Getting F-Bounded Polymorphism into Shape - PowerPoint Presentation

Slide1

Getting F-Bounded Polymorphism into Shape

Ben Greenman, Fabian Muehlboeck, and Ross TateCornell UniversitySlide2
Slide3

Typesafe

Equality + Generic Lists?Slide4

(Typesafe) Equality

@override

public

boolean

equals(Object other) {

if(other instanceof String){…}

else { return false; }}

“Hello”.equals

(5)Slide5

(Typesafe) Equality

interface

Eq

<T> {

boolean equalTo

(T other);}

class String extends

Eq<String> {

boolean equalTo

(String other) {…} …

}

“Hello”.

equalTo

(5)Slide6

(Typesafe

) Equality

{“

Hello”,”World

!”}

.equalTo

{“Ahoi

”,”World!”}

{inc

,

}

.equalTo

{

,id}

 Slide7

List (read-only)

Eq

covariant

contravariant

List<String>

List<Object>

Eq

<Object>

Eq

<String>

List<out T>

Eq

<in T>

:>

:>Slide8

i

nterface List<out T>

extends

Eq

<List<

Eq

<T>>>Slide9

i

nterface List<out T>

extends

Eq

<List<Eq

<T>>>

List<String>

<:

Eq<List<String>>

Eq

<List<

Eq

<String>>>

<:

Eq

<List<String>>

List<String>

<:

List<

Eq

<String>>

String

<:

Eq

<String>

Done!

List<String>

<:

Eq

<List<String>>

Eq

<List<

Eq

<String>>>

<:

Eq

<List<String>>

List<String>

<:

List<

Eq

<String>>

String

<:

Eq

<String>

Done!

List<String>

List<

Eq

<String>>

Eq

<

List<

Eq

<String>>

>

Eq

<

List<String>

>

String

Eq

<String>

List<

String

>

List<

Eq

<String>

>Slide10

List<T> extends

Eq

<List<

Eq

<T>>>

Andrew J. Kennedy and Benjamin C. Pierce

On Decidability of Nominal Subtyping with Variance

, FOOL-WOOD 2007

Expansive Inheritance!

List<T> extends Eq

<List<Eq<T>>>

List<T

>

List<

Eq

<T>>

Ross Tate, Alan Leung, and

Sorin

Lerner

Taming Wildcards in Java's Type System

, PLDI 2011

Nested

Contravariance

!

List<T> extends

Eq

<List<

Eq

<T>>>

List<T> extends

Eq

<List<

Eq

<T>>>Slide11

Trees

class Tree extends List<Tree>

Are trees equatable?Slide12

Are Trees equatable?Slide13

Are Trees

equatable?

Tree

<:

List<

Eq

<Tree>>

List<Tree>

<:

List<

Eq

<Tree>>

Tree

<:

Eq

<Tree>

List<Tree>

<:

Eq

<Tree>

Eq

<List<

Eq

<Tree>>>

<:

Eq

<Tree>

Tree

<:

List<

Eq

<Tree>>

Tree

<:

List<

Eq

<Tree>>

List<Tree>

<:

List<

Eq

<Tree>>

Tree

<:

Eq

<Tree>

List<Tree>

<:

Eq

<Tree>

Eq

<List<

Eq

<Tree>>>

<:

Eq

<Tree>

Tree

<:

List<

Eq

<Tree>>

Eq

<Tree>

List<

Eq

<Tree>

>

List<

Tree

>

Tree

Eq

<

Tree

>

Eq

<

List<

Eq

<Tree>>

>

List<

Eq

<Tree>>

TreeSlide14

Meh!Slide15

i

nterface List<out T>

extends

Eq

<List<

Eq

<T>>>Slide16
Slide17

WHY?Slide18

i

nterface List<out T>

extends

Eq

<List<

Eq

<T>>>

List<

Eq

<T

>>Slide19

List

<

String

>

List

<

Eq<

…>>

How do we use

Eq

<

…>?

With F-bounded polymorphism!

class String extends

Eq

<

String

>

class Set

<

T extends

Eq

<

T

>>

NOT as type arguments!

NOT for parameters!

NOT for fields!

NOT for local variables!

