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Enumerating the Rationals
Jeremy Gibbons, David Lester and Richard Bird (2004). Enumerating the Rationals. May 2004.
In this paper,we explain an elegant technique for enumerating the positive rationals without duplicates. Moreover, we show how to do so as a simple iteration, generating each element of the enumeration from the previous one alone,with constant cost per element (assuming unit cost for simple operations on arbitrary-precision rationals). Best of all, the resulting program is extremely simple... Cute. Nothing earth shattering, but fun none the less. |
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