Taming Wildcards - PowerPoint Presentation

Slide1

Taming Wildcardsin Java’s Type System

Ross TateAlan LeungSorin Lerner

University of California, San DiegoSlide2

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 varianceSlide3

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〉Slide4

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 semanticsSolvedSlide5

Subtyping WildcardsSlide6

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

YesSlide7

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 Numberextends Number

direct supertype

direct supertype

direct supertype

extends NumberSlide8

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)Slide9

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

Inheritance

Instantiation

Instantiation

Infinite Proof

of Subtyping

ContrivedSlide10

Restrictions

Inheritance RestrictionNo 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〉〉〉〉〉Contrived

ContrivedTermination GuaranteedSlide11

Survey

Wildcards in InheritanceWildcards in Constraints

Only Unconstrained

Wildcards

0

100000

10000

1000

# of Superclass

Declarations9.2 Million Lines of Code Analyzed

No Violations of

Our Restrictions

All at covariant locations



Slide12

Summary of Contributions

Sound and Complete Subtyping Algorithmgiven practical language restrictionsTheory of Existential Typesdesign of implicit constraintsTechniques for Type-Argument Inference

lazy joins for wildcards

Fixes to the Type System

improved equivalence and intersectionsCompatible Extensions to Javamixing use-site and declaration-site variance