Related papers: Mechanizing Refinement Types (extended)
We introduce skipping refinement, a new notion of correctness for reasoning about optimized reactive systems. Reasoning about reactive systems using refinement involves defining an abstract, high-level specification system and a concrete,…
We formally verify an abstract machine for a call-by-value lambda-calculus with de Bruijn terms, simple substitution, and small-step semantics. We follow a stepwise refinement approach starting with a naive stack machine with substitution.…
We introduce MLFMF, a collection of data sets for benchmarking recommendation systems used to support formalization of mathematics with proof assistants. These systems help humans identify which previous entries (theorems, constructions,…
The reasoning abilities are one of the most enigmatic and captivating aspects of large language models (LLMs). Numerous studies are dedicated to exploring and expanding the boundaries of this reasoning capability. However, tasks that embody…
This paper introduces a simple type system for combinatory logic in which combinators have at most one type, whose polymorphism is revealed by application. The combinatory types exactly describe the structure of their values, which may be…
We present Dependent Lambek Calculus, a domain-specific dependent type theory for verified parsing and formal grammar theory. In $\textrm{Lambek}^D$, linear types are used as a syntax for formal grammars,and parsers can be written as linear…
Unsupervised methods are widely used to induce latent semantic structure from large text collections, yet their outputs often contain incoherent, redundant, or poorly grounded clusters that are difficult to validate without labeled data. We…
Formal verification via theorem proving enables the expressive specification and rigorous proof of software correctness, but it is difficult to scale due to the significant manual effort and expertise required. While Large Language Models…
We present a logic named L_{LF} whose intended use is to formalize properties of specifications developed in the dependently typed lambda calculus LF. The logic is parameterized by the LF signature that constitutes the specification. Atomic…
Fine-tuning LLMs for classification typically maps inputs directly to labels. We ask whether attaching brief explanations to each label during fine-tuning yields better models. We evaluate conversational response quality along three axes:…
We consider the extensions of modal transition systems (MTS), namely Boolean MTS and parametric MTS and we investigate the refinement problems over both classes. Firstly, we reduce the problem of modal refinement over both classes to a…
We present three projects concerned with applications of proof assistants in the area of programming language theory and mathematics. The first project is about a certified compilation technique for a domain-specific programming language…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
Implementing a complex concept as an executable model in a strongly typed, purely functional language hits a sweet spot between mere simulation and formal specification. For research and education it is often desirable to enrich the…
In this paper, we examine a number of additive and multiplicative multilevel iterative methods and preconditioners in the setting of two-dimensional local mesh refinement. While standard multilevel methods are effective for uniform…
This paper provides an in-depth examination of the concept of semantic diffusion as a complementary instrument to large language models (LLMs) for design applications. Conventional LLMs and diffusion models fail to induce a convergent,…
To take advantage of Large Language Model in theorem formalization and proof, we propose a reinforcement learning framework to iteratively optimize the pretrained LLM by rolling out next tactics and comparing them with the expected ones.…
Side-channel attacks, which are capable of breaking secrecy via side-channel information, pose a growing threat to the implementation of cryptographic algorithms. Masking is an effective countermeasure against side-channel attacks by…
Fact-checking aims to verify the truthfulness of a claim based on the retrieved evidence. Existing methods typically follow a decomposition paradigm, in which a claim is broken down into sub-claims that are individually verified. However,…
Fully automated verification of large-scale software and hardware systems is arguably the holy grail of formal methods. Large language models (LLMs) have recently demonstrated their potential for enhancing the degree of automation in formal…