We present an automated approach to relatively completely verifying safety (i.e., reachability) property of higher-order functional programs. Our contribution is twofold. First, we extend the refinement type system framework employed in the recent work on (incomplete) automated higher-order verification by drawing on the classical work on relatively complete "Hoare logic like" program logic for higher-order procedural languages. Then, by adopting the recently proposed techniques for solving constraints over quantified first-order logic formulas, we develop an automated type inference method for the type system, thereby realizing an automated relatively complete verification of higher-order programs.

Motivated by recent research in abstract model checking, we present a new approach to inferring dependent types. Unlike many of the existing approaches, our approach does not rely on programmers to supply the candidate (or the correct) types for the recursive functions and instead does counterexample-guided refinement to automatically generate the set of candidate dependent types. The main idea is to extend the classical fixed-point type inference routine to return a counterexample if the program is found untypable with the current set of candidate types. Then, an interpolating theorem prover is used to validate the counterexample as a real type error or generate additional candidate dependent types to refute the spurious counterexample. The process is repeated until either a real type error is found or sufficient candidates are generated to prove the program typable. Our system makes non-trivial use of "linear" intersection types in the refinement phase.The paper presents the type inference system and reports on the experience with a prototype implementation that infers dependent types for a subset of the Ocaml language. The implementation infers dependent types containing predicates from the quantifierfree theory of linear arithmetic and equality with uninterpreted function symbols.

We present a new static analysis for race freedom and race detection. The analysis checks race freedom by reducing the problem to (rational) linear programming. Unlike conventional static analyses for race freedom or race detection, our analysis avoids explicit computation of locksets and lock linearity/must-aliasness. Our analysis can handle a variety of synchronization idioms that more conventional approaches often have difficulties with, such as thread joining, semaphores, and signals. We achieve efficiency by utilizing modern linear programming solvers that can quickly solve large linear programming instances. This paper reports on the formal properties of the analysis and the experience with applying an implementation to real world C programs.

We present a new approach to the old problem of adding global mutable state to purely functional languages. Our idea is to extend the language with "witnesses," which is based on an arguably more pragmatic motivation than past approaches. We give a semantic condition for correctness and prove it is sufficient. We also give a somewhat surprising static checking algorithm that makes use of a network flow property equivalent to the semantic condition via reduction to a satisfaction problem for a system of linear inequalities.