Types versus classes

  • types -- type checking predicates
  • classes -- templates for object creation

Type specification

  • syntactically -- signature

    • (under)


  • semantically -- behavior

    • (right)


  • pragmatically -- implementation

    • (over)


slide: Types and classes

Modifications
  • types -(predicate constraints)-> subtypes
  • classes -(template modification)-> subclasses

Varieties of (compatible) modifications
  • behaviorally -- algebraic, axiomatic

    • (type)


  • signature -- type checking

    • (signature)


  • name -- method search algorithm

    • (classes)


slide: Type modifications

Signature compatible modifications
  • behavior is approximated by signature

Semantics preserving extensions
  • horizontal -- Person = Citizen + { age : 0..120 }
  • vertical -- Retiree = Person + { age : 65..120 }

Principle of substitutability

  • an instance of a subtype can always be used in any context in which an instance of a supertype can be used

  
 subsets are not subtypes

  Retiree \not<_{subtype} Person

Read-only substitutability

  • subset subtypes, isomorphically embedded subtypes
slide: The principle of substitutability

Name compatible modifications

 


  procedure search(name, module)
  if name = action then do action
  elsif inherited = nil
  	       then undefined
  else search(name, inherited)
slide: The inheritance search algorithm