23/4/18 PADL04 1

A Typeful Approach to Object-Oriented Programming with

Multiple Inheritance

Chiyan Chen, Rui Shi, Hongwei Xi

Computer Science Dept.

Boston University

23/4/18 PADL04 2

Motivation

Through translating high-level OOP syntax to a typed -calculus, the soundness of the typing rules for the OOP features follows from the soundness of the target system.

Within the Applied Type System (ATS) framework, we want to support OOP as an additional package without complicating the existing system.

23/4/18 PADL04 3

Objects as Functions

Examples: Smalltalk Interpretation: An object is represented as a

message interpreter, that is, a function which takes messages dispatched to it as arguments and then selects the appropriate behavior according to the messages.

Message passing: function application.

23/4/18 PADL04 4

Constructing an Integer Pair Object

fun newIntPair x y = let val xref = ref x and yref = ref y fun dispatch msg = case msg of | MSGgetfst => !xref | MSGgetsnd => !yref | MSGsetfst x' => (xref := x') | MSGsetsnd y' => (yref := y') | _ => raise UnknownMessage in dispatch end withtype int -> int -> OBJ(ip)

Given a class C, OBJ(C) is a shorthand for the following type:

:type.MSG(C,) →

23/4/18 PADL04 5

Typed OOP Model

An improved typed OOP model based on the previous work (POPL’03, Xi, Chen and Chen)Takes the “objects as functions” viewModels the basic features: message passing, single

inheritance.Provides a natural solution to the notion of “self type”.Subclassing is modeled with explicit proof terms.Supports multiple inheritance

23/4/18 PADL04 6

Single Inheritance vs. Multiple Inheritance

Single Inheritance:Examples: Smalltalk, JavaEasy to reason and implement.

Multiple Inheritance:Examples: Eiffel, C++Complicated modelInteraction with other OO features

23/4/18 PADL04 7

Subtlety with MI in C++

A

B1 B2

C

A :: foo() = 0

B2 :: foo() = 2B2 :: bar2() = foo()

B1 :: foo() = 1B1 :: bar1() = foo()

C :: foo() = 3

C* pc = new C();pc->bar1() returns 3

23/4/18 PADL04 8

Subtlety with MI in C++

A

B1 B2

C

A :: foo() = 0

B2 :: foo() = 2B2 :: bar2() = foo()

B1 :: foo() = 1B1 :: bar1() = foo()

foo() is not overridden.C* pc = new C();

pc->bar1() returns 1

23/4/18 PADL04 9

Subtlety with MI in C++

A

B1 B2

C

A :: foo() = 0

B2 :: foo() = 2B2 :: bar2() = foo()

B1 :: foo() = 1B1 :: bar1() = foo()

C :: bar3 () = B1 :: foo()D* pd = new D();

pd->bar3() returns 1

D D :: foo() = 4

23/4/18 PADL04 10

Subtlety with MI in C++

A

B1 B2

C

A :: foo() = 0

B2 :: foo() = 2B2 :: bar2() = foo()

B1 :: foo() = 1B1 :: bar1() = foo()

C :: foo () = B1 :: foo()D* pd = new D();

pd->bar2() returns 1

D foo() is not overridden.

23/4/18 PADL04 11

Our Solution

Using explicit inheritance paths to direct method lookup.

A

B1 B2

C

A :: foo() = 0

B2 :: foo() = 2B2 :: bar2() = A ::

B2 :: foo()

B1 :: foo() = 1B1 :: bar1() = A ::

B1 :: foo()

C :: bar3 () = A :: B1 :: C :: foo()

D* pd = new D();pd->C :: D :: bar3() returns 4

D D :: foo() = 4

23/4/18 PADL04 12

Run-Time Class Tags

datasort cls = obj | eq | ip | cip | … datatype ClS (cls) =

| CLSobj (obj) | CLSeq (eq) | CLSip (ip) | CLScip (cip) | ...

