Abstract
The usual definition facilities in theorem provers cannot handle all recursive functions on lazy lists; the filter function is a prime counterexample. We present two new ways of directly defining functions like filter by exploiting their dual nature as producers and consumers. Borrowing from domain theory and topology, we define them as a least fixpoint (producer view) and as a continuous extension (consumer view). Both constructions yield proof principles that allow elegant proofs. We expect that the approach extends to codatatypes with finite truncations.
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Lochbihler, A., Hölzl, J. (2014). Recursive Functions on Lazy Lists via Domains and Topologies. In: Klein, G., Gamboa, R. (eds) Interactive Theorem Proving. ITP 2014. Lecture Notes in Computer Science, vol 8558. Springer, Cham. https://doi.org/10.1007/978-3-319-08970-6_22
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DOI: https://doi.org/10.1007/978-3-319-08970-6_22
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