Related papers: Refinement Reflection: Complete Verification with …

Existing refinement calculi provide frameworks for the stepwise development of imperative programs from specifications. This paper presents a refinement calculus for deriving logic programs. The calculus contains a wide-spectrum logic…

Lighthouse projects such as CompCert, seL4, IronFleet, and DeepSpec have demonstrated that full verification of entire systems is feasible by establishing a refinement relation between an abstract system specification and an executable…

Widely used complex code refactoring tools lack a solid reasoning about the correctness of the transformations they implement, whilst interest in proven correct refactoring is ever increasing as only formal verification can provide true…

In recent years, Large Language Models (LLMs) have demonstrated remarkable generative abilities, but can they judge the quality of their own generations? A popular concept, referred to as self-refinement, postulates that LLMs can detect and…

Contextual refinement and separation logics are successful verification techniques that are very different in nature. First, the former guarantees behavioral refinement between a concrete program and an abstract program while the latter…

We consider extensions of the language of Peano arithmetic by transfinitely iterated truth definitions satisfying uniform Tarskian biconditionals. Without further axioms, such theories are known to be conservative extensions of the original…

We present the design, implementation, and foundation of a verifier for higher-order functional programs with generics and recursive data types. Our system supports proving safety and termination using preconditions, postconditions and…

Refinement types turn typechecking into lightweight verification. The classic form of refinement type is the datasort refinement, in which datasorts identify subclasses of inductive datatypes. Existing type systems for datasort refinements…

Self-reflection -- the ability of a large language model (LLM) to revisit, evaluate, and revise its own reasoning -- has recently emerged as a powerful behavior enabled by reinforcement learning with verifiable rewards (RLVR). While…

Dependent types offer great versatility and power, but developing proofs with them can be tedious and requires considerable human guidance. We propose to integrate Satisfiability Modulo Theories (SMT)-based refinement types into the…

The refinement calculus for logic programs is a framework for deriving logic programs from specifications. It is based on a wide-spectrum language that can express both specifications and code, and a refinement relation that models the…

The program synthesis problem within the Inductive Logic Programming (ILP) community has typically been seen as untyped. We consider the benefits of user provided types on background knowledge. Building on the Meta-Interpretive Learning…

Large language models (LLMs) have achieved strong performance on complex reasoning tasks using techniques such as chain-of-thought and self-consistency. However, ensemble-based approaches, especially self-consistency which relies on…

Chain-of-Thought (CoT) prompting has become the de facto method to elicit reasoning capabilities from large language models (LLMs). However, to mitigate hallucinations in CoT that are notoriously difficult to detect, current methods such as…

The refinement calculus provides a methodology for transforming an abstract specification into a concrete implementation, by following a succession of refinement rules. These rules have been mechanized in theorem-provers, thus providing a…

We present a new type system combining occurrence typing, previously used to type check programs in dynamically-typed languages such as Racket, JavaScript, and Ruby, with dependent refinement types. We demonstrate that the addition of…

We introduce a self-play framework for semantic equivalence in Haskell, utilizing formal verification to guide adversarial training between a generator and an evaluator. The framework leverages Liquid Haskell proofs for validating…

Large Reasoning Models (LRMs) achieve strong performance by generating long reasoning traces with reflection. Through a large-scale empirical analysis, we find that a substantial fraction of reflective steps consist of self-verification…

We describe techniques for synthesis and verification of recursive functional programs over unbounded domains. Our techniques build on top of an algorithm for satisfiability modulo recursive functions, a framework for deductive synthesis,…

Software model checkers based on under-approximations and SMT solvers are very successful at verifying safety (i.e. reachability) properties. They combine two key ideas -- (a) "concreteness": a counterexample in an under-approximation is a…