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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.

OO typing systems still topic of research!