PADL041 A Typeful Approach to Object- Oriented Programming with Multiple Inheritance Chiyan Chen, Rui Shi, Hongwei Xi Computer Science Dept. Boston University

PADL042 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.

PADL043 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.

PADL044 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,  ) → 

PADL045 Typed OOP Model  An improved typed OOP model based on the previous work (POPL ’ 03, Xi, Chen and Chen) Takes the “ objects as functions ” view Models 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

PADL046 Single Inheritance vs. Multiple Inheritance  Single Inheritance: Examples: Smalltalk, Java Easy to reason and implement.  Multiple Inheritance: Examples: Eiffel, C++ Complicated model Interaction with other OO features

PADL047 Subtlety with MI in C++ A B1B2 C A :: foo() = 0 B2 :: foo() = 2 B2 :: bar2() = foo() B1 :: foo() = 1 B1 :: bar1() = foo() C :: foo() = 3 C* pc = new C(); pc->bar1() returns 3

PADL048 Subtlety with MI in C++ A B1B2 C A :: foo() = 0 B2 :: foo() = 2 B2 :: bar2() = foo() B1 :: foo() = 1 B1 :: bar1() = foo() foo() is not overridden. C* pc = new C(); pc->bar1() returns 1

PADL049 Subtlety with MI in C++ A B1B2 C A :: foo() = 0 B2 :: foo() = 2 B2 :: bar2() = foo() B1 :: foo() = 1 B1 :: bar1() = foo() C :: bar3 () = B1 :: foo() D* pd = new D(); pd->bar3() returns 1 D D :: foo() = 4

PADL0410 Subtlety with MI in C++ A B1B2 C A :: foo() = 0 B2 :: foo() = 2 B2 :: bar2() = foo() B1 :: foo() = 1 B1 :: bar1() = foo() C :: foo () = B1 :: foo() D* pd = new D(); pd->bar2() returns 1 D foo() is not overridden.

PADL0411 Our Solution  Using explicit inheritance paths to direct method lookup. A B1B2 C A :: foo() = 0 B2 :: foo() = 2 B2 :: bar2() = A :: B2 :: foo() B1 :: foo() = 1 B1 :: bar1() = A :: B1 :: foo() C :: bar3 () = A :: B1 :: C :: foo() D* pd = new D(); pd->C :: D :: bar3() returns 4 D D :: foo() = 4

PADL0412 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

PADL0413 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 C 1 and C 2 to form a type PTH(C 1, C 2 ) for paths from C 1 to C 2  E.g. Abbreviate a path from class obj to cip as [CLSobj, CLSip, CLScip]

PADL0414 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:  c 0 :cls.  :type.PTH(c 0,C) → MSG(c 0,C,  ) →   There is another form of objects that are only constructed during run-time called temporary objects. Given a static class tag C, OBJ 0 (C) stands for the type:  c 0 :cls.  :type.MSG(c 0,C,  ) →   Note that a temporary object is not constructed by applying a regular object to a given path.

PADL0415 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) → OBJ 0 (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.

PADL0416 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 C 0, the super function associated with C 0 is assigned the type SUPER(C 0 ), which is the shorthand for the following type:  c:cls.PTH(C 0,c) → WRP (c) → WRP (c)

PADL0417 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)

PADL0418 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))

PADL0419 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)

PADL0420 Example for Method Lookup  Given two integer pair objects o 1 and o 2, let us consider O1O1 (MSGneq(o 2 )) [CLSeq, CLSip] No message handler for MSGneq(o 2 ) path2wrapper [CLSeq, CLSip] o 1 (MSGneq(o 2 )) SUPERip [CLSip] (SUPEReq [CLSeq, CLSip] nullWrapper) o 1 (MSGneq(o 2 )) No message handler for MSGneq(o 2 ) (SUPEReq [CLSeq, CLSip] nullWrapper) o 1 (MSGneq(o 2 )) Has message handler for MSGneq(o 2 ) O1O1 (MSGeq(o 2 )) [CLSeq, CLSip] not MSGeq(o 2 ) finally be handled by SUPERip

PADL0421 Conclusion  We have developed a general approach to multiple inheritance in a typed setting Representing inheritance paths as (typed) run- time proof-terms. Different strategies to resolve dispatching ambiguity Interaction between multiple inheritance and parametric polymorphism A clear model which can be implemented efficiently (e.g. by following C++ implementation)