Michael D. Adams Eric Griffis Thomas J. Porter Sundara Vishnu Satish Eric Zhao Cyrus Omar 2025 1 9 https://mustardfox.org/adams-et-al-2025/ adams-et-al-2025 /adams-et-al-2025/ Grove: A Bidirectionally Typed Collaborative Structure Editor Calculus reference POPL 2025 10.1145/3704909 zzhaoe-000Q /bafkrmigmhnqhc24zxmxphoaw3khagv6xahf4k23h6lzwiogafvjk6prgce.pdf Michael D. Adams Eric Griffis Thomas J. Porter Sundara Vishnu Satish Eric Zhao Cyrus Omar 2025 1 9 abstract Version control systems typically rely on a patch language, heuristic patch synthesis algorithms like diff, and three-way merge algorithms. Standard patch languages and merge algorithms often fail to identify conflicts correctly when there are multiple edits to one line of code or code is relocated. This paper introduces Grove, a collaborative structure editor calculus that eliminates patch synthesis and three-way merge algorithms entirely. Instead, patches are derived directly from the log of the developer’s edit actions and all edits commute, i.e. the repository state forms a commutative replicated data type (CmRDT). To handle conflicts that can arise due to code relocation, the core datatype in Grove is a labeled directed multi-graph with uniquely identified vertices and edges. All edits amount to edge insertion and deletion, with deletion being permanent. To support tree-based editing, we define a decomposition from graphs into groves, which are a set of syntax trees with conflicts—including local, relocation, and unicyclic relocation conflicts—represented explicitly using holes and references between trees. Finally, we define a type error localization system for groves that enjoys a totality property, i.e. all editor states in Grove are statically meaningful, so developers can use standard editor services while working to resolve these explicitly represented conflicts. The static semantics is defined as a bidirectional marking system in line with recent work, with gradual typing employed to handle situations where errors and conflicts prevent type determination. We then layer on a unification-based type inference system to opportunistically fill type holes and fail gracefully when no solution exists. We mechanize the metatheory of Grove using the Agda theorem prover. We implement these ideas as the Grove Workbench, which generates the necessary data structures and algorithms in OCaml given a syntax tree specification. References Context Backlinks Eric Zhao 2025 1 https://mustardfox.org/zzhaoe-003A/ zzhaoe-003A /zzhaoe-003A/ Grove published at POPL 2025 news Our paper on Grove, a collaborative structured editing calculus, is published at POPL! Michael D. Adams Eric Griffis Thomas J. Porter Sundara Vishnu Satish Eric Zhao Cyrus Omar 2024 https://mustardfox.org/zzhaoe-000Q/ zzhaoe-000Q /zzhaoe-000Q/ Grove (Agda) software 10.5281/zenodo.14026532 POPL 2025 fplab/grove-agda An Agda mechanization of the Grove collaborative structure editor calculus described in "Grove: A Bidirectionally Typed Collaborative Structure Editor Calculus". Related 2024 1 19 2024 1 25 https://mustardfox.org/popl-2025/ popl-2025 /popl-2025/ POPL 2025 venue https://popl25.sigplan.org Denver, Colorado, United States of America Contributions