The Liskov Substitution Principle



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1

 



The Liskov Substitution Principle

 

This is the second of my 



 

Engineering Notebook

 

 columns for 



 

The C++ Report

 

. The articles



that will appear in this column will focus on the use of C++ and OOD, and will address

issues of software engineer-

ing. I will strive for articles

that are pragmatic and

directly useful to the soft-

ware engineer in the

trenches. In these articles I

will make use of Booch’s

and Rumbaugh’s new 

 

uni-

fied

 

 notation (Version 0.8)



for documenting object ori-

ented designs. The sidebar

provides a brief lexicon of

this notation.



 

Introduction

 

My last column (Jan, 96) talked about the Open-Closed principle. This principle is the



foundation for building code that is maintainable and reusable. It states that well designed

code can be extended without modification; that in a well designed program new features

are added by adding new code, rather than by changing old, already working, code. 

The primary mechanisms behind the Open-Closed principle are abstraction and poly-

morphism. In statically typed languages like C++, one of the key mechanisms that sup-

ports abstraction and polymorphism is inheritance. It is by using inheritance that we can

create derived classes that conform to the abstract polymorphic interfaces defined by pure

virtual functions in abstract base classes.

What are the design rules that govern this particular use of inheritance? What are the

characteristics of the best inheritance hierarchies? What are the traps that will cause us to

create hierarchies that do not conform to the Open-Closed principle? These are the ques-

tions that this article will address.

Base Class

Base Class

Base Class

Derived 1

Derived 2

Had by


Reference

Had By Value

Used

Sidebar: Unified Notation 0.8



 

2

 



The Liskov Substitution Principle

 

The Liskov Substitution Principle

 

F

 

UNCTIONS

 

 

 

THAT

 

 

 

USE

 

 

 

POINTERS

 

 

 

OR

 

 

 

REFERENCES

 

 

 

TO

 

 

 

BASE

 

 

 

CLASSES

 

 

 

MUST

 

 

 

BE

 

 

 

ABLE

 

 

 

TO

 

 

 

USE

 

 

 

OBJECTS

 

 

 

OF

 

 

 

DERIVED

 

 

 

CLASSES

 

 

 

WITHOUT

 

 

 

KNOWING

 

 

 

IT

 

.

 

The above is a paraphrase of the Liskov Substitution Principle (LSP). Barbara Liskov first



wrote it as follows nearly 8 years ago

 

1



 

:

 



What is wanted here is something like the following substitution property: If

for each object o

 

1

 

 of type S there is an object o

 

2

 

 of type T such that for all

programs P

 

 



 

defined in terms of T, the behavior of P is unchanged when o

 

1

 

 is

substituted for o

 

2

 

 then S is a subtype of T.

 

The importance of this principle becomes obvious when you consider the conse-



quences of violating it. If there is a function which does not conform to the LSP, then that

function uses a pointer or reference to a base class, but must 



 

know

 

 about all the derivatives



of that base class. Such a function violates the Open-Closed principle because it must be

modified whenever a new derivative of the base class is created.



 

A Simple Example of a Violation of LSP

 

One of the most glaring violations of this principle is the use of C++ Run-Time Type



Information (RTTI) to select a function based upon the type of an object. i.e.:

 

void DrawShape(const Shape& s)



{

if (typeid(s) == typeid(Square))

DrawSquare(static_cast(s));

else if (typeid(s) == typeid(Circle))

DrawCircle(static_cast(s));

}

 



[Note: 

 

static_cast



 

 is one of the new cast operators. In this example it works

exactly like a regular cast. i.e. 

 

DrawSquare((Square&)s);



 

. However the new syn-

tax has more stringent rules that make is safer to use, and is easier to locate with tools such

as grep. It is therefore preferred.]

Clearly the 

 

DrawShape



 

 function is badly formed. It must know about every possible

derivative of the 

 

Shape



 

 class, and it must be changed whenever new derivatives of

 

Shape


 

 are created. Indeed, many view the structure of this function as anathema to

Object Oriented Design.

 

1. Barbara Liskov, “Data Abstraction and Hierarchy,” 



 

SIGPLAN Notices, 

 

23,5 (May, 1988).




 

3

 



: The Liskov Substitution Principle

 

Square and Rectangle, a More Subtle Violation.

