Lean 4 fork for HoTT-compatible kernel extensions (Path types, transport, HITs). Maintained against upstream leanprover/lean4.
57915af218
This PR fixes a bug in the Lean kernel. During reduction of `Nat.pow`, the kernel did not validate that the WHNF of the first argument is a `Nat` literal before interpreting it as an `mpz` number. This PR adds the missing check. ### Explanation In `type_checker::reduce_pow`, an expression was interpreted as a `Nat` literal without previously validating that it actually was a `Nat` literal. We (@TwoFX and me) noticed this while fuzzing the Lean kernel with GMP and Mimalloc disabled. Until now, the fuzzer found one crash, leading us to this issue. What are the consequences? If GMP is disabled, the Lean kernel will crash on some inputs after the memory allocator returns `null`. (MPZ tries to clone the `.const` expression in disguise of a `Nat` literal which accidentally has a size field indicating that the number has 88 trillion `mpz` digits. This is too much for every allocator.) If GMP is enabled, it is possible to [prove `False`](https://live.lean-lang.org/#codez=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) because the kernel doesn't crash on a memory allocation and instead just happily interprets the `.const` expression as a GMP number. Importantly, this is _not_ a flaw in Lean's type theory. It is an implementation bug in the built-in kernel, related to the efficient reduction of `Nat.pow`, that will be fixed with this PR; see the test file. Because Lean's kernel is relatively small, there are third-party kernel implementations such as `lean4lean` and `nanoda`. `lean4lean` catches the bogus proof, and looking at its code `nanoda` will, too, but I haven't tried it yet. |
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