Mechanized Metatheory for User-Defined Type Extensions

Motivation Type systems are a natural discipline for ensuring that programs maintain certain runtime invariants. Of course, language designers cannot anticipate all the invariants that programmers will want to enforce. Therefore, it is desirable to allow programmers to specify and statically check invariants of interest for their applications. Researchers have designed expressive type systems that allow programmer-defined invariants to be directly encoded as types. However, there is a tradeoff between type-system expressiveness and ease of use for programmers. First, the more expressive the type system, the more annotation burden there is on the programmer. For example, expressive type systems often require programmers to manually discharge proof obligations to ensure that a program fragment meets its specified type. Second, the more expressive the type system, the more difficult it is for programmers to understand. In traditional type systems, each type has a relatively simple set of syntax-directed rules, which constitutes a programming discipline for programmers to obey. As type systems become more expressive, it becomes more difficult for programmers to understand what programming idioms can and cannot be typechecked and why. As a result, languages with expressive type systems may be challenging for programmers to use effectively.