Abstract

F was an extension of a second-order -calculus F which has parametric polymorphism with subtyping and bounded quantification, introduced by Ghelli to apply second-order -calculi to the framework of object-oriented languages. However, it is impossible to know the amount of information of a type-checked term before evaluation since the subsumption rules are included in F . To overcome this problem, we provided new calculi cF + and cF ++ as extensions of F , and investigated their proof-theoretic properties. cF + includes a new type Range(X) , and cF ++ includes two new types Range(X) and Inst(X; T ) . For example, the type Range(X) is provided for a type variable X whose upper bound is a function type, as a codomain type of X . When a function type S ! T is substituted for X , Range(S ! T ) is reduced to T . For a type variable X whose upper bound is a universal type, the type Inst(X; U) is provided. When a universal type 8Y S:T is substituted for X , Inst(8Y S:T;U) is re...

Citations