Related papers: A Framework for Automated and Certified Refinement…
ALAMO is a computational methodology for leaning algebraic functions from data. Given a data set, the approach begins by building a low-complexity, linear model composed of explicit non-linear transformations of the independent variables.…
Software tools of Automated Reasoning are too sophisticated for general use in mathematics education and respective reasoning, while Lucas-Interpretation provides a general concept for integrating such tools into educational software with…
Multi-step reasoning improves the capabilities of large language models (LLMs) but increases the risk of errors propagating through intermediate steps. Process reward models (PRMs) mitigate this by scoring each step individually, enabling…
Proof by induction plays a central role in formal verification. However, its automation remains as a formidable challenge in Computer Science. To solve inductive problems, human engineers often have to provide auxiliary lemmas manually. We…
The paper describes the refinement algorithm for the Calculus of (Co)Inductive Constructions (CIC) implemented in the interactive theorem prover Matita. The refinement algorithm is in charge of giving a meaning to the terms, types and proof…
Mathematical theorem proving is an important testbed for large language models' deep and abstract reasoning capability. This paper focuses on improving LLMs' ability to write proofs in formal languages that permit automated proof…
Our objective is to formally verify the correctness of the hundreds of expression optimization rules used within the GraalVM compiler. When defining the semantics of a programming language, expressions naturally form abstract syntax trees,…
Scientific software is often driven by multiple parameters that affect both accuracy and performance. Since finding the optimal configuration of these parameters is a highly complex task, it extremely common that the software is used…
Despite its many unquestionable benefits, formal specifications are not widely used in industrial software development. In order to reduce the time and effort required to write formal specifications, in this paper we propose a technique for…
We present a one-fits-all programmatic approach to reason about a plethora of objectives on probabilistic programs. The first ingredient is to add a reward-statement to the language. We then define a program transformation applying a…
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…
Recent advances in large language models (LLMs) have yielded impressive performance on various tasks, yet they often depend on high-quality feedback that can be costly. Self-refinement methods attempt to leverage LLMs' internal evaluation…
This paper presents PRISM: an instruction-conditioned refinement method for imitation policies in robotic manipulation. This approach bridges Imitation Learning (IL) and Reinforcement Learning (RL) frameworks into a seamless pipeline, such…
Self-awareness, i.e., the ability to assess and correct one's own generation, is a fundamental aspect of human intelligence, making its replication in large language models (LLMs) an important yet challenging task. Previous works tackle…
As machine learning is increasingly used in essential systems, it is important to reduce or eliminate the incidence of serious bugs. A growing body of research has developed machine learning algorithms with formal guarantees about…
Users of program analyses expect that results change predictably in response to changes in their programs, but many analyses fail to provide such robustness. This paper introduces a theoretical framework that provides a unified language to…
To derive a program for a given specification R means to find an artifact P that satisfies two conditions: P is executable in some programming language; and P is correct with respect to R. Refinement-based program derivation achieves this…
Capture calculus has recently been proposed as a solution to effect checking, achieved by tracking the captured references of terms in the types. Boxes, along with the box and unbox operations, are a crucial construct in capture calculus,…
Almost-sure termination is an important correctness property for probabilistic programs, and a number of program logics have been developed for establishing it. However, these logics have mostly been developed for first-order programs…
Can language models (LMs) self-refine their own responses? This question is increasingly relevant as a wide range of real-world user interactions involve refinement requests. However, prior studies have largely tested LMs' refinement…