Automatic Abstraction for Intervals Using Boolean Formulae

Traditionally, transfer functions have been manually designed for each operation in a program. Recently, however, there has been growing interest in computing transfer functions, motivated by the desire to reason about sequences of operations that constitute basic blocks. This paper focuses on deriving transfer functions for intervals — possibly the most widely used numeric domain — and shows how they can be computed from Boolean formulae which are derived through bit-blasting. This approach is entirely automatic, avoids complicated elimination algorithms, and provides a systematic way of handling wrap-arounds (integer over-flows and underflows) which arise in machine arithmetic.