David Evans CS655: Programming Languages University of Virginia Computer Science Lecture 17: Inheritance & Behavioral Subtyping (when is S  T safe?) What’s the difference between a Black Bear and a Grizzly Bear? When you climb up the tree, the Grizzly climbs up after you. The Black Bear knocks down the tree. (Which is the behavioral subtype?) Killer BlackBearGrizzlyBear Climber Bear KillingBear

27 March 2001CS 655: Lecture 172 Menu Wrap-up “What is Object-Oriented Programming?” Behavioral Notion of Subtyping

27 March 2001CS 655: Lecture 173 Last time Defined subtyping as subsumption Showed typing judgments that support subtype polymorphism Some language features that support subtype polymorphism: –Dynamic type-directed method dispatch –Subclassing (Implementation inheritance)

27 March 2001CS 655: Lecture 174 Implementation Reuse: Subclassing, Inheritance Use implementation of one type to implement another type Often use implementation of supertype to implement subtype Commonly used OO languages confuse issue by combining subtyping and inheritance: –Eiffel – cannot separate –Java – cannot separate, can use interfaces for subtyping only –C++ - can use implementation inheritance without subtyping ( private, protected inheritance)

27 March 2001CS 655: Lecture 175 Language Principle: Getting Defaults Right Matters Shouldn’t require extra work to hide things, should require extra work to expose them (forgetting something should be safer) Possible Examples: –Algol60: call-by-value requires extra work (should have been call-by-name) –Java: preventing overriding requires extra work ( final ) / opposite of C++ –C++: preventing subtyping requires extra work ( public inheritance is default, need private to reuse implementation without subtyping) –Java access: default is package protected, need private to hide variables and methods

27 March 2001CS 655: Lecture 176 A Type and Class Hierarchy Shape Quadrangle Triangle Rectangle Parallelogram Rhombus Square Equilateral EquilateralTriangle

27 March 2001CS 655: Lecture 177 Add an attribute Shapes should have a color and set_color method Change Shape, Quadrangle, Parallelogram, Triangle, Equilateral, EquilateralTriangle, Rhombus, Rectangle, Square, etc. Change Shape, others inherit new attribute and method automatically

27 March 2001CS 655: Lecture 178 Add is_equilateral bool Shape::is_equilateral () { return false; } bool Equilateral::is_equilateral () { return true; }

27 March 2001CS 655: Lecture 179 Is a Rhombus equilateral? Shape Quadrangle Parallelogram Rhombus Equilateral is_equilateral? is_equilateral () { return false; } is_equilateral () { return true; } Multiple inheritance can be tricky!

27 March 2001CS 655: Lecture 1710 Solutions Java, Ada95 –Don’t allow it (Java: interfaces for multiple supertypes, not implementation sharing) –Pro: Safe and Simple, Con: Limits Reuse C++ –Allow it, let programmers shoot themselves if they want Eiffel –Explicit renaming or hiding (error if not done)

27 March 2001CS 655: Lecture 1711 Smalltalk Design Principles Personal Mastery: If a system is to serve the creative spirit, it must be entirely comprehensible to a single individual. Storage Management: To be truly "object- oriented", a computer system must provide automatic storage management. Uniform Metaphor: A language should be designed around a powerful metaphor that can be uniformly applied in all areas.

27 March 2001CS 655: Lecture 1712 Smalltalk Design Principles 2 Operating System: An operating system is a collection of things that don't fit into a language. There shouldn't be one. Natural Selection: Languages and systems that are of sound design will persist, to be supplanted only by better ones.

