Related papers: Refinement Types for Logical Frameworks and Their …
It has been argued that reduction procedures are closely connected to the question about identity of proofs and that accepting certain reductions would lead to a trivialization of identity of proofs in the sense that every derivation of the…
This article first provides an algorithm W based type inference algorithm for an affine type system. Then the article further assumes the language equipped with the above type system uses lazy evaluation, and explores the possibility of…
Refinement types are a popular way to specify and reason about key program properties. In this paper, we introduce RTR, a new system that adds refinement types to Ruby. RTR is built on top of RDL, a Ruby type checker that provides basic…
Modern language models (LMs) exhibit strong deductive reasoning capabilities, yet standard evaluations emphasize correctness while overlooking a key aspect of reasoning: efficiency. In real-world reasoning scenarios, much of the available…
While model checking has often been considered as a practical alternative to building formal proofs, we argue here that the theory of sequent calculus proofs can be used to provide an appealing foundation for model checking. Since the…
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…
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.…
Model-driven design of software for safety-critical applications often relies on mathematically grounded techniques such as the B method. Such techniques consist in the successive applications of refinements to derive a concrete…
Given a machine learning (ML) model and a prediction, explanations can be defined as sets of features which are sufficient for the prediction. In some applications, and besides asking for an explanation, it is also critical to understand…
Iterative self-refinement is a simple inference-time strategy for machine translation: an LLM revises its own translation over multiple inference-time passes. Yet document-scale refinement remains poorly understood: 1) which pipelines work…
We present Refined TypeScript (RSC), a lightweight refinement type system for TypeScript, that enables static verification of higher-order, imperative programs. We develop a formal core of RSC that delineates the interaction between…
We propose a method for inferring \emph{parameterized regular types} for logic programs as solutions for systems of constraints over sets of finite ground Herbrand terms (set constraint systems). Such parameterized regular types generalize…
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…
This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…
We introduce two-sided type systems, which are sequent calculi for typing formulas. Two-sided type systems allow for hypothetical reasoning over the typing of compound program expressions, and the refutation of typing formulas. By…
Felty and Miller have described what they claim to be a faithful encoding of the dependently typed lambda calculus LF in the logic of hereditary Harrop formulas, a sublogic of an intuitionistic variant of Church's Simple Theory of Types.…
The fast development of Large Language Models (LLMs) offers growing opportunities to further improve sequential recommendation systems. Yet for some practitioners, integrating LLMs to their existing base recommendation systems raises…
Bidirectional typechecking, in which terms either synthesize a type or are checked against a known type, has become popular for its scalability (unlike Damas-Milner type inference, bidirectional typing remains decidable even for very…
The recently introduced dependent typed higher-order logic (DHOL) offers an interesting compromise between expressiveness and automation support. It sacrifices the decidability of its type system in order to significantly extend its…
We present the definition of the logical framework TF, the Type Framework. TF is a lambda-free logical framework; it does not include lambda-abstraction or product kinds. We give formal proofs of several results in the metatheory of TF, and…