 

However, there are other, far more subtle, ways of violating the LSP. Consider an



application which uses the 

 

Rectangle



 

 class as described below:

 

class Rectangle



{

public:


void   SetWidth(double w)  {itsWidth=w;}

void   SetHeight(double h) {itsHeight=w;}

double GetHeight() const   {return itsHeight;}

double GetWidth() const    {return itsWidth;}

private:

double itsWidth;

double itsHeight;

};

 



Imagine that this application works well, and is installed in

many sites. As is the case with all successful software, as its

users’ needs change, new functions are needed. Imagine that

one day the users demand the ability to manipulate squares in

addition to rectangles.

It is often said that, in C++, inheritance is the ISA relation-

ship. In other words, if a new kind of object can be said to fulfill

the ISA relationship with an old kind of object, then the class of

the new object should be derived from the class of the old

object.


Clearly, a square is a rectangle for all normal intents and

purposes. Since the ISA relationship holds, it is logical to

model the 

 

Square



 

 class as being derived from 

 

Rectangle



 

.

(See Figure 1.)



This use of the ISA relationship is considered by many to be one of the fundamental

techniques of Object Oriented Analysis. A square is a rectangle, and so the 

 

Square


 

 class


should be derived from the 

 

Rectangle



 

 class. However this kind of thinking can lead to

some subtle, yet significant, problems. Generally these problem are not foreseen until we

actually try to code the application. 

Our first clue might be the fact that a 

 

Square



 

 does not need both 

 

itsHeight



 

 and


 

itsWidth


 

 member variables. Yet it will inherit them anyway. Clearly this is wasteful.

Moreover, if we are going to create hundreds of thousands of 

 

Square



 

 objects (e.g. a

CAD/CAE program in which every pin of every component of a complex circuit is drawn

as a square), this waste could be extremely significant. 

However, let’s assume that we are not very concerned with memory efficiency. Are

there other problems? Indeed! 

 

Square


 

 will inherit the 

 

SetWidth


 

 and 


 

SetHeight

 

functions. These functions are utterly inappropriate for a 



 

Square


 

, since the width and

height of a square are identical.”. This should be a significant clue that there is a problem

Rectangle

Square

Figure 1.



 

4

 



The Liskov Substitution Principle

 

with the design. However, there is a way to sidestep the problem. We could override 



 

Set-


Width

 

 and 



 

SetHeight

 

 as follows:



 

void Square::SetWidth(double w)

{

Rectangle::SetWidth(w);



Rectangle::SetHeight(w);

}

void Square::SetHeight(double h)



{

Rectangle::SetHeight(h);

Rectangle::SetWidth(h);

}

 



Now, when someone sets the width of a 

 

Square



 

 object, its height will change corre-

spondingly. And when someone sets its height, the width will change with it. Thus, the

invariants of the 

 

Square


 

 remain intact. The 

 

Square


 

 object will remain a mathematically

proper square.

 

Square s;



s.SetWidth(1); // Fortunately sets the height to 1 too.

s,SetHeight(2); // sets width and heigt to 2, good thing.

 

But consider the following function:



 

void f(Rectangle& r)

{

r.SetWidth(32); // calls Rectangle::SetWidth



}

 

If we pass a reference to a 



 

Square


 

 object into this function, the 

 

Square


 

 object will

be corrupted because the height won’t be changed. This is a clear violation of LSP. The 

 

f



 

function does not work for derivatives of its arguments. The reason for the failure is that

 

SetWidth


 

 and 


 

SetHeight

 

 were not declared 



 

virtual


 

 in 


 

Rectangle

 

.

We can fix this easily. However, when the creation of a derived class causes us to



make changes to the base class, it often implies that the design is faulty. Indeed, it violates

the Open-Closed principle. We might counter this with argument that forgetting to make

 

SetWidth


 

 and 


 

SetHeight

 

 

 



virtual

 

 was the real design flaw, and we are just fixing it



now. However, this is hard to justify since setting the height and width of a rectangle are

exceedingly primitive operations. By what reasoning would we make them 

 

virtual


 

 if


we did not anticipate the existence of 

 

Square



 

.

