tree-sitter-lean

A tree-sitter grammar for the Lean 4 theorem prover.

The parser is designed to be a drop-in for Neovim's nvim-treesitter and any other editor that consumes tree-sitter grammars. Highlight, fold, indent, locals, and injection queries live under queries/.

What this is

A static concrete-syntax parser that covers enough of Lean 4 for editor tooling: highlighting, folding, indentation, scope-aware features. Node names mirror Lean's own SyntaxNodeKinds where doing so costs nothing — Lean.Parser.Command.import becomes import, Lean.Parser.Term.app becomes app. Highlight captures use the nvim-treesitter naming that maps back to Lean's SemanticTokenType vocabulary, so cold-start coloring lines up with what the LSP server emits at runtime.

What this is not

A faithful reproduction of Lean's parser. Lean's parser is dynamic and extensible: users register new tokens, notation, and categories at runtime, and macros expand inside a Syntax tree the parser materializes. Tree-sitter is LR(1) + GLR over a static grammar — it cannot model any of that.

Concretely, this grammar does not support:

• User-defined notation / syntax / macro extensions. The notation, prefix, infix, infixl, infixr, postfix, syntax, macro, and macro_rules commands themselves parse, but uses of the operators they introduce inside other code are only recognized when they're already in the static operator table.
• Custom precedence numbers via :N suffixes (e.g. leading_parser:max).
• The full set of Mathlib tactics. Tactics are uniformly parsed as generic term-shaped invocations; tooling can dispatch on the head identifier of an app node for highlighting.
• Multi-name structure fields (x y : T) and inline doc-comments / attributes on individual fields. One name per field, one line per field; this matches the dominant style in practice.

end is treated as a top-level command rather than a nested closer. Files in lean4 and Mathlib routinely leave namespaces unclosed relative to a strict scope discipline, and a flat end recovers better.

Layout

Tactic and do blocks use the external scanner's indent stack. A newline-introduced indented region opens a block; subsequent same- indent lines are separators; a dedent closes the block. EOF closes every open block. This matches Lean's behavior closely enough for all real source we've tested.

State-count budget

The generated parser.c is currently under 5 MB. An earlier draft with one rule per built-in tactic produced a 10 MB file; the grammar intentionally keeps tactic, do-element, and Mathlib operator vocabularies generic to avoid LR state explosion. Adding rules that recurse into _term is the most expensive thing you can do here — double-check the budget after every such change.

Layout

grammar.js               — grammar definition
src/scanner.c            — external scanner (identifiers, comments,
                           raw strings, indent tracking)
queries/
  highlights.scm         — syntax highlighting
  injections.scm         — markdown injection in doc-comments
  locals.scm             — scope-aware definition/reference tracking
  folds.scm              — block-level folds
  indents.scm            — auto-indent hints
test/corpus/             — tree-sitter test corpus

Development

tree-sitter generate
tree-sitter test

prek (drop-in for pre-commit) is configured via .pre-commit-config.yaml.

License

MIT — see LICENSE.