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Modern web browsers rely on layout engines to convert HTML documents to layout trees that specify color, size, and position. However, existing layout engines are notoriously difficult to maintain because of the complexity of web standards. This is especially true for incremental layout engines, which are designed to improve performance by updating only the parts of the layout tree that need to be changed. In this paper, we propose Medea, a new framework for automatically generating incremental layout engines. Medea separates the specification of the layout engine from its incremental implementation, and guarantees correctness through layout engine synthesis. The synthesis is driven by a new iterative algorithm based on detecting conflicts that prevent optimality of the incremental algorithm. We evaluated Medea on a fragment of HTML layout that includes challenging features such as margin collapse, floating layout, and absolute positioning. Medea successfully synthesized an incremental layout engine for this fragment. The synthesized layout engine is both correct and efficient. In particular, we demonstrated that it avoids real-world bugs that have been reported in the layout engines of Chrome, Firefox, and Safari. The incremental layout engine synthesized by Medea is up to 1.82× faster than a naive incremental baseline. We also demonstrated that our conflict-driven algorithm produces engines that are 2.74× faster than a baseline without conflict analysis. 

3D Computer-Aided Design (CAD) modeling is ubiquitous in mechanical engineering and design. Modern CAD models are programs that produce geometry and can be used to implement high-level geometric changes by modifying input parameters. While there has been a surge of recent interest in program-based tooling for the CAD domain, one fundamental problem remains unsolved. CAD programs pass geometric arguments to operations using references, which are queries that select elements from the constructed geometry according to programmer intent. The challenge is designing reference semantics that can express programmer intent across all geometric topologies achievable with model parameters, including topologies where the desired elements are not present. In current systems, both users and automated tools may create invalid models when parameters are changed, as references to geometric elements are lost or silently and arbitrarily switched. While existing CAD systems use heuristics to attempt to infer user intent in cases of this undefined behavior, this best-effort solution is not suitable for constructing automated tools to edit and optimize CAD programs. We analyze the failure modes of existing referencing schemes and formalize a set of criteria on which to evaluate solutions to the CAD referencing problem. In turn, we propose a domain-specific language that exposes references as a first-class language construct, using user-authored queries to introspect element history and define references safely over all paths. We give a semantics for fine-grained element lineage that can subsequently be queried; and show that our language meets the desired properties. Finally, we provide an implementation of a lineage-based referencing system in a 2.5D CAD kernel, demonstrating realistic referencing scenarios and illustrating how our system safely represents models that cause reference breakage in existing CAD systems. 

Abstract Modern CAD tools represent 3D designs not only as geometry, but also as a program composed of geometric operations, each of which depends on a set of parameters. Program representations enable meaningful and controlled shape variations via parameter changes. However, achieving desired modifications solely through parameter editing is challenging when CAD models have not been explicitly authored to expose select degrees of freedom in advance. We introduce a novel bidirectional editing system for 3D CAD programs. In addition to editing the CAD program, users can directly manipulate 3D geometry and our system infers parameter updates to keep both representations in sync. We formulate inverse edits as a set of constrained optimization objectives, returning plausible updates to program parameters that both match user intent and maintain program validity. Our approach implements an automatically differentiable domain‐specific language for CAD programs, providing derivatives for this optimization to be performed quickly on any expressed program. Our system enables rapid, interactive exploration of a constrained 3D design space by allowing users to manipulate the program and geometry interchangeably during design iteration. While our approach is not designed to optimize across changes in geometric topology, we show it is expressive and performant enough for users to produce a diverse set of design variants, even when the CAD program contains a relatively large number of parameters.