Systems, methods, and structures are discussed that enhance type reconstruction for programs. Whereas previous methods insufficiently provide the set of types necessary for program analysis, the embodiments of the present invention can accept any verifiable bytecode programs and produce a set of types needed for program analysis. The embodiments of the present invention provide a technique called subtype completion that transforms a subtyping system by extending its type hierarchy to a lattice. However, such transformation inserts only a minimal amount of elements so as to enhance the computation of reconstructed types.