Subtyping of Function Types

Solution to method redefinition problem

• Object types:
  • N2: rec $n$.[$n$/selftype]
       {NUM: intloc, EQ: selftype $->$ boolexp}
  • I2: rec $i$.[$i$/selftype]
       {NUM: intloc, ISNEG: boolloc,
          EQ: selftype $->$ boolexp}
• Resolution of selftype
  • $n$ = {NUM: intloc, EQ: $n$ $->$ boolexp}
  • $i$ = {NUM: intloc, ..., EQ: $i$ $->$ boolexp}
  • $i$ <= $n$ does not imply $i$$->$boolexp <= $n$$->$boolexp!
  • call Q(I2) is not well-typed!
• Methods that take objects as parameters can destroy subtype relation!
  • C++: methods in subclasses must have same argument types.