematics.