A New Formalization of Subtyping to Match Subclasses to Subtypes

Transcription

1 A New Formalization of Subtyping to Match Subclasses to Subtypes Hyunik Na and Sukyoung Ryu Programming Language Research Group KAIST June 6, 2014 Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 1/28

2 This Paper A New Formalization of Subtyping to Match Subclasses to Subtypes Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 2/28

3 Goal A New Formalization of Subtyping to Match Subclasses to Subtypes Subclassing class ColorPoint extends Point explicit by declarations easy for programmers Subtyping ColorPoint <: Point implicit by inference easy for type checkers Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 3/28

4 Goal A New Formalization of Subtyping to Match Subclasses to Subtypes Subclassing class ColorPoint extends Point explicit by declarations easy for programmers Subtyping ColorPoint <: Point implicit by inference easy for type checkers Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 3/28

5 Goal A New Formalization of Subtyping to Match Subclasses to Subtypes Subclassing class ColorPoint extends Point explicit by declarations easy for programmers Subtyping ColorPoint <: Point implicit by inference easy for type checkers Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 3/28

6 Solution A New Formalization of Subtyping to Match Subclasses to Subtypes Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 4/28

7 Motivation The self-type idiom in Fortress: trait Equality Self extends Equality Self abstract opr =(self, other : Self) : Boolean end This type Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 5/28

8 Motivation The self-type idiom in Fortress: trait Equality Self extends Equality Self abstract opr =(self, other : Self) : Boolean end This type Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 5/28

9 This Type in Practice Abstract domains for analyzing JavaScript programs Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 6/28

10 This Type in Practice Abstract domains for analyzing JavaScript programs SAFE: Scalable Analysis Framework for ECMAScript Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 7/28

11 This Type in Practice Abstract domains for analyzing JavaScript programs ˆv Value = PValue ( Loc) pv ˆ PValue = Ûndef Null Bool Number Ŝtring Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 8/28

12 This Type in Practice Abstract domains for analyzing JavaScript programs ˆv Value = PValue ( Loc) pv ˆ PValue = Ûndef Null Bool Number Ŝtring Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 9/28

13 This Type in Practice Abstract domains for analyzing JavaScript programs abstract class AbsBase { def istop(): Boolean def isbottom(): Boolean def isconcrete(): Boolean def toabsstring(): AbsString } Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 10/28

14 This Type in Practice Abstract domains for analyzing JavaScript programs sealed abstract class AbsNull extends AbsBase { /* partial order */ def <= (that: AbsNull) = {... } /* join */ def + (that: AbsNull) = {... } /* meet */ def <> (that: AbsNull) = {... } }... Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 11/28

15 This Type in Practice Abstract domains for analyzing JavaScript programs sealed abstract class AbsString extends AbsBase { /* partial order */ def <= (that: AbsString) = {... } /* join */ def + (that: AbsString) = {... } /* meet */ def <> (that: AbsString) = {... } }... Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 12/28

16 This Type in Practice Abstract domains for analyzing JavaScript programs abstract class AbsBase { /* partial order */ def <= (that: ThisType): Boolean } /* join */ def + (that: ThisType): ThisType /* meet */ def <> (that: ThisType): ThisType... Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 13/28

17 This Type in Practice Abstract domains for analyzing JavaScript programs Signatures of required methods in AbsBase Exact class matches at run time Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 14/28

18 This Type in Practice Abstract domains for analyzing JavaScript programs Signatures of required methods in AbsBase Exact class matches at run time Bruno Oliveira s solution abstract class AbsBase { type ThisType <: AbsBase def + (that: ThisType): ThisType... } case class AbsString extends AbsBase { type ThisType = AbsString override def + (that : ThisType): ThisType =... new AbsString()... } Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 15/28

19 This Type in Practice Abstract domains for analyzing JavaScript programs Signatures of required methods in AbsBase Exact class matches at run time Multiple implementations for one abstract domain abstract class AbsDomain {... } abstract class AbsBase[A] extends AbsDomain {... } class AbsString extends AbsBase[String] {... } class AbsStringSet extends AbsString {... } class AbsStringAutomata extends AbsString {... } Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 16/28

20 This Type in Practice Abstract domains for analyzing JavaScript programs Signatures of required methods in AbsBase Exact class matches at run time Multiple implementations for one abstract domain abstract class AbsDomain {... } abstract class AbsBase[A] extends AbsDomain {... } class AbsString extends AbsBase[String] {... } class AbsStringSet extends AbsString {... } class AbsStringAutomata extends AbsString {... } Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 16/28

21 This Type in Practice Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 17/28

22 This Type in Theory This-typed methods: owner types in their parameter types or return types abstract class AbsBase { /* partial order */ def <= (that: ThisType): Boolean } /* join */ def + (that: ThisType): ThisType /* meet */ def <> (that: ThisType): ThisType... Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 18/28

23 This Type in Theory This-typed methods: owner types in their parameter types or return types Traditional This type declared type of a receiver inexact compile-time type Our This type run-time type of a receiver exact run-time type not available but sayable at compile time Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 19/28

24 This Type in Theory This-typed methods: owner types in their parameter types or return types Traditional This type declared type of a receiver inexact compile-time type Our This type run-time type of a receiver exact run-time type not available but sayable at compile time Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 19/28

