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Taming Wildcards in Javas Type System Ross Tate Alan Leung Sorin Lerner University of California, San Diego

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Why Use Wildcards? long average(List nums) { long sum = 0; for (Object num : nums) sum += ((Number)num).longValue(); return sum / nums.size(); } Runtime Type Cast long average(List Number nums) { long sum = 0; for (Number num : nums) sum += num.longValue(); return sum / nums.size(); } What about List Integer ? P extends Number long average(List P nums) { long sum = 0; for (Number num : nums) sum += num.longValue(); return sum / nums.size(); } Used only once long average(List ? extends Number nums) { long sum = 0; for (Number num : nums) sum += num.longValue(); return sum / nums.size(); } Not covariant Need use-site variance

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Why Use Wildcards? P void addSuperclasses(Class P c, List ? super Class ? super P list) { Class ? super P sup = c.getSuperclass(); if (sup != null) { list.add(sup); addSuperclasses(sup, list); } Inexpressible with polymorphism Untypeable with use-site variance X : X : > P. Class X

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Open Problems with Wildcards No known subtyping algorithm Subtyping rules are overly restrictive Join algorithm is incomplete Type checker is non-deterministic Type checker can affect program semantics Solved

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Broken Subtyping Algorithm class C P extends D D ? super C L P {} C X < : D ? super C X class Numbers P extends Number extends ArrayList P {} List Numbers ? < : List ? extends List ? extends Number javac Stack Overflow Java No javac No Java Yes

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False Negatives List ? extends List ? extends Number List ? extends List ? List ? extends ArrayList ? List ? extends Numbers ? List Numbers ? class Numbers P extends Number extends ArrayList P {} extends Number direct supertype extends Number

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Our Algorithm List Numbers ? < : List ? extends List ? extends Number Numbers ? < : List ? extends Number Numbers X < : List ? extends Number List X < : List ? extends Number X < : Number class Numbers P extends Number extends ArrayList P {} X < : Number Context Sound & Complete Instantiation Inheritance Opening Instantiation Assumption (if it terminates)

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Non-Termination C X < : D ? super C X D D ? super C L X < : D ? super C X C X < : D ? super C L X D D ? super C L X < : D ? super C L X C L X < : D ? super C L X class C P extends D D ? super C L P {} Inheritance Instantiation Infinite Proof of Subtyping Infinite Proof of Subtyping

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Restrictions Inheritance Restriction No use of ? super in the inheritance hierarchy Parameter Restriction When constraining type parameters, ? super may only be used at covariant locations class C P extends D D ? super C L P {} P extends List List ? super C L P Termination Guaranteed

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Survey Wildcards in InheritanceWildcards in Constraints Only Unconstrained Wildcards 0 100000 10000 1000 # of Superclass Declarations 9.2 Million Lines of Code Analyzed No Violations of Our Restrictions No Violations of Our Restrictions All at covariant locations

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Summary of Contributions Sound and Complete Subtyping Algorithm given practical language restrictions Theory of Existential Types design of implicit constraints Techniques for Type-Argument Inference lazy joins for wildcards Fixes to the Type System improved equivalence and intersections Compatible Extensions to Java mixing use-site and declaration-site variance

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