SHF: Small: Declaratively Creating Semantics-driven Visualizations

可视化图表对于交流困难的技术概念至关重要;例如，有充分的证据表明，当使用图表而不是纯文本时，学生可以更有效地学习和解决问题。科学概念的有效沟通受到难以创建良好图表的事实的限制：抽象的逻辑或数学概念对于非专家来说很难转化为引人注目的图形，传统的软件工具生成的静态图表不容易促进交互或探索。 该项目开发了一个名为Penrose的下一代框架，在该框架中，可以通过简单地键入特定于领域的语言中的表达式来创建高质量的图表，这些语言反映了学生和科学家谈论数学的方式。 该项目的新颖之处在于系统地编码抽象数学语句及其视觉表示之间的关系，并通过约束非线性优化自动生成满足这些关系的图表。 该项目的影响是大大降低了创建有效图表的障碍，并加快了复杂技术思想的交流速度-特别是在科学教育和研究领域。该项目采用了编程语言和计算机图形学之间的跨学科方法。 在语言层面上，Penrose通过两种可扩展的规范语言Substance和Style（类似于HTML和CSS），将数学内容和其视觉表示清晰地分离开来。在图形方面，程序被编译成一个约束优化程序，其解决方案描述了一个家庭的可能图。 然后可以使用自动或用户辅助工具来选择或交互式地探索特定的图表。 Penrose提供的系统编码也可以用来智能地搜索有用的例子、特例或反例。 一个免费的基于网络的彭罗斯界面鼓励社区开发新的用户设计的模块;这些模块集成到一个互动的数学导师系统有助于丰富和加速美国下一代科学家和工程师的培训。这个奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

Visual diagrams are essential for communicating difficult technical concepts; for instance, there is ample evidence that students learn more effectively and can solve problems more efficiently when using diagrams rather than plain text. Effective communication of scientific concepts is limited by the fact that good diagrams remain hard to create: abstract logical or mathematical concepts are difficult for non-experts to translate into compelling graphical figures, and traditional software tools produce static diagrams that do not easily facilitate interaction or exploration. This project develops a next-generation framework called Penrose, where high-quality diagrams can be created by simply typing expressions in domain-specific languages that reflect the way students and scientists already talk about mathematics. The project's novelties are to systematically encode the relationships between abstract mathematical statements and their visual representations, and to automatically generate diagrams satisfying these relationships via constrained nonlinear optimization. The project's impacts are to significantly lower the barrier to creating effective diagrams, and to accelerate the rate at which complex technical ideas are communicated---especially in the domain of scientific education and research.The project takes an interdisciplinary approach between programming languages and computer graphics. At the language level, Penrose enforces a clean separation between mathematical content and its visual representation via two extensible specification languages, Substance and Style, akin to HTML and CSS. On the graphics side, programs are compiled into a constrained optimization program whose solutions describe a family of possible diagrams. Automatic or user-assisted tools can then be used to select or interactively explore specific diagrams. The systematic encodings provided by Penrose can also be used to intelligently search for useful examples, special cases, or counterexamples. A free web-based Penrose interface encourages community development of new user-designed modules; integration of these modules into an interactive mathematical tutor system helps to enrich and accelerate the training of the next generation of scientists and engineers in the US.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.