| 1. |
- Botta, N., et al.
(författare)
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Extensional equality preservation and verified generic programming
- 2021
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Ingår i: Journal of Functional Programming. - : Cambridge University Press (CUP). - 0956-7968 .- 1469-7653. ; 31
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Tidskriftsartikel (refereegranskat)abstract
- In verified generic programming, one cannot exploit the structure of concrete data types but has to rely on well chosen sets of specifications or abstract data types (ADTs). Functors and monads are at the core of many applications of functional programming. This raises the question of what useful ADTs for verified functors and monads could look like. The functorial map of many important monads preserves extensional equality. For instance, if f, g : A -> B are extensionally equal, that is, for all x is an element of A, f x = g x, then map f : List A -> List B and map g are also extensionally equal. This suggests that preservation of extensional equality could be a useful principle in verified generic programming. We explore this possibility with a minimalist approach: we deal with (the lack of) extensional equality in Martin-Lof's intensional type theories without extending the theories or using full-fledged setoids. Perhaps surprisingly, this minimal approach turns out to be extremely useful. It allows one to derive simple generic proofs of monadic laws but also verified, generic results in dynamical systems and control theory. In turn, these results avoid tedious code duplication and ad-hoc proofs. Thus, our work is a contribution toward pragmatic, verified generic programming.
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| 2. |
- Sawicki, J., et al.
(författare)
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Perspectives on adaptive dynamical systems
- 2023
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Ingår i: Chaos. - 1054-1500 .- 1089-7682. ; 33:7
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Tidskriftsartikel (refereegranskat)abstract
- Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems, such as the power grid, social, and neural networks, and they form the backbone of closed-loop control strategies and machine learning algorithms. In this article, we provide an interdisciplinary perspective on adaptive systems. We reflect on the notion and terminology of adaptivity in different disciplines and discuss which role adaptivity plays for various fields. We highlight common open challenges and give perspectives on future research directions, looking to inspire interdisciplinary approaches.
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