  Modern languages are equipped with static type checking/inference that helps
programmers to keep a clean programming style and to reduce errors. However,
the ever-growing size of programs and their continuous evolution require
building fast and efficient analysers. A promising solution is incrementality,
so one only re-types those parts of the program that are new, rather than the
entire codebase. We propose an algorithmic schema driving the definition of an
incremental typing algorithm that exploits the existing, standard ones with no
changes. Ours is a grey-box approach, meaning that just the shape of the input,
that of the results and some domain-specific knowledge are needed to
instantiate our schema. Here, we present the foundations of our approach and we
show it at work to derive three different incremental typing algorithms. The
first two implement type checking and inference for a functional language. The
last one type-checks an imperative language to detect information flow and
non-interference. We assessed our proposal on a prototypical implementation of
an incremental type checker. Our experiments show that using the type checker
incrementally is (almost) always rewarding.
