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Turing-completeness totally free

McBride, Conor (2015) Turing-completeness totally free. In: Mathematics of Program Construction. Springer, Cham, Switzerland, pp. 257-275. ISBN 978-3-319-19796-8

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In this paper, I show that general recursive definitions can be represented in the free monad which supports the ‘effect’ of making a recursive call, without saying how these calls should be executed. Diverse semantics can be given within a total framework by suitable monad morphisms. The Bove-Capretta construction of the domain of a general recursive function can be presented datatype-generically as an instance of this technique. The paper is literate Agda, but its key ideas are more broadly transferable.