Covariance and contravariance (computer science): Difference between revisions

Revision as of 14:45, 22 June 2024

Revision as of 00:46, 28 June 2024

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==== Inferring variance ====

It is possible to design a type system where the compiler automatically infers the best possible variance annotations for all datatype parameters.<ref name="tamingCombining">{{cite conference |first1=John |last1=Altidor |first2=Huang Shan |last2=Shan |first3=Yannis |last3=Smaragdakis |title=Taming the wildcards: combining definition- and use-site variance |book-title=Proceedings of the 32nd ACM SIGPLAN conference on Programming language design and implementation (PLDI'11) |year=2011 |publisher=ACM |date=2011 |isbn=9781450306638 |pages=602–613 |doi=10.1145/1993316.1993569 |citeseerx=10.1.1.225.8265 }}</ref> However, the analysis can get complex for several reasons. First, the analysis is nonlocal since the variance of an interface {{java|I}} depends on the variance of all interfaces that {{java|I}} mentions. Second, in order to get unique best solutions the type system must allow ''bivariant'' parameters (which are simultaneously co- and contravariant). And finally, the variance of type parameters should arguably be a deliberate choice by the designer of an interface, not something that just happens.

For these reasons<ref>{{cite web|title=Covariance and Contravariance in C# Part Seven: Why Do We Need A Syntax At All? |first=Eric |last=Lippert |date=October 29, 2007 |access-date=16 August 2016

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Ross Tate argues<ref name="MixedSiteVariance">{{cite conference |first=Ross |last=Tate |title=Mixed-Site Variance |book-title=FOOL '13: Informal Proceedings of the 20th International Workshop on Foundations of Object-Oriented Languages |year=2013 |url=http://www.cs.cornell.edu/~ross/publications/mixedsite/index.html |citeseerx=10.1.1.353.4691}}</ref> that part of the complexity of Java wildcards is due to the decision to encode use-site variance using a form of existential types. The original proposals<ref>

{{cite conference |first1=Atsushi |last1=Igarashi |first2=Mirko |last2=Viroli |title=On Variance-Based Subtyping for Parametric Types |book-title=Proceedings of the 16th European Conference on Object-Oriented Programming (ECOOP '02) |year=2002 |isbn=3-540-47993-7 |pages=441–469 |doi=10.1007/3-540-47993-7_19 |series=Lecture Notes in Computer Science |volume=2374 |citeseerx=10.1.1.66.450}}</ref><ref>{{cite conference |first1=Kresten Krab |last1=Thorup |first2=Mads |last2=Torgersen |title=Unifying Genericity: Combining the Benefits of Virtual Types and Parameterized Classes |book-title=Object-Oriented Programming (ECOOP '99) |year=1999 |publisher=Springer |date=1999 |isbn=3-540-48743-3 |pages=186–204 |doi=10.1007/3-540-48743-3_9 |series=Lecture Notes in Computer Science |volume=1628 |citeseerx=10.1.1.91.9795 }}</ref> used special-purpose syntax for variance annotations, writing {{java|List<+Animal>}} instead of Java's more verbose {{java|List<? extends Animal>}}.

Since wildcards are a form of existential types they can be used for more things than just variance. A type like {{java|List<?>}} ("a list of unknown type"<ref>{{cite web |url=https://docs.oracle.com/javase/tutorial/java/generics/unboundedWildcards.html |title=The Java™ Tutorials, Generics (Updated), Unbounded Wildcards |access-date=July 17, 2020}}</ref>) lets objects be passed to methods or stored in fields without exactly specifying their type parameters. This is particularly valuable for classes such as {{Javadoc:SE|java/lang|Class}} where most of the methods do not mention the type parameter.