25 This Type in Calculus (TLDI 12) CoreThisJava, a formal core calculus to support the This type: new typing features exact class types of the form #C for a class C This type variable named wildcards of the form </X/> to describe more equality relationships between exact types exact type inference to lessen the programmers burden of using explicit annotations new language constructs virtual constructors to describe methods with ThisTyped results classesmatch to compare run-time types Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 20/28

26 This Type in Java (APLAS 13) ThisJava, an open-source implementation using JastAddJ: backward compatible compilation to Java bytecode practical interactions with existing Java features Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 21/28

27 This Type in Type System (FLOPS 14) Traditional subtyping cannot support subtyping by inheritance. class Point { int x; Point(int i) { this.x = i; } boolean equals(this other) { return this.x == other.x; } } class ColorPoint extends Point { int color; ColorPoint(int i, int c) { super(i); this.color = c; } boolean equals(this other) { return this.x == other.x && this.color == other.color; } } Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 22/28

28 This Type in Type System (FLOPS 14) Traditional subtyping cannot derive the following: µt.{x: int, c: int, eq: t bool } µt.{x: int, eq: t bool } New subtyping can derive the following: s < µt.{x: int, c: int, eq: t bool}.s <: s < µt.{x: int, eq: t bool}.s by distinguishing record types µt.{l i : τ i i 1..n } and some-record types s < µt.{l i : τ i i 1..n }.s explicitly Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 23/28

29 This Type in Type System (FLOPS 14) Traditional subtyping cannot derive the following: µt.{x: int, c: int, eq: t bool } µt.{x: int, eq: t bool } New subtyping can derive the following: s < µt.{x: int, c: int, eq: t bool}.s <: s < µt.{x: int, eq: t bool}.s by distinguishing record types µt.{l i : τ i i 1..n } and some-record types s < µt.{l i : τ i i 1..n }.s explicitly Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 23/28

30 This Type in Type System (FLOPS 14) Traditional subtyping cannot derive the following: µt.{x: int, c: int, eq: t bool } µt.{x: int, eq: t bool } New subtyping can derive the following: s < µt.{x: int, c: int, eq: t bool}.s <: s < µt.{x: int, eq: t bool}.s by distinguishing record types µt.{l i : τ i i 1..n } and some-record types s < µt.{l i : τ i i 1..n }.s explicitly Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 23/28

31 This Type in Type System (FLOPS 14) Record types µt.{l i : τ i i 1..n } types of run-time objects that have exactly those members l 1, l 2,..., l n exact run-time types Some-record types s < µt.{l i : τ i i 1..n }.s types of compile-time expressions that may evaluate to objects of record types specializing µt.{l i : τ i i 1..n } inexact compile-time types Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 24/28

32 This Type in Type System (FLOPS 14) Record types µt.{l i : τ i i 1..n } types of run-time objects that have exactly those members l 1, l 2,..., l n exact run-time types Some-record types s < µt.{l i : τ i i 1..n }.s types of compile-time expressions that may evaluate to objects of record types specializing µt.{l i : τ i i 1..n } inexact compile-time types Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 24/28

33 This Type in Type System (FLOPS 14) τ, υ ::= t ρ α γ τ τ type (revised) α, β ::= i µt.{l i : τ 1..n i } record type (revised) γ ::= s < α.s some-record type Specializing: α < β where ::= {t i i 1..n } [Specializing] n 0, m 0 t / i 1..n: {t} τ i <: υ i µt.{l i : τ i i 1..n+m } < µt.{l i : υ i i 1..n } Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 25/28

34 This Type in Type System (FLOPS 14) τ, υ ::= t ρ α γ τ τ type (revised) α, β ::= i µt.{l i : τ 1..n i } record type (revised) γ ::= s < α.s some-record type Specializing: α < β where ::= {t i i 1..n } [Specializing] n 0, m 0 t / i 1..n: {t} τ i <: υ i µt.{l i : τ i i 1..n+m } < µt.{l i : υ i i 1..n } Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 25/28

35 This Type in Type System (FLOPS 14) τ, υ ::= t ρ α γ τ τ type (revised) α, β ::= i µt.{l i : τ 1..n i } record type (revised) γ ::= s < α.s some-record type Revised subtyping: τ <: υ where ::= {t i i 1..n } [RS-Prim] ρ <: ρ [RS-Func] υ <: τ τ <: υ τ τ <: υ υ [RS-TVar] t t <: t [RS-RtoR] [RS-RtoS] [RS-StoS] α <: α α < β α <: s < β.s α < β s < α.s <: s < β.s Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 26/28

36 This Type in Type System (FLOPS 14) i Record types µt.{l i : τ 1..n i } i Some-record types s < µt.{l i : τ 1..n i }.s Revised subtyping [RS-RtoS] α < β α <: s < β.s [RS-StoS] α < β s < α.s <: s < β.s Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 27/28

37 Conclusion Supporting ThisTyped methods is an important real-world problem. Adding typing features and language constructs can support more ThisTyped methods. An open-source prototype implementation is available: Inheritance can be subtyping. s < µt.{x: int, c: int, eq: t bool}.s <: s < µt.{x: int, eq: t bool}.s Hyunik Na and Sukyoung Ryu A New Formalization of Subtyping to Match Subclasses to Subtypes 28/28