Reification, Curry-Howard correspondence, and didactical consequences

  • The roles of languages, processes, and objects in mathematical thinking have led to many theories, yet no consistent big picture has evolved from this. This paper puts forth the hypothesis that the Curry-Howard correspondence from computer science and the theories it is built on provide a unification framework. This correspondence asserts that (formal) proofs and programs (in functional programming languages) do not only have some similarities, but can, at least if formalized in an appropriate way, be mapped to each other by an isomorphism such that proofs are programs and vice versa. Moreover, objects can be realized as function evaluation strategies, and this provides a model of the reification process. The paper explores all this and discusses the didactical relevance; especially, the reification theories are revisited. Computer-based realizations of concepts are used as a tool to show the consistency of ideas and the practicability of concepts.

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Metadaten
Author:Reinhard OldenburgORCiDGND
URN:urn:nbn:de:bvb:384-opus4-1119810
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/111981
ISSN:2632-3834OPAC
Parent Title (English):Qeios
Publisher:Qeios
Place of publication:London
Type:Article
Language:English
Year of first Publication:2024
Publishing Institution:Universität Augsburg
Release Date:2024/03/14
First Page:S1074V
DOI:https://doi.org/10.32388/s1074v
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Didaktik der Mathematik
Dewey Decimal Classification:3 Sozialwissenschaften / 37 Bildung und Erziehung / 370 Bildung und Erziehung
Licence (German):CC-BY 4.0: Creative Commons: Namensnennung (mit Print on Demand)