Logic-flow analysis of higher-order programs

This work presents a framework for fusing flow analysis and theorem proving called logic-flow analysis (LFA). The framework itself is the reduced product of two abstract interpretations: (1) an abstract state machine and (2) a set of propositions in a restricted first-order logic. The motivating application for LFA is the safe removal of implicit array-bounds checks without type information, user interaction or program annotation. LFA achieves this by delegating a given task to either the prover or the flow analysis depending on which is best suited to discharge it. Described within are a concrete semantics for continuation-passing style; a restricted, first-order logic; a woven product of two abstract interpretations; proofs of correctness; and a worked example.