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m (Changing the order of the table-of-contents and the Dijkstra-motto)
(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)

Revision as of 19:44, 22 April 2006

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

-- E. W. Dijkstra


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

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