27 March 2001CS 655: Lecture 1713 “Object-oriented programming is programming with inheritance. Data abstraction is programming using user-defined types. With few exceptions, object-oriented programming can and ought to be a superset of data abstraction. These techniques need proper support to be effective. Data abstraction primarily needs support in the form of language features and object-oriented programming needs further support from a programming environment. To be general purpose, a language supporting data abstraction or object-oriented programming must enable effective use of traditional hardware.” Stroustrup’s Conclusions

27 March 2001CS 655: Lecture 1714 My Conclusions Object-Oriented Programming is a state of mind. It is difficult to reach that state of mind if your language doesn’t have a way to declare S  T and the type judgment: Other language features can help, but we aren’t yet sure what the right ones are: dynamic dispatch, implementation inheritance, mixins, automated delegation, etc. A E : S, S  T A E : T [subsumption]

27 March 2001CS 655: Lecture 1715 Analogies Structured Programming is a state of mind. It is difficult to reach that state of mind if your language doesn’t have structured control statements (e.g., while, for, if, blocks, procedures) Data Abstraction is a state of mind. It is difficult to reach that state of mind if your language doesn’t have type checking and mechanisms for restricting access

How do we know if S  T is safe?

27 March 2001CS 655: Lecture 1717 What does it mean for S  T to be safe? Liskov & Wing: “objects of the subtype ought to behave the same as those of the supertype as far as anyone or any program using supertype objects can tell.” For all functions f, if f behaves correctly when passed a T, f behaves correctly when passed an S. Too Strong For all programs f, if f can be shown to satisfy its specification using the specification of T, then f can be shown to satisfy its specification using the specification of S.

27 March 2001CS 655: Lecture 1718 L & W’s Subtype Requirement Let  (x) be a property provable about objects x of type T. Then  (y) should be true for objects y of type S where S is a subtype of T. Same meaning? For all programs P, if P can be shown to satisfy its specification using the specification of T, then P can be shown to satisfy its specification using the specification of S.

27 March 2001CS 655: Lecture 1719 Type Specification Description of type’s value space Type invariant and history properties (constraint) –How different from rep invariant? For each method: –Behavior in terms of pre-conditions and post- conditions No creators – allows subtypes to provide different creators –Need to prove creators establish invariant and constraint

27 March 2001CS 655: Lecture 1720 Two-Tiered Specification Separate interface-level specification from sort specification Specs in paper are interface-level specifications only: bag = type uses BBag (bag for B)... get = proc () returns (int) requires b pre.elems  { } What does this mean?

27 March 2001CS 655: Lecture 1721 LSL Specification Bag (E, C) : trait introduces { } :  C; insert : E, C  C; count : E, C  Int asserts C generated by {}, insert C partitioned by count  b: C, e, e1, e2: E count (e, {}) == 0; count (e1, insert (e2, b)) == count (e1, b) + (if e1 = e2 then 1 else 0) BBag (B) tuple of bound: Int, elems: Bag (Int, B for C)

27 March 2001CS 655: Lecture 1722 Subtype Definition ( S  T) 1.Subtype methods preserve the supertype methods’ behavior: Signatures have contravariant arguments, covariant results Pre-conditions of T imply preconditions of S; post-conditions of S imply post- conditions of T. 2.Subtypes preserve supertype properties Invariant of S implies invariant of T. Constraint of S implies constraint of T.

27 March 2001CS 655: Lecture 1723 Subtype Condition 1: Signature Rule Subtype methods preserve the supertype methods’ behavior: –Signature: Contravariance of arguments, covariance of result (typing rule we saw last time) Exceptions by m s are contained in set of exceptions signed by m T

27 March 2001CS 655: Lecture 1724 Methods rule: –Pre-condition  x : s m T.pre [ A (x pre ) / x pre ]  m S.pre Replace every x pre in m T.pre with A (x pre ). Abstraction function, A : s  t. –Post-condition m S.post  m T.post [A (x pre ) / x pre, A (x post ) / x post ] Subtype Condition 1: Methods Rule “contravariance – subtype is weaker” “covariance – subtype is stronger”

27 March 2001CS 655: Lecture Subtypes preserve supertype properties For all states p and q such that p precedes q, for all x: S: Invariant Rule I S  I T [ A (x p ) / x p ] Constraint Rule C S  C T [A (x p ) / x p, A (x q ) / x q ] “covariance – subtype is stronger” Subtype Relation 2: Preserves supertype Properties

27 March 2001CS 655: Lecture 1726 Charge Don’t stop working on your projects just because you turned in your proposal... Next time: pragmatic aspects of OO languages - comparison of Sather, Eiffel, Java and C++