Automating Verification of Functional Programs with Quantified Invariants

We present the foundations of a verifier for higher-order functional programs with generics and recursive algebraic data types. Our verifier supports finding sound proofs and counterexamples even in the presence of certain quantified invariants and recursive functions. Our approach uses the same language to describe programs and invariants and uses semantic criteria for establishing termination. Our implementation makes effective use of SMT solvers by encoding first-class functions and quantifiers into a quantifier-free fragment of first-order logic with theories. We are able to specify properties of datastructure operations involving higher-order functions with minimal annotation overhead and verify them with a high degree of automation. Our system is also effective at reporting counterexamples, even in the presence of first-order quantification.