Higher-order and Symbolic Computation Manuscript No. Functional Un|unparsing

Danvy’s functional unparsing problem (Danvy 1998) is to implement a typesafe ‘printf’ function, which converts a sequence of heterogeneous arguments to a string according to a given format. The dual problem is to implement a type-safe ‘scanf’ function, which extracts a sequence of heterogeneous arguments from a string by interpreting (Friedman and Wand 1984, 2008) the same format as an equally heterogeneous sequence of patterns that binds zero or more variables. We derive multiple solutions to both problems (Wand 1980b) from their formal specifications (Wand 1982b). On one hand, our solutions show how the Hindley-Milner type system, unextended, permits accessing heterogeneous sequences with the static assurance of type safety. On the other hand, our solutions demonstrate the use of control operators (Felleisen et al. 1988; Meyer and Wand 1985; Wand 1985) to communicate with formats as coroutines (Haynes et al. 1984; Wand 1980a).