obj eq

Ip

cip

23/4/18 PADL04 13

Inheritance Paths

Paths from (super)classes to (sub)classes are treated as run-time proof terms (of subclass relation)

Declare PTH as a guarded datatype, which takes two static class tags C1 and C2 to form a type PTH(C1, C2) for paths from C1 to C2

E.g. Abbreviate a path from class obj to cip as [CLSobj, CLSip, CLScip]

23/4/18 PADL04 14

Regular/Temporary Objects

Given a static class tag C, OBJ(C) is the type for regular objects in class C, which is the shorthand for the following type:

c0:cls.:type.PTH(c0,C) → MSG(c0,C,) → There is another form of objects that are only

constructed during run-time called temporary objects. Given a static class tag C, OBJ0(C) stands for the type:

c0:cls. :type.MSG(c0,C,) → Note that a temporary object is not constructed by

applying a regular object to a given path.

23/4/18 PADL04 15

Wrapper Functions

A wrapper function for a class C is assigned the type WRP(C), where WRP(C) stands for the following type:

OBJ(C) → OBJ0(C)

Intuitively, a wrapper function turns a regular object in class C into a temporary object in class C.

A wrapper function is mainly used to “hard-wire” a method lookup strategy into a regular object.

23/4/18 PADL04 16

Super Functions

For each class C, there is a super function associated with it, which plays a key role in implementing (multiple) inheritance.

Given a static class tag C0, the super function associated with C0 is assigned the type SUPER(C0), which is the shorthand for the following type:

c:cls.PTH(C0,c) → WRP (c) → WRP (c)

23/4/18 PADL04 17

An Example of Super Function

fun SUPEReq pth wrp obj = let fun dispatch msg = case msg of | MSGeq (obj') => not (obj pth (MSGneq (obj')))

| MSGneq (obj') => not (obj pth (MSGeq (obj')))

| _ => wrp obj msg in dispatch end withtype {c:cls} PTH (eq,c) → WRP(c) → WRP (c)

23/4/18 PADL04 18

Chaining Super Functions Together

Given an object o, nullwrapper(o) constructs a temporary object, which raises the UnknownMessage exception for any message received.

Given a run-time inheritance path p, path2wrapper(p) turns the path to a wrapper.

e.g. path2wrapper [CLSobj, CLSip, CLScip] = SUPERcip [CLScip] (SUPERip [CLSip, CLScip] (SUPERobj [CLSobj, CLSip, CLScip] nullWrapper))

23/4/18 PADL04 19

Constructing Objects newintPair is an object constructor function, which takes two integers

to create an integer pair object. fun newIntPair x y = let val xref = ref x and yref = ref y fun dispatch pth msg = case msg of | MSGcopy => newIntPair (!xref) (!yref) | MSGgetfst => !xref | MSGsetfst x' => (xref := x') | … | _ => path2wrapper pth dispatch msg in dispatch end withtype int -> int -> OBJ (ip)

23/4/18 PADL04 20

Example for Method Lookup

Given two integer pair objects o1 and o2, let us consider

O1(MSGneq(o2))

[CLSeq, CLSip]No message handler for MSGneq(o2)

path2wrapper [CLSeq, CLSip] o1 (MSGneq(o2))

SUPERip [CLSip] (SUPEReq [CLSeq, CLSip] nullWrapper) o1 (MSGneq(o2))

No message handler for MSGneq(o2)

(SUPEReq [CLSeq, CLSip] nullWrapper) o1 (MSGneq(o2))

Has message handler for MSGneq(o2)

O1(MSGeq(o2))

[CLSeq, CLSip]not

MSGeq(o2) finally be handled by SUPERip

23/4/18 PADL04 21

Conclusion

We have developed a general approach to multiple inheritance in a typed settingRepresenting inheritance paths as (typed) run-ti

me proof-terms.Different strategies to resolve dispatching ambi

guityInteraction between multiple inheritance and par

ametric polymorphismA clear model which can be implemented efficie

ntly (e.g. by following C++ implementation)