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Verifying the Problem of the Dutch National Flag in Agda

Published online by Cambridge University Press:  12 October 2011

WOUTER SWIERSTRA
WOUTER SWIERSTRA*
Affiliation:
Heijendaalseweg 135, 6525 AJ Nijmegen, the Netherlands (e-mail: w.swierstra@cs.ru.nl)
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The problem of the Dutch national flag was formulated by Dijkstra (1976) as follows:

There is a row of buckets numbered from 1 to n. It is given that:

  1. P1: each bucket contains one pebble

  2. P2: each pebble is either red, white, or blue.

A minicomputer is placed in front of this row of buckets and has to be programmed in such a way that it will rearrange (if necessary) the pebbles in the order of the Dutch national flag.

The minicomputer in question should perform this rearrangement using two commands:

  • • swapi j for 1≤i≤n and 1≤j≤n exchanges the pebbles stored in the buckets numbered i and j;

  • • read (i) for 1≤i≤n returns the colour of the pebble currently lying in bucket number i. Dijkstra originally named this operation buck.

Type
Functional Pearls
Information
Journal of Functional Programming , Volume 21 , Issue 6 , November 2011 , pp. 573 - 583
Copyright
Copyright © Cambridge University Press 2011

References

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