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On compositionality of dinatural transformations
conference contribution
posted on 2023-06-10, 06:24 authored by Guy McCusker, Alessio SantamariaNatural transformations are ubiquitous in mathematics, logic and computer science. For operations of mixed variance, such as currying and evaluation in the lambda-calculus, Eilenberg and Kelly's notion of extranatural transformation, and often the even more general dinatural transformation, is required. Unfortunately dinaturals are not closed under composition except in special circumstances. This paper presents a new sufficient condition for composability. We propose a generalised notion of dinatural transformation in many variables, and extend the Eilenberg-Kelly account of composition for extranaturals to these transformations. Our main result is that a composition of dinatural transformations which creates no cyclic connections between arguments yields a dinatural transformation. We also extend the classical notion of horizontal composition to our generalized dinaturals and demonstrate that it is associative and has identities.
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Publication status
- Published
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- Published version
Journal
Leibniz International Proceedings in Informatics, LIPIcsISSN
1868-8969Publisher
Schloss Dagstuhl--Leibniz-Zentrum fuer InformatikExternal DOI
Volume
119Page range
1-22Event name
27th EACSL Annual Conference on Computer Science LogicEvent location
Birmingham, UKEvent type
conferenceEvent date
4th - 7th September, 2018ISBN
9783959770880Department affiliated with
- Informatics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2023-03-03First Open Access (FOA) Date
2023-03-03First Compliant Deposit (FCD) Date
2023-03-03Usage metrics
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