juno-machine/src/Equiv.i3

 Copyright (C) 1992, Digital Equipment Corporation                         
 All rights reserved.                                                      
 See the file COPYRIGHT for a full description.                            
                                                                           
 Last modified on Thu Aug 18 11:15:55 PDT 1994 by heydon                   


 An Equiv.T is an element of an equivalence relation. 


INTERFACE Equiv;

EXCEPTION Forbidden;

TYPE
  T <: Public;
  Public = OBJECT
    root: T;
  METHODS
    init(): T;
    union(y: T): T RAISES {Forbidden};
  END;

END Equiv.

 A NEW(Equiv.T).init() is in an equivalence class by itself. For any
   existing element x, x.init().root = x. However, the element
   x' = x.init() is not necessarily in its own equivalence class; there may
   be other existing elements y such that y.root = x'.


   The field x.root is the distinguished representative of x's
   equivalence class.


   The call x.union(y) combines the equivalence classes represented by x
   and y and returns the representative of the new class. It is a checked
   run-time error for x and y not to be roots of their equivalence
   classes. The method raises Forbidden if the union operation is illegal;
   the default union method never raises Forbidden, but it may be useful
   for subtypes to override it.


   After the call x.union(y), x.root = y.root. The distinguished
   representative of the class formed by x.union(y) is guaranteed to be
   either the distinguished representative of x's class or the distinguished
   representative of y's class before the union.