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pinFrom Mechanism to Method: Substitutability

Overload Journal #39 - Sep 2000 + Programming Topics   Author: Kevlin Henney

If I were to say that C++ is a language with a large number of features, it is unlikely that I would be in much danger of igniting a flame war. Where fact gives way to opinion - and sometimes on to the holiest and heated of wars - is in the recommendation of how to work with these features. What is their purpose? What concepts do they express? In short, what methods give sense to the mechanisms, raising the programmer's view of the language from a shopping list of features to recipes that marshal features into designs? Sure, programmers need knowledge of syntax and semantics to make any headway with the language, but this learning curve pretty soon peters out to a plateau, with the sheer face of design rising above it.

Idioms offer a steady and complementary companion route; patterns that capture an understanding of problem and solution married together at the level of the language [Coplien1992, Coplien1996]. They establish a vocabulary for communicating and formulating design, where "design is the activity of aligning the structure of the application analysis with the available structures of the solution domain" [Coplien1999].

On the other hand, while practices based on accepted wisdom generate comfortable habits, generally simplifying day to day development, this is no reason to be complacent. Occasionally revisiting old maxims can reveal other useful insights that were hiding in the shadows [Henney1998].

'Is a' is not Enough

Attractive as the idea at first seems, the English language does not offer consistently useful advice for the analysis of problems and the statement of software structure. Excitement about nouns as objects and verbs as methods often wears off when the nouning of verbs and verbing of nouns is recognized as common usage.

So it is with the common good practice recommendation guiding the use of public inheritance: It should model an is a relationship rather than ad hoc code reuse. For example, a save-dialog is a dialog box and a list is a sequence, whereas a bounded list is not an unbounded list and vice-versa. The view is that reuse (over)driven approaches lead to the kind of spaghetti inheritance hierarchies that give inheritance a bad name, and the is a approach constrains inheritance hierarchies to more closely model expected classifications.

However, like all analogies it has a breaking point, beyond which rhyme and reason denatures to protracted theological debate around the coffee machine. For instance, Rex is a dog, and although his owner might regard him in a class of his own, it is more likely that developers would view this as an instance of relationship. Preferring is a kind of to is a steers us clear of many of the vagaries of natural language, but not so clear that it clarifies how state models are inherited or how a virtual function should be overridden. For example, can a function that in the base class is guaranteed to accommodate null pointer arguments and never returns a null pointer be sensibly overridden to accept only non-null arguments and return null pointers? The linguistic view does not provide a useful map through such territory.

Liskov Substitution Principle

The Liskov Substitution Principle (LSP) [Liskov1987, Coplien1992] is often cited as giving more detailed guidance on the use of inheritance. It makes a clear separation between type - described in terms of the behavior of operations - and class - the realization of the behavior in programmatic detail - before establishing the criteria for a subtyping relationship in terms of conformant behavior:

A type hierarchy is composed of subtypes and supertypes. The intuitive idea of a subtype is one whose objects provide all the behavior of objects of another type (the supertype) plus something extra. What is wanted here is something like the following substitution property: If for each object o1 of type S there is an object o2 of type T such that for all programs P defined in terms of T, the behavior of P is unchanged when o1 is substituted for o2, then S is a subtype of T.

So, in answer to the previous question: No, a function cannot sensibly be overridden to strengthen the requirements on its arguments and weaken the requirements on its return type. This same recommendation can be found echoed in Design by Contract [Meyer1997].

Polymorphic Polymorphism

LSP is normally presented as an inheritance guideline, but taking a step back we can see that it need not be so narrow: It is a relationship about types and not implementations, i.e. subtyping and not subclassing. LSP relies on polymorphism; the concept of structural relationship, such as public inheritance, need not enter into it.

C++ developers have inherited (sic) from other OO languages and literature the notion that polymorphism concerns only inheritance and virtual functions. Deserving of its name, polymorphism manifests itself in many forms (see Table 1). This classification [Cardelli-1985] gives us a broader and more liberated view of type relationships. Constraining C++ solely to OO usage ignores its other strengths and denies its multiparadigm nature.

