Abstract

System F ! is an extension of system F ! with subtyping and bounded quantification. Order-sorted algebra is an extension of many-sorted algebra with overloading and subtyping. We combine both formalisms to obtain IF ! , a higher-order typed -calculus with subtyping, bounded quantification and order-sorted inductive types, i.e. data types with built-in subtyping and overloading. Moreover we show that IF ! enjoys important meta-theoretic properties, including confluence, strong normalization, subject reduction and decidability of type-checking. 1 Introduction Typed functional programming languages such as Haskell and ML and typetheory based proof-development systems such as Coq and Lego support the introduction of inductively defined types such as natural numbers or booleans, parameterized inductively defined types such as lists and even parameterized mutual inductively defined types such as trees and forests. In addition, those languages support the definition of functions ...

Citations