Induktiiviset tyypit

Induktiiviset tyypit ovat tapa mallintaa erilaisia tietotyyppejä kuten listoja, luonnollisia lukuja ja binäärihakupuita tyyppiteoriassa. Induktiivisia tyyppejä käytetään laajasti todistusassistenteissa erilaisten teoreemojen ja tietokoneohjelmien toteutukseen. Yleistys induktiivisista tyypeistä ovat...

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Main Author: Vitikainen, Maxim
Other Authors: Informaatioteknologian tiedekunta, Faculty of Information Technology, Informaatioteknologia, Information Technology, Jyväskylän yliopisto, University of Jyväskylä
Format: Bachelor's thesis
Language:fin
Published: 2024
Subjects:
Online Access: https://jyx.jyu.fi/handle/123456789/96254
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author Vitikainen, Maxim
author2 Informaatioteknologian tiedekunta Faculty of Information Technology Informaatioteknologia Information Technology Jyväskylän yliopisto University of Jyväskylä
author_facet Vitikainen, Maxim Informaatioteknologian tiedekunta Faculty of Information Technology Informaatioteknologia Information Technology Jyväskylän yliopisto University of Jyväskylä Vitikainen, Maxim Informaatioteknologian tiedekunta Faculty of Information Technology Informaatioteknologia Information Technology Jyväskylän yliopisto University of Jyväskylä
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description Induktiiviset tyypit ovat tapa mallintaa erilaisia tietotyyppejä kuten listoja, luonnollisia lukuja ja binäärihakupuita tyyppiteoriassa. Induktiivisia tyyppejä käytetään laajasti todistusassistenteissa erilaisten teoreemojen ja tietokoneohjelmien toteutukseen. Yleistys induktiivisista tyypeistä ovat korkeammat induktiiviset tyypit, jotka laajentavat induktiivisia tyyppejä mahdollistamalla tyypin alkioiden välisten ekvivalenssirelaatioiden määrittämisen. Tässä kirjallisuuskatsauksessa käsitellään induktiivisten ja korkeampien induktiivisten tyyppien teoriaa, niiden toteutuksia eri ohjelmointikielissä sekä erilaisia sovelluskohteita. Inductive types are a way to represent complex datatypes such as lists, natural numbers and binary search trees in type theory. Inductive types are currently widely used in proof assistants to implement mathematical theorems and computer programs. A generalization of inductive types are higher inductive types, which extend inductive types by making it possible to define equivalence relations between inhabitants of a type. This thesis explores theory behind inductive and higher inductive types, their implementations in different programming languages and their use cases.
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spellingShingle Vitikainen, Maxim Induktiiviset tyypit induktiiviset tyypit todistusassistentit Tietotekniikka Mathematical Information Technology 602
title Induktiiviset tyypit
title_full Induktiiviset tyypit
title_fullStr Induktiiviset tyypit Induktiiviset tyypit
title_full_unstemmed Induktiiviset tyypit Induktiiviset tyypit
title_short Induktiiviset tyypit
title_sort induktiiviset tyypit
title_txtP Induktiiviset tyypit
topic induktiiviset tyypit todistusassistentit Tietotekniikka Mathematical Information Technology 602
topic_facet 602 Mathematical Information Technology Tietotekniikka induktiiviset tyypit todistusassistentit
url https://jyx.jyu.fi/handle/123456789/96254 http://www.urn.fi/URN:NBN:fi:jyu-202407015088
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