Abstract
We propose a novel approach to stream definition and manipulation. Our solution is based on two key ideas. Regular corecursion, which avoids non termination by detecting cyclic calls, is enhanced, by allowing in equations defining streams other operators besides the stream constructor. In this way, some non-regular streams are definable. Furthermore, execution includes a runtime check to ensure that the stream generated by a function call is well-defined, in the sense that access to an arbitrary index always succeeds. We extend the technique beyond the simple stream operators considered in previous work, notably by adding an interleaving combinator which has a non-trivial recursion scheme.
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Notes
- 1.
Here we use the syntax of our calculus, where, differently from Haskell, functions are uncurried, that is, take as arguments possibly empty tuples delimited by parentheses.
- 2.
For simplicity, here indexing and numeric expressions coincide.
- 3.
Indeed, it does not affect derivability, see Lemma 4 in the following.
- 4.
Non-well-definedness can only be detected on closed results.
- 5.
This holds for any valid derivation tree and not for this specific case.
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Ancona, D., Barbieri, P., Zucca, E. (2022). Enhancing Expressivity of Checked Corecursive Streams. In: Hanus, M., Igarashi, A. (eds) Functional and Logic Programming. FLOPS 2022. Lecture Notes in Computer Science, vol 13215. Springer, Cham. https://doi.org/10.1007/978-3-030-99461-7_1
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