NOT for return types!Slide20

Shapes

Materials

Used in

Recursive inheritance definitions

Recursive type variable constraints

Used for

Type arguments

Method parametersReturn typesFieldsVariables

String

List<T>

Throwable

FileStream

Eq

<T>

Comparable<T>

Clonable

<T>

Summable

<T>Slide21

All Sheep in Scotland are blackSlide22

Read these 13 million lines of Code!

Can I script it?

NO!

I mean… YES!Slide23

Survey

13.5 million lines of open-source generic Java code

*http

://qualitascorpus.com

taken primarily from the

Qualitas Corpus*

No class was ever both a shape

and a material

from 60 projects

- Type arguments- Method parameters- Return

types- Fields & VariablesRecursive

- inheritance definitions

- type variable

constraintsSlide24

Thou shalt not

mix shapes

and materials!

Material-Shape SeparationSlide25
Slide26

Shapes

Materials

Used in

Recursive inheritance definitions

Recursive type variable

constraints

Used for

Type argumentsMethod parametersFieldsVariables

Recursive inheritance only through Shapes

Well-founded inheritanceSlide27

Well-founded Material Inheritance

class A extends B<C>, D<E> {…}

Inheritance hierarchies defined

independent of A

MaterialsSlide28

Well-founded Material Inheritance

class A extends B {…}

class B extends A {…}

class A extends List<B> {…}

class B extends List<A> {…}Slide29

Decidable Subtyping

With naïve algorithmsProven with a simple measureSlide30

Decidable Subtyping

Pred

<List<Object>>

<:

Pred

<Matrix<String>>

Matrix<String>

<:

List<Object>

List<List<String>>

<:

List<Object>

List<String>

<:

Object

Done!

Pred

<List<Object>>

<:

Pred

<Matrix<String>>

Matrix<String>

<:

List<Object>

List<List<String>>

<:

List<Object>

List<String>

<:

Object

Done!

material interface

Pred

<in T>

material interface Matrix<out T>

extends List<List<T>>Slide31

Decidable Subtyping

Pred

<

List<Object>

>

<:

Pred

<

Matrix<String>>

Matrix<String>

<:

List<Object>

List<

List<String>

>

<:

List<

Object

>

List<String>

<:

Object

Done!

Pred

<

List<Object>

>

<:

Pred

<

Matrix<String>

>

Matrix<String>

<:

List<Object>

List<

List<String>

>

<:

List<

Object

>

List<String>

<:

Object

Done!Slide32

Decidable Subtyping

Pred

<List<Object>>

<:

Pred

<Matrix<String>>

Matrix<String

>

<:

List<Object>

List<List<String

>>

<:

List<Object>

List<String>

<:

Object

Done!

Pred

<List<Object>>

<:

Pred

<Matrix<String>>

Matrix<String

>

<:

List<Object>

List<List<String

>>

<:

List<Object>

List<String>

<:

Object

Done!Slide33

Decidable Subtyping

A<T> extends B<C<T>>

Inheritance well-founded



measure function terminates

 Slide34

A<in T> extends

Eq

<A<List<T>>>

A<in T> extends

Eq

<

A<List<T>>

>Decidable Subtyping

All Materials

No Shapes in here

 Slide35
Slide36
Slide37

Joins

Most precise common supertype

someBool

? 42 : “Hello”

String

Integer = ?

 Slide38

Joins

Integer extends

Clonable

<Integer>

String extends

Clonable

<String>

String

Integer = ?

Clonable<Object>

Clonable<

Clonable

<

Object

>>

Clonable

<

Clonable

<

Clonable

<

Object

>>>Slide39

Computable Material Joins

Materials only: Object

Integer extends

Clonable

<Integer>

String extends

Clonable

<String>

String

Integer = ?

someBool ? 42 : “Hello”Slide40

Recursion on

and

E<

’>

Recursion

on

and

E<

’>

 MaterialJoins

A<T> extends C<T>

B<T> extends C<E<T>>

A<

>

B<

’>

Finite due to

well-founded

material inheritance

C<…>

C<

> C<E<

’>>

 Slide41

Higher KindsSlide42
Slide43

Conditional InheritanceSlide44

Decidable Subtyping

Higher Kinds

Computable Joins

Material-Shape SeparationSlide45
Slide46