Still, let’s assume that we accept the argument, and fix the classes. We wind up with



the following code:

 

class Rectangle



{

public:


virtual void SetWidth(double w)  {itsWidth=w;}

virtual void SetHeight(double h) {itsHeight=h;}

double       GetHeight() const   {return itsHeight;}

double       GetWidth() const    {return itsWidth;}




 

5

 



: The Liskov Substitution Principle

 

private:



double itsHeight;

double itsWidth;

};

class Square : public Rectangle



{

public:


virtual void SetWidth(double w);

virtual void SetHeight(double h);

};

void Square::SetWidth(double w)



{

Rectangle::SetWidth(w);

Rectangle::SetHeight(w);

}

void Square::SetHeight(double h)



{

Rectangle::SetHeight(h);

Rectangle::SetWidth(h);

}

 



The Real Problem

 

At this point in time we have two classes, 



 

Square


 and 

Rectangle

, that appear to work.

No matter what you do to a 

Square

 object, it will remain consistent with a mathematical



square. And regardless of what you do to a 

Rectangle

 object, it will remain a mathe-

matical rectangle. Moreover, you can pass a 

Square

 into a function that accepts a pointer



or reference to a 

Rectangle

, and the 

Square


 will still act like a square and will remain

consistent. 

Thus, we might conclude that the model is now self consistent, and correct. However,

this conclusion would be amiss. A model that is self consistent is not necessarily consis-

tent with all its users! Consider function 

g

 below. 



void g(Rectangle& r)

{

r.SetWidth(5);



r.SetHeight(4);

assert(r.GetWidth() * r.GetHeight()) == 20);

}

This function invokes the 



SetWidth

 and 


SetHeight

 members of what it believes

to be a 

Rectangle

. The function works just fine for a 

Rectangle

, but declares an

assertion error if passed a 

Square

. So here is the real problem: Was the programmer who



wrote that function justified in assuming that changing the width of a 

Rectangle



 leaves

its height unchanged

Clearly, the programmer of 

g

 made this very reasonable assumption. Passing a



Square

 to functions whose programmers made this assumption will result in problems.

Therefore, there exist functions that take pointers or references to 

Rectangle

 objects,



6

The Liskov Substitution Principle

but cannot operate properly upon 

Square

 objects. These functions expose a violation of



the LSP. The addition of the 

Square


 derivative of 

Rectangle

 has broken these func-

tion; and so the Open-Closed principle has been violated.



Validity is not Intrinsic

This leads us to a very important conclusion. A model, viewed in isolation, can not be

meaningfully validated. The validity of a model can only be expressed in terms of its cli-

ents. For example, when we examined the final version of the 

Square

 and 


Rectangle

classes in isolation, we found that they were self consistent and valid. Yet when we looked

at them from the viewpoint of a programmer who made reasonable assumptions about the

base class, the model broke down.

Thus, when considering whether a particular design is appropriate or not, one must

not simply view the solution in isolation. One must view it in terms of the reasonable

assumptions that will be made by the users of that design.

What Went Wrong? (W

3

)

So what happened? Why did the apparently reasonable model of the 

Square

 and 


Rect-

angle


 go bad. After all, isn’t a 

Square


 a 

Rectangle

? Doesn’t the ISA relationship

hold?


No! A square might be a rectangle, but a 

Square


 object is definitely not a 

Rectan-


gle

 object. Why? Because the behavior of a 

Square

 object is not consistent with the



behavior of a 

Rectangle

 object. Behaviorally, a 

Square


 is not a 

Rectangle

! And it

is behavior that software is really all about. 

The LSP makes clear that in OOD the ISA relationship pertains to behavior. Not

intrinsic private behavior, but extrinsic public behavior; behavior that clients depend upon.

For example, the author of function 

g

 above depended on the fact that 



Rectangles

behave such that their height and width vary independently of one another. That indepen-

dence of the two variables is an extrinsic public behavior that other programmers are likely

to depend upon. 

In order for the LSP to hold, and with it the Open-Closed principle, all derivatives

must conform to the behavior that clients expect of the base classes that they use.



Design by Contract

There is a strong relationship between the LSP and the concept of Design by Contract as

expounded by Bertrand Meyer

2

. Using this scheme, methods of classes declare precondi-



tions and postconditions. The preconditions must be true in order for the method to exe-

cute. Upon completion, the method guarantees that the postcondition will be true.

2. Object Oriented Software Construction, Bertrand Meyer, Prentice Hall, 1988



7

: The Liskov Substitution Principle

We can view the postcondition of 

Rectangle::SetWidth(double w)

 as:


assert((itsWidth == w) && (itsHeight == old.itsHeight));

Now the rule for the preconditions and postconditions for derivatives, as stated by

Meyer

3

, is:



...when redefining a routine [in a derivative], you may only replace its

precondition by a weaker one, and its postcondition by a stronger one.

