Contemporary proof assistants impose restrictive syntactic guardedness conditions that reject many valid corecursive definitions. Existing approaches to overcome these restrictions present a fundamental trade-off between coverage and automation. We present Compositional Heterogeneous Productivity (CHP), a theoretical framework that unifies high automation with extensive coverage for corecursive definitions. CHP introduces heterogeneous productivity applicable to functions with diverse domain and codomain types, including non-coinductive types. Its key innovation is compositionality: the productivity of composite functions is systematically computed from their components, enabling modular reasoning about complex corecursive patterns. Building on CHP, we develop Coco, a corecursion library for Rocq that provides extensive automation for productivity computation and fixed-point generation.

In this paper, we present the competition “Real-time Machine Learning Competition on Data Streams a BigData Cup Challenge of the IEEE Big Data 2019 conference. Data streams, such as data originated from sensors, have increasingly gained the interest of researchers and companies and are currently widely studied in data science. Companies in the telecommunication and energy industries are trying to exploit these data and get real-time insights on their services and equipment. In order to extract valuable knowledge from data streams, one must be able to analyze the data as they arrive and make meaningful predictions. For this purpose, we use fast incremental learners. There already exists a great community that is organizing various competitions on machine learning tasks for batch learners. Our goal was to introduce the same approach to engage the whole community in solving essential problems in data stream mining. We performed a new kind of data science competition based on a real-time prediction setting, using a novel competition platform on data streams. The examples to predict were released in real-time, and the predictions had also to be submitted in real-time. To the best of our knowledge, this was the first data science competition conducted in real-time. The task of the competition was to predict network activity, and the data has been provided by one of our partner companies.