We prove that partial type reconstruction for the pure polymorphic *-calculus is undecidable by a reduction from the second-order unification problem, extending a previous result by H.-J. Boehm. We show further that partial type reconstruction remains undecidable even in a very small predicative fragment of the polymorphic *-calculus, which implies undecidability of partial type reconstruction for * ML as introduced by Harper, Mitchell, and Moggi.

ing RationalFun from Rational yields a higher order type operator that, given a specification, forms the type of objects that satisfy it. Philip Santas DeclareDomain := (Fun: Type-?Category) +? (((Rep: Type) +? with(Rep,Fun(Rep))) SomeRep) The type of Rational objects can now be expressed by applying the DeclareDomain constructor to the specification RationalFun: Rational := DeclareDomain(RationalFun) or the shortcut: Rational : RationalFun In order to give proper treatment to the interaction between representations and subtyping, it is necessary to separate Rational into the specifications of its functions and the operators which capture the common structure of all object types. This separation is also important for the semantical construction of categories and the definition of the internal structures of the types. 2.1. Multiple Representations Rationals are created using the function box, which captures the semantics of dynamic objects in object oriented programming.A rational...