In other words, when using an object through its base class interface, the user knows

only the preconditions and postconditions of the base class. Thus, derived objects must not

expect such users to obey preconditions that are stronger then those required by the base

class. That is, they must accept anything that the base class could accept. Also, derived

classes must conform to all the postconditions of the base. That is, their behaviors and out-

puts must not violate any of the constraints established for the base class. Users of the base

class must not be confused by the output of the derived class.

Clearly, the postcondition of 

Square::SetWidth(double w)

 is weaker than

the postcondition of 

Rectangle::SetWidth(double w)

 above, since it does not

conform to the base class clause “

(itsHeight == old.itsHeight)

”. Thus,

Square::SetWidth(double w)

 violates the contract of the base class.

Certain languages, like Eiffel, have direct support for preconditions and postcondi-

tions. You can actually declare them, and have the runtime system verify them for you.

C++ does not have such a feature. Yet, even in C++ we can manually consider the precon-

ditions and postconditions of each method, and make sure that Meyer’s rule is not vio-

lated. Moreover, it can be very helpful to document these preconditions and postconditions

in the comments for each method.

A Real Example.

Enough of squares and rectangles! Does the

LSP have a bearing on real software? Let’s

look at a case study that comes from a

project that I worked on a few years ago. 

Motivation

I was unhappy with the interfaces of the

container classes that were available through

3. ibid, p256

Set

BoundedSet



ThirdParty

BoundedSet

UnboundedSet

ThirdParty

UnboundedSet

Figure 2: Container Hierarchy



8

A Real Example.

third parties. I did not want my application code to be horribly dependent upon these con-

tainers because I felt that I would want to replace them with better classes later. Thus I

wrapped the third party containers in my own abstract interface. (See Figure 2) 

I had an abstract class called 

Set


 which presented pure virtual 

Add


Delete


, and

IsMember


 functions.

template  

class Set

{

public:



virtual void Add(const T&) = 0;

virtual void Delete(const T&) = 0;

virtual bool IsMember(const T&) const = 0;

};

This structure unified the Unbounded and Bounded varieties of the two third party



sets and allowed them to be accessed

through a common interface. Thus

some client could accept an argument

of type 


Set&

 and would not care

whether the actual 

Set


 it worked on

was of the 

Bounded

 or


Unbounded

 variety. (See the

PrintSet

 function listing.)

This ability to neither know nor care the type of 

Set


 you are operating on is a big

advantage. It means that the programmer can decide which kind of 

Set

 is needed in each



particular instance. None of the client functions will be affected by that decision. The pro-

grammer may choose a 

BoundedSet

 when memory is tight and speed is not critical, or

the programmer may choose an 

UnboundedSet

 when memory is plentiful and speed is

critical. The client functions will manipulate these objects through the interface of the base

class 

Set


, and will therefore not know or care which kind of 

Set


 they are using.

Problem

I wanted to add a 

Persistent-

Set


 to this hierarchy. A persistent set is

a set which can be written out to a

stream, and then read back in later, pos-

sibly by a different application. Unfor-

tunately, the only third party container

that I had access to, that also offered

persistence, was not a template class.

Instead, it accepted objects that were

template

void PrintSet(const Set& s)

{

for (Iteratori(s); i; i++)



cout << (*i) << endl;

}

Set



PersistentSet

ThirdParty

PersistentSet

PersistentObject



Figure 3. Persistent Set


9

: The Liskov Substitution Principle

derived from the abstract base class 

PersistentObject

. I created the hierarchy

shown in Figure 3. 

On the surface of it, this might look all right. However there is an implication that is

rather ugly. When a client is adding members to the base class Set, how is that client sup-

posed to ensure that it only adds derivatives of 

PersistentObject

 if the 


Set

 happens


to be a 

PersistentSet

?

Consider the code for 



PersistentSet::Add:

template

void PersistentSet::Add(const T& t)

{

PersistentObject& p = 



dynamic_cast
(t); // throw bad_cast

itsThirdPartyPersistentSet.Add(p);

}

This code makes it clear that if any client tries to add an object that is not derived from



the class 

PersistentObject

 to my 

PersistentSet



, a runtime error will ensue.

The 


dynamic_cast

 will throw 

bad_cast

 (one of the standard exception objects).

