Abstract

In “Functional Unparsing ” (JFP 8(6): 621–625, 1998), Danvy presented a type-safe printf function using continuations and an accumulator to achieve the effect of dependent types. The key technique employed in Danvy’s solution is the non-standard use of continuations: not all of its calls are tail calls, i.e., it uses delimited continuations. Against this backdrop, we present three new solutions to the printf problem: a simpler one that also uses delimited continuations but that does not use an accumulator, and the corresponding two in direct style with the delimited-control operators, shift and reset. These two solutions are the direct-style counterparts of the two continuation-based ones. The last solution pinpoints the essence of Danvy’s solution: shift is used to change the answer type of delimited continuations. Besides providing a new application of shift and reset, the solutions in direct style raise a key issue in the typing of first-class delimited continuations and require Danvy and Filinski’s original type system. The resulting types precisely account for the behavior of printf. This is the extended version of the previous technical report OCHA-IS 07-1. It contains an introduction to continuation-passing style and delimited-control operators, shift and reset.

Citations