Computer science
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(New section - →To do: : implementing the different approaches of concept of algorithm as programming languages, and using them in teaching foundations of mathematics and metaprogramming) |
m (Creating new wikipage Recursive function theory by making this word a link to it) |
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* [http://en.wikipedia.org/wiki/Markov_algorithm Markov algorithm] | * [http://en.wikipedia.org/wiki/Markov_algorithm Markov algorithm] | ||
* [http://en.wikipedia.org/wiki/Post_system Post system] | * [http://en.wikipedia.org/wiki/Post_system Post system] | ||
| - | * Recursive function theory | + | * [[Recursive function theory]] |
* ... | * ... | ||
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At least | At least | ||
* to write a combinatory logic expression which is equivalent to its own quotation (term representation) | * 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 [http://www.madore.org/~david/computers/quine.html iteration theorem, recursion theorem, fixed point theorem] | + | * 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] |
Although there are many differences between [[Combinatory logic]] and recursive function theory, I suspect they have some important common features | Although there are many differences between [[Combinatory logic]] and recursive function theory, I suspect they have some important common features | ||
Revision as of 09:23, 23 April 2006
Computer Science is no more about computers than astronomy is about telescopes.
-- E. W. Dijkstra
Contents |
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).
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.
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
