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dc.contributor.authorFiore, Marceloen
dc.contributor.authorSaville, Philipen
dc.contributor.editorDale Milleren
dc.date.accessioned2017-09-21T12:42:31Z
dc.date.available2017-09-21T12:42:31Z
dc.date.issued2017-09en
dc.identifier.issn1868-8969
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/267327
dc.description.abstractWe introduce and study the notion of list object with algebraic structure. The first key aspect of our development is that the notion of list object is considered in the context of monoidal structure; the second key aspect is that we further equip list objects with algebraic structure in this setting. Within our framework, we observe that list objects give rise to free monoids and moreover show that this remains so in the presence of algebraic structure. Furthermore, we provide a basic theory explicitly describing as an inductively defined object such free monoids with suitably compatible algebraic structure in common practical situations. This theory is accompanied with the study of two technical themes that, besides being of interest in their own right, are important for establishing applications. These themes are: parametrised initiality, central to the universal property defining list objects; and approaches to algebraic structure, in particular in the context of monoidal theories. The latter leads naturally to a notion of nsr (or near semiring) category of independent interest. With the theoretical development in place, we touch upon a variety of applications, considering Natural Numbers Objects in domain theory, giving a universal property for the monadic list transformer, providing free instances of algebraic extensions of the Haskell Monad type class, elucidating the algebraic character of the construction of opetopes in higher-dimensional algebra, and considering free models of second-order algebraic theories.
dc.publisherSchloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
dc.rightsAttribution 4.0 Internationalen
dc.rightsAttribution 4.0 Internationalen
dc.rightsAttribution 4.0 Internationalen
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/en
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/en
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/en
dc.subjectlist objecten
dc.subjectfree monoiden
dc.subjectstrong monaden
dc.subject(cartesian,linear, and second-order) algebraic theoryen
dc.subjectnear semiringen
dc.subjectHaskell Monad type classen
dc.subjectopetopeen
dc.titleList Objects with Algebraic Structureen
dc.typeConference Object
prism.number16en
prism.publicationDate2017en
prism.publicationNameLIPIcs : Leibniz International Proceedings in Informaticsen
prism.volume84en
dcterms.dateAccepted2017-06-14en
rioxxterms.versionofrecord10.4230/LIPIcs.FSCD.2017.16en
rioxxterms.versionVoR*
rioxxterms.licenseref.urihttp://creativecommons.org/licenses/by/4.0/en
rioxxterms.licenseref.startdate2017-09en
dc.contributor.orcidFiore, Marcelo [0000-0001-8558-3492]
dc.contributor.orcidSaville, Philip [0000-0002-8320-0280]
rioxxterms.typeConference Paper/Proceeding/Abstracten
pubs.funder-project-idEPSRC (1649725)
cam.issuedOnline2017-09en
pubs.conference-name2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)en
pubs.conference-start-date2017-09-03en


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Attribution 4.0 International
Except where otherwise noted, this item's licence is described as Attribution 4.0 International