<colgroup> <col> <col></colgroup> <thead> </thead> <tbody> </tbody>
Polymorphism Description
Inclusion Conventional OO model of polymorphism, i.e. virtual functions
Parametric Based on provision or deduction of extra type information that determines the types used in a function, i.e. templates
Overloading Based on the use of the same name denoting different functions, with selection based on the context of use, i.e. argument number and type
Coercion Based on the conversion of an object of one type to an object of another based on its context of use

Table 1. Different kinds of polymorphism

Types of Substitutability

Substitutability is the property that different elements have if they are grouped - and then treated - in terms of their commonality; variations that are not relevant to their use are not a part of this abstraction, or rather they do not dominate [Coplien1999]. Building on the previous discussion allows us to think outside the box, giving a broader view of substitutability grounded in C++'s mechanisms (see Table 2).

The substitutability types are neither perfect peers nor perfectly hierarchical: They overlap and build on each other. Nonetheless they offer a useful way to understand and reason about features. There is a close correspondence between these substitutability types and the polymorphism categories described in Table 1.

<colgroup> <col> <col></colgroup> <thead> </thead> <tbody> </tbody>
Substitutability Mechanisms
Conversions Implicit and explicit conversions
Overloading Overloaded functions and operators, often in combination with conversions
Derivation Inheritance
Mutability Qualification (typically const) and the use of conversions, overloading, and derivation
Genericity Templates and the use of conversions, overloading, derivation, and mutability

Table 2. Different kinds of substitutability in C++.


Conversions may be implicit or explicit, which places them under the control of the compiler and the developer, respectively. Whether a conversion should be implicit or explicit is a mixed matter of taste, safety and requirement. Widening conversions - where a conversion is from a specific to a general type - are always safe and can be implicit without offending sensibilities or the compiler, e.g. int to double or derived to base. Narrowing conversions - where a conversion is from a general to a specific type - are not guaranteed to be safe and should be explicit.

One would hope that it would be required of narrowing conversions to be explicit, but this is not always the case, e.g. double to int. Even though the compiler does not require it one might argue that taste does. Where possible, narrowing conversions should be checked, e.g. the use of dynamic_cast to go from base to derived.

Developers need to consider the way in which new types interoperate with one another and with existing types. Particularly for value types, i.e. for fine-grained objects - such as strings - that express quantities rather than persistent or strongly behavioral objects, the use of conversions to and from other types makes more sense than the use of inheritance relationships.

A single argument constructor is also, by default, a converting constructor. Where a type be safely, sensibly, and easily used in place of another type, an implicit conversion into that type either by converting constructor or a user defined conversion (UDC) operator may be justified, e.g. use of const char * in many places that a string may be used:

class string
    string(const char *);

class file
    explicit file(const string &);
const char *const log_name =
file log(log_name ? 
         : "default.log");

Otherwise - and this applies especially to UDCs - single argument constructors should be declared explicit and UDCs left unwritten, e.g. a string may not be sensibly used in most of the places a file object is expected, nor may a string always be used safely where a const char * is expected:

class string
    operator const char *() const;
                    // questionable
string operator+(const string &
              , const string &);
const string log_suffix = ".log";
const char *const log_name 
    = getenv("LOGBASENAME") + log_suffix;
file log(log_name);


Overloading is based on the idea that common name implies common purpose, and this frees programmers from indulging in their own name mangling to differentiate similar functions (this is the job of the compiler). Overloading works closely with - and sometimes against - conversions. Developers are cautioned to keep any eye open for any such interference.

Operators provide a predefined set of names and definitions, and therefore expectations: Overloading operator-> suggests the smart pointer idiom and overloading operator() suggests the function object idiom. Although compilers do not run through your code checking it for stylistic content (e.g. use of meaningful variable names, sensible use of overloading, and conformant use of inheritance) these conventions derive from the language itself to establish a common frame for working with the language - "when in doubt, do as the ints do" [Meyers1996].

Extension through overloading forms is an important part of operator overloading based substitutability. For instance, a class that is otherwise closed to change can apparently be extended to work within a framework, e.g. 'extending' I/O streams to understand new types.

