// Last edited on 2000-03-20 22:46:58 by stolfi

class Quant {
  // Computer representeation of the value of a real variable

  class Float  extends double {};  // Finite `double' value
  class FloatN extends double {};  // Either a `Float' or `-oo'
  class FloatP extends double {};  // Either a `Float' or `+oo'
  class FloatI extends double {};  // Either a `Float' or `ħoo'
 
  boolean is_empty(); // Variable has no valid value.

  FloatN lo();  // Guaranteed lower bound for the variable.
  FloatP hi();  // Guaranteed upper bound for the variable.
  
  static Float  mid(); // Approximate midpoint of range.
  static FloatI rad(); // Half-width of range.
  
  /* 
    Let `X' be a continuous variable, and `x' a `Quant' object
    that represents the value of  `X'.   The following 
    invariants are satisfied whenever `x.is_empty() == true':
    
      1. `x.lo() < +oo' and `x.hi() > -oo'.
      
      2. `x.lo() \leq X \leq y.lo()'.
      
      3. `x.mid() > -oo' and `x.mid() < +oo'
      
      4. `x.mid() - x.rad() \leq X \leq x.mid() + x.rad()'
    
  */
}