arXiv subjects

Emilio Jesùs Gallego Arias

Publications and source records attributed to Emilio Jesùs Gallego Arias.

2 recordsLinked to original sources

arXiv2025

MiniF2F in Rocq: Automatic Translation Between Proof Assistants -- A Case Study

In this work, we conduct an experiment using state-of-the-art LLMs to translate MiniF2F into Rocq. The translation task focuses on generating a Rocq theorem based on three sources: a natural language description, the Lean formalization, and the Isabelle formalization. We conducted our experiment in 3 stages of increasing complexity, from basic one-shot prompting to multi-turn conversations that incorporate feedback from unsuccessful attempts. At each stage, we perform multiple rounds of translation using increasingly advanced models: GPT-4o mini, Claude 3.5 Sonnet, o1 mini, and o1. We successfully translated 478 out of 488 theorems. The dataset is opensource: https://github.com/LLM4Rocq/miniF2F-rocq.

cs.LO↗

arXiv2016

Differentially Private Bayesian Programming

We present PrivInfer, an expressive framework for writing and verifying differentially private Bayesian machine learning algorithms. Programs in PrivInfer are written in a rich functional probabilistic programming language with constructs for performing Bayesian inference. Then, differential privacy of programs is established using a relational refinement type system, in which refinements on probability types are indexed by a metric on distributions. Our framework leverages recent developments in Bayesian inference, probabilistic programming languages, and in relational refinement types. We demonstrate the expressiveness of PrivInfer by verifying privacy for several examples of private Bayesian inference.

cs.PL↗