brendanzab / lean-holes

Interactive holes for Lean 4

lean-holes

Warning

This is an experimental and incomplete proof-of-concept!

A syntax extension for Lean 4 that adds support for interactive holes¹. The goal is to make it easier to interactively construct programs and direct-style proofs in a type directed way.

Holes can be introduced using following custom syntax:

syntax "?" : term
syntax "{!" (term)? "!}" : term

For examples, see Examples/Sample.lean.

A series of code actions are provided:

• Fill with contents
• Fill with elaborated contents
• Automatically fill a hole (NOTE: rudimentary support²)
• Refine hole
• Split hole
• Make definition

The same actions have been added to _, ?_, and sorry.

Resources

This was inspired by this conversation with David Christiansen on Mastodon.

Agda docs:

• Agda: A Taste of Agda – Holes and case splitting
• Agda: Lexical structure – Holes
• Agda: Emacs Mode – Commands in the context of a goal
• Agda: Automatic Proof Search (Auto)

Idris:

• Idris 2: Interactive Editing
• Idris 2: The IDE Protocol
• Idris 2: TTImp.Interactive.ExprSearch

Footnotes

1. As seen in Agda and Idris. I’m not exactly sure when interactive holes where first introduced however... possibly in Epigram? ↩

2. Auto-filling currently just looks up the local context for a matching declaration. ↩