Porting Mathlib from Lean 3 to Lean 4 is a huge effort, and I'm sure it's not undertaken on a whim. Could you please point me to documentation explaining the motivation for the incompatible changes? Is Lean 4 faster? More expressive?

The Lean 4 survival guide for Lean 3 users showcases many changes, but those look superficial to me.

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    $\begingroup$ Sorry for the basic question. Google search results are all fitness motivation videos and discussion of goals in the theorem proving sense. :( $\endgroup$ Jun 9, 2023 at 12:12
  • $\begingroup$ Perhaps "leanprover" is a good search keyword. That's the downside of naming your language with a common word! $\endgroup$
    – Trebor
    Jun 9, 2023 at 13:19
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    $\begingroup$ It looks like the port will be finished in a few weeks, by the way; the community is over 80% of the way through. $\endgroup$ Jun 9, 2023 at 15:48
  • $\begingroup$ I saw! I wrote 71% in a doc a week or so ago and today it's 85%! Fantastic work! That's why I want to know exact what I'm excited for! :) $\endgroup$ Jun 9, 2023 at 17:50

1 Answer 1


There are many aspects to this:

  • It's faster (e.g. the ~80% portion of mathlib that has been ported so far compiles between 3 and 4 times faster than it did under Lean 3.)
  • The metaprogramming framework (which is even more different relative to Lean 3 than the proving experience) is massively more capable. Most of Lean 4 is written in Lean 4, and users adding tactics can hook into and modify the internals in all sorts of new ways.
  • It's intended as a general purpose programming language, not just an interactive theorem prover. (Lean 4 produces quite impressively fast executables. You can call into C++. It has reference counting tricks that allows functional code to be compiled to update-in-place when appropriate, and the Do unchained paper explains how to write functional code in an imperative style.)
  • The type theory itself is essentially unchanged, although there are some usability improvements (in particular typeclass search is faster, and can cope with loops).

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