  Automated verification of functional correctness of imperative programs with
references (a.k.a. pointers) is challenging because of reference aliasing.
Ownership types have recently been applied to address this issue, but the
existing approaches were limited in that they are effective only for a class of
programs whose reference usage follows a certain style. To relax the
limitation, we combine the approaches of ConSORT (based on fractional
ownership) and RustHorn (based on borrowable ownership), two recent approaches
to automated program verification based on ownership types, and propose the
notion of borrowable fractional ownership types. We formalize a new type system
based on the borrowable fractional ownership types and show how we can use it
to automatically reduce the program verification problem for imperative
programs with references to that for functional programs without references. We
also show the soundness of our type system and the translation, and conduct
experiments to confirm the effectiveness of our approach.
