Turing-completeness totally free

McBride, Conor; Hinze, Ralf and Voigtländer, Janis, eds. (2015) Turing-completeness totally free. In: Mathematics of Program Construction. Lecture Notes in Computer Science, 9129 . Springer, DEU, pp. 257-275. ISBN 9783319197968 (https://doi.org/10.1007/978-3-319-19797-5_13)

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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.


McBride, Conor ORCID logoORCID: https://orcid.org/0000-0003-1487-0886; Hinze, Ralf and Voigtländer, Janis