Update README.md

README.md

@@ -4,7 +4,21 @@ Noir is a Domain Specific Language for SNARK proving systems. With `coq-of-noir`
 
 ## Status
 
-This is still a work in progress. Contact us at [Formal Land](https://formal.land/) if you are interested.
+This is still a work in progress. Contact us at [contact@formal.land](mailto:contact@formal.land) or by direct message on our [X account](https://x.com/FormalLand) if you are interested.
+
+## Goal and Vision
+
+The goal is to enable each team developing critical applications (meaning handling user money) to verify the correctness of their code with the higest degree of certainty thanks to **formal verification**.
+
+For those who do not know, formal verification is a technique to verify software for 100% of possible execution parameters. **This means that the code cannot have bugs or vulnerabilities!** Initially applied to software from the spacial/defense industry, the key idea is to mathematically reason about the code to talk about possibly infinitely many possible cases, and to verify all the reasoning by a dedicated tool called a proof checker, in our case 🐓 Coq.
+
+In this repository, we provide a command to automatically translate a Noir program to a representation in Coq. We translate the code after the monomorphisation phase of the Noir compiler so that we do not have to deal with polymorphism or type classes. Instead, one can reconstruct this organization of the code on the Coq side in a refinement step, if needed.
+
+This translation is a shallow embedding optimized to write specifications and proofs about the code. As we erase all the types during the translation to keep only the values, we recommend doing a first proof step that reconstructs these types. This first proof step is also an opportunity to explicit the structure of the global state.
+
+Our initial target is to verify a part of the [base64](https://github.com/noir-lang/noir_base64), which uses field arithmetic for optimizations. It also includes many loops, which are generally non-trivial to fully verify with formal verification.
+
+_If you have a Noir project that you want to formally verify, either start using `coq-of-noir` or contact us!_
 
 ## Blog posts