Lsp stéphane Ducasse 2005

LSP

• Stéphane Ducasse --- 2005

A step deeper in Subtyping...

Liskov Substitution Principle (LSP)

• if for each object o1 of type S there is another 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.

• Barbara Liskov, "Data Abstraction and Hierarchy," SIGPLAN Notices, 23,5 (May 1988)

A Simple Bag

• We will define a Bag as an object that accepts two messages: put and count

• (send a-Bag 'put x)

• puts an element x into the Bag, and

• (send a-Bag 'count x)

• gives the count of occurrences of x in the Bag (without changing a-Bag's state).

A Simple Set

• Likewise, a Set is defined as an object that accepts two messages:

• (send a-Set 'put x)

• puts an element x into a-Set unless it was already there,

• (send a-Set 'count x)

• gives the count of occurrences of x in a-Set (which is always either 0 or 1).

A Bag Function

• (define (fnb bag)

• (send bag 'put 5)

• (send bag 'put 5)

• (send bag 'count 5))

• The behavior of this function can be summed as follows: given a Bag, the function adds two elements into it and returns

•     (+ 2 (send orig-bag 'count 5))

The problem

• Technically you can pass to fnb a Set object as well. Just as a Bag, a Set object accepts messages put and count. However applying fnb to a Set object will break the function's post-condition

• Therefore, passing a set object where a bag was expected changes behavior of some program. According to the Liskov Substitution Principle (LSP), a Set is not substitutable for a Bag -- a Set cannot be a subtype of a Bag.

Another function

• (define (fns set)

• (send set 'put 5)

• (send set 'count 5))

• The behavior of this function is: given a Set, the function adds an element into it and returns 1.

Problem two

• If you pass to this function a bag (which -- just as a set -- replies to messages put and count), the function fns may return a number greater than 1. This will break fns's contract, which promised always to return 1.

Finally

• Therefore, from the OO point of view, neither a Bag nor a Set are a subtype of the other.

• Bag and Set only appear similar. The interface or an implementation of a Bag and a Set appear to invite subclassing of a Set from a Bag (or vice versa). Doing so however will violate the LSP -- and you have to brace for very subtle errors.

• Sets and Bags are very simple types, far simpler than the ones you deal with in a production code. either. It's manual work -- you have to see the problem

Watch out

• Alas, LSP when considered from an OOP point of view is undecidable.

• You cannot count on a compiler for help in pointing out an error. You cannot rely on regression tests

In C++

• typedef int const * CollIterator; // Primitive but will do

• class CBag {

• public:

• int size(void) const; // The number of elements in the bag

• virtual void put(const int elem); // Put an element into the bag

• int count(const int elem) const; // Count the number of occurrences

• // of a particular element in the bag

• virtual bool del(const int elem); // Remove an element from the bag

• // Return false if the element

• // didn't exist

• CollIterator begin(void) const; // Standard enumerator interface

• CollIterator end(void) const;

• CBag(void);

• virtual CBag * clone(void) const; // Make a copy of the bag

• private:

• // implementation details elided

• };

CSet

• class CSet : public CBag {

• public:

• bool memberof(const int elem) const { return count(elem) > 0; }

• // Overriding of CBag::put

• void put(const int elem)

• { if(!memberof(elem)) CBag::put(elem); }

• CSet * clone(void) const

• { CSet * new_set = new CSet(); *new_set += *this; return new_set; }

• CSet(void) {}

• };

Summary

• Subtyping...