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Turner, Bird, Eratosthenes: An eternal burning thread
Turner, Bird, Eratosthenes: An eternal burning thread - Volume 35
The paper includes an epilogue that presents a purely list-based but circular implementation of the Genuine Sieve, contributed by Bird during the editing process. He explicitly admits in that paper that “rewriting the well known sieve of Eratosthenes program [by which he means trial division] in this discipline involves coding in some bound on the distance from one prime to the next”. But still, one would either have to prove the theorem—a decidedly non-trivial matter (Théry, Reference Théry2003)—or accept it as an unverified axiom; Turner said that he was “interested in finding something simpler” than full dependent types.
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