Till sidans topp

Sidansvarig: Webbredaktion
Sidan uppdaterades: 2012-09-11 15:12

Tipsa en vän
Utskriftsversion

Leibniz equality is isomo… - Göteborgs universitet Till startsida
Webbkarta
Till innehåll Läs mer om hur kakor används på gu.se

Leibniz equality is isomorphic to Martin-Lof identity, parametrically

Artikel i vetenskaplig tidskrift
Författare Andreas Abel
J. Cockx
D. Devriese
A. Timany
P. Wadler
Publicerad i Journal of Functional Programming
Volym 30
Sidor 14
ISSN 0956-7968
Publiceringsår 2020
Publicerad vid Institutionen för data- och informationsteknik (GU)
Sidor 14
Språk en
Länkar dx.doi.org/10.1017/s095679682000015...
Ämnesord model, Computer Science
Ämneskategorier Data- och informationsvetenskap

Sammanfattning

Consider two widely used definitions of equality. That of Leibniz: one value equals another if any predicate that holds of the first holds of the second. And that of Martin-Lof: the type identifying one value with another is occupied if the two values are identical. The former dates back several centuries, while the latter is widely used in proof systems such as Agda and Coq. Here we show that the two definitions are isomorphic: we can convert any proof of Leibniz equality to one of Martin-Lof identity andvice versa, and each conversion followed by the other is the identity. One direction of the isomorphism depends crucially on values of the type corresponding to Leibniz equality satisfying functional extensionality and Reynolds' notion of parametricity. The existence of the conversions is widely known (meaning that if one can prove one equality then one can prove the other), but that the two conversions form an isomorphism (internally) in the presence of parametricity and functional extensionality is, we believe, new. Our result is a special case of a more general relation that holds between inductive families and their Church encodings. Our proofs are given inside type theory, rather than meta-theoretically. Our paper is a literate Agda script.

Sidansvarig: Webbredaktion|Sidan uppdaterades: 2012-09-11
Dela:

På Göteborgs universitet använder vi kakor (cookies) för att webbplatsen ska fungera på ett bra sätt för dig. Genom att surfa vidare godkänner du att vi använder kakor.  Vad är kakor?