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Welcome to the yatima-lang wiki!

The end goal of this repository is to:

• Independently evaluate and typecheck Lean 4 programs with a kernel implemented both in Rust and Lean 4
• Content-address every Lean 4 environment, declaration, expression and universe level via using the IPLD data format, with a name-irrelevant representation similar to the Unison language
• Compile Lean programs to the Lurk zk-SNARK language, so that we can generate zero-knowledge proof, which can be verified in constant-time and space, that a Lean program f, with input x, evaluates to y
• Compile the Yatima typechecker itself to Lurk, so we can generate zero-knowledge proofs that our Lean typechecker, with inputs env : Yatima.Environment and const : Yatima.Constant, returns successfully without error. For example, we can produce a cryptographic witness that some definition def foo : M := N correctly typechecks, which can be validated without re-running the typechecker.

This will enable us to produce a succinct and efficiently verifiable correctness certificate for e.g. Lean's mathematical library (and for each of its declarations) once it's ported to Lean 4, which currently takes over 4 hours to be typechecked by the Lean 3 kernel (as of May '22).

Execution plan

1. Since we want to build on top of Lean 4 source files, we can take advantage from the fact that its API becomes available for any Lean 4 code that does import Lean. Thus, we are creating an application in Lean 4 to make use of its Lean.Elab.runFrontend function, which can parse the source files and instantiate Lean.Environment for us.

2. With a Lean.Environment at hand, we can translate its declarations to our own content-addressed Yatima types, such as Yatima.Expr, Yatima.Univ etc, outputting a .ya file

3. Then we can have our Yatima types typechecked with our own Rust/Lean 4 kernels

4. We will also be able to generate Lurk programs from Yatima types

Learning resources

• Created by the team

  • Yatima Presentation
  • Inductive types in Lean 4
  • Universe levels in Lean 4
  • IPLD and CID
  • Zero knowledge proofs and zk-SNARKs
  • An example of content addressing Universes

• Official documentation

  • Lean 4
  • IPLD
  • Lurk

• Literature, books, repositories, videos, pages etc

  • Curry–Howard correspondence
  • A presentation about Lurk
  • Type-Directed Partial Evaluation
  • Checking Dependent Types with Normalization by Evaluation: A Tutorial
  • pi-forall