Bidirectional live programming not only allows software developers to see continuous feedback on the output as they write the program, but also allows them to modify the program by directly manipulating the output, so that the modified program can get the output that was directly manipulated. Despite the appealing of existing bidirectional live programming systems, there is a big limitation: they cannot deal with incomplete programs where code blanks exist in the source programs.

In this paper, we propose a framework to support bidirectional live programming for incomplete programs, by extending the output value structure, introducing hole binding, and formally defining bidirectional evaluators that are well-behaved. To illustrate the usefulness of the framework, we realize the core bidirectional evaluations of incomplete programs in a tool called Bidirectional Preview. Our experimental results show that our extended backward evaluation for incomplete programs is as efficient as that for complete programs in that it is only $21ms$ slower on a program with $10$ holes than that on its full program, and our extended forward evaluation makes no difference. Furthermore, we use quick sort and student grades, two nontrivial examples of incomplete programs, to demonstrate its usefulness in algorithm teaching and program debugging.