Some extensions are less transparent, but importantly follow as much of the base form as possible. An obvious example is the use of placement new operators which, in spite of taking additional arguments, have the same purpose and much of the sameform as the vanilla new. Tagged overloads, such as new(std::nothrow), provide a means of compile time selection that is a compromise between operators and named functions.


Substitutability with respect to derivation is perhaps the most familiar category for programmers coming to C++ with a conventional OO angle. A public class interface establishes a behavioral contract the user relies on; derivation through public inheritance tells the compiler that the types are interchangeable, which only makes sense if the derived class developer promises to still fulfil the contract, even if it is extended in some way. Dropping LSP can lead to some surprising behavior.

In terms of coupling, derivation is also the strongest relationship one can have in a C++ system: It defines a dependency that is strongly physical, e.g. with respect to #include, as well as one that is strongly logical. The combined effect can lead to a tsunami-like recompilation of a whole system rather than a gentle ripple effect whenever the slightest change is made. Although C++ does not clearly separate the concepts of subtyping and subclassing in its inheritance mechanism, it is possible to effect this with interface classes [Carroll-1995], i.e. abstract classes containing only pure virtual functions. This offers a vehicle for substitutability that is independent of representation issues. Interestingly this means that as a mechanism, inheritance may be used either to significantly increase or significantly decrease the coupling in a system.


Mutability is concerned with the effects of change. For objects in C++ this means qualification: const and volatile... well, const if we are being really honest with ourselves. From this perspective every class has two public interfaces: The interface for const qualified objects and the interface for non-const qualified objects. The const interface is effectively a subset of the non-const interface, and therefore a non-const object may be used wherever a const one is expected, i.e. the qualified interface may be considered a supertype of the unqualified one. Note that the subtyping relationship need not be strict: Overloaded functions differing only in respect of const or non-const will be selected according to the calling const-ness. In OO terms this can be considered a form of compile time overriding of the const function by the non-const variant, typically to return something more specific:

class string
    char operator[](size_t) const;
    char &operator[](size_t); 
          // 'overrides' const version
const string read_only = ...;
cout << read_only[0];
string read_write = ...;
cin >> read_write[0];
cout << read_write[0];


Templates offer a route to substitutability that grows out of the basic concept of overloading. A templated function can be considered to have a potentially infinite number of overloads all sharing a common name, purpose and structure, but differing in their parameter types. A similar view can be extended to template classes, and from that member templates.

Generic programming, as typified by the part of the standard library derived from the STL, is based on the compile time polymorphism of C++ templates, as well as the concepts and mechanisms of the other substitutability categories.


Substitutability provides a useful way to structure the meaning of a system. It can be recognized as reaching further than a common place recommendation for inheritance, drawing together many C++ features in a set of practices that make sense of mechanism.

The next few columns will explore the different types of substitutability in greater detail; looking at language features and their use in idioms; highlighting the practices that commonly (or uncommonly) appear in application and library code.


[Cardelli-1985] Luca Cardelli and Peter Wegner, "On Understanding Types, Data Abstraction, and Polymorphism", Computing Surveys, 17(4):471-522, December 1985.

[Carroll-1995] Martin D Carroll and Margaret A Ellis, Designing and Coding Reusable C++, Addison-Wesley, 1995.

[Coplien1992] James O Coplien, Advanced C++: Programming Styles and Idioms, Addison-Wesley, 1992.

[Coplien1996] James O Coplien, Software Patterns, SIGS, 1996.

[Coplien1999] James O Coplien, Multi-Paradigm Design for C++, Addison-Wesley, 1999.

[Henney1998] Kevlin Henney, "Creating Stable Assignments", C++ Report 10(6), June 1998.

[Liskov1987] Barbara Liskov, "Data Abstraction and Hierarchy", OOPSLA '87 Addendum to the Proceedings, October 1987.

[Meyer1997] Bertrand Meyer, Object-Oriented Software Construction, 2nd edition, Prentice Hall, 1997.

[Meyers1996] Scott Meyers, More Effective C++: 35 New Ways to Improve Your Programs and Designs, Addison-Wesley, 1996.

Overload Journal #39 - Sep 2000 + Programming Topics