In the seminal paper Functional unparsing, Olivier Danvy used
continuation passing to reanalyse printf-like format strings as
combinators. In the intervening decades, the conversation shifted
towards a concurrent line of work — applicative, monadic or
arrow-based combinator libraries — in an effort to find combinators
for invertible syntax descriptions that
simultaneously determine a parser as well
as a printer, and with more expressive power, able to handle
inductive structures such as lists and trees. Along the way,
continuation passing got lost. This paper argues that Danvy's
insight remains as relevant to the general setting as it was to the
restricted setting of his original paper. Like him, we present three
solutions that exploit continuation-passing style as an alternative
to both dependent types and monoidal aggregation via nested pairs,
in our case to parse and print structured data with increasing
expressive power.