None of the existing clients of the abstract base class 

Set


 expect exceptions to be thrown

on 


Add

. Since these functions will be confused by a derivative of 

Set

, this change to the



hierarchy violates the LSP.

Is this a problem? Certainly. Functions that never before failed when passed a deriva-

tive of 

Set


, will now cause runtime errors when passed a 

PersistentSet

. Debugging

this kind of problem is relatively difficult since the runtime error occurs very far away

from the actual logic flaw. The logic flaw is either the decision to pass a 

Persistent-

Set

 into the failed function, or it is the decision to add an object to the 



Persistent-

Set


 that is not derived from 

PersistentObject

. In either case, the actual decision

might be millions of instructions away from the actual invocation of the 

Add

 method.


Finding it can be a bear. Fixing it can be worse.

A Solution that does not conform to the LSP.

How do we solve this problem? Several years ago, I solved it by convention. Which is

to say that I did not solve it in source code. Rather I instated a convention whereby 

Per-


sistentSet

 and 


PersistentObject

 were not known to the application as a whole.

They were only known to one particular module. This module was responsible for reading

and writing all the containers. When a container needed to be written, its contents were

copied into 

PersistentObjects

 and then added to 

PersistentSets

, which were

then saved on a stream. When a container needed to be read from a stream, the process

was inverted. A 

PersistentSet

 was read from the stream, and then the 

Persisten-

tObjects

 were removed from the 

PersistentSet

 and copied into regular (non-per-

sistent) objects which were then added to a regular 

Set


.


10

A Real Example.

This solution may seem overly restrictive, but it was the only way I could think of to

prevent PersistentSet objects from appearing at the interface of functions that would want

to add non-persistent objects to them. Moreover it broke the dependency of the rest of the

application upon the whole notion of persistence.

Did this solution work? Not really. The convention was violated in several parts of the

application by engineers who did not understand the necessity for it. That is the problem

with conventions, they have to be continually re-sold to each engineer. If the engineer does

not agree, then the convention will be violated. And one violation ruins the whole struc-

ture.


An LSP Compliant Solution

How would I solve this now? I

would acknowledge that a 

Persis-


tentSet

 does not have an ISA rela-

tionship with 

Set


; that it is not a proper

derivative of 

Set

. Thus I would Sepa-



rate the hierarchies. But not completely.

There are features that 

Set

 and 


Per-

sistentSet

 have in common. In fact,

it is only the 

Add

 method that causes the



difficulty with LSP. Thus I would create

a hierarchy in which both 

Set

 and


PersistentSet

 were siblings

beneath an abstract interface that

allowed for membership testing, itera-

tion, etc. (See Figure 4.) This would

allow 


PersistentSet

 objects to be

Iterated and tested for membership, etc. But would not afford the ability to add objects that

were not derived from 

PersistentObject

 to a 


PersistentSet

.

template



void PersistentSet::Add(const T& t)

{

itsThirdPartyPersistentSet.Add(t);



// This will generate a compiler error if t is

// not derived from PersistentObject.

}

As the listing above shows, any attempt to add an object that is not derived from



PersistentObject

 to a 


PersistentSet

 will result in a compilation error. (The

interface of the third party persistent set expects a 

PersistentObject&

).

Figure 4: Separate Hierarchy

Iterable


Container

Member


Container

Set


PersistentSet

ThirdParty

PersistentSet

Persistent

Object

Abstract

Abstract

Abstract

Allows iterators to be

created.

Allows for 

Membershi

p

Testing.




11

: The Liskov Substitution Principle

Conclusion

The Open-Closed principle is at the heart of many of the claims made for OOD. It is when

this principle is in effect that applications are more maintainable, reusable and robust. The

Liskov Substitution Principle (A.K.A Design by Contract) is an important feature of all

programs that conform to the Open-Closed principle. It is only when derived types are

completely substitutable for their base types that functions which use those base types can

be reused with impunity, and the derived types can be changed with impunity.

This article is an extremely condensed version of a chapter from my new book: Pat-



terns and Advanced Principles of OOD, to be published soon by Prentice Hall. In subse-

quent articles we will explore many of the other principles of object oriented design. We

will also study various design patterns, and their strengths and weaknesses with regard to

implementation in C++. We will study the role of Booch’s class categories in C++, and

their applicability as C++ namespaces. We will define what “cohesion” and “coupling”

mean in an object oriented design, and we will develop metrics for measuring the quality



of an object oriented design. And, after that, many other interesting topics.


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