Ordering multiple continuations on the stack

TL;DR: It is shown that tail calls can be generalized efficiently for many continuations because the run-time check to determine which continuation to pop to can be avoided with a simple static analysis.

Abstract: Passing multiple continuation arguments to a function in CPS form allows one to encode a wide variety of direct-style control constructs, such as conditionals, exceptions, and multi-return function calls. We show that, with a simple syntactic restriction on the CPS language, one can prove that these multi-continuation arguments can be compiled into stack frames in the traditional manner. The restriction comes with no loss in expressive power, since we can still encode the same control mechanisms.In addition, we show that tail calls can be generalized efficiently for many continuations because the run-time check to determine which continuation to pop to can be avoided with a simple static analysis. A prototype implementation in Scheme48 shows that our analysis is very precise.