CVE-2026-72844 in Lean 4
Summary
by MITRE • 08/20/2026
The Lean 4 kernel does not verify that the structure named in a projection expression matches the type of the value being projected, and environment::add_inductive in src/kernel/inductive.cpp did not type check the nested inductive applications that are replaced by auxiliary types, so their parametric arguments escaped checking. A metaprogram running in the Lean process can register an ill-typed nested inductive whose constructor applies a .proj C 0 projection to a value of the unrelated type W, and the kernel admits the declaration through the ordinary checked addDecl path at maximum kernel checking, without sorry, unsafeCast, debug.skipKernelTC, addDeclWithoutChecking, FFI, or a modified .olean file. The result is a type confusion yielding a proof of False that carries no axioms, from which any proposition can be derived. The published proof of concept additionally pads two expressions until their hashes and approximate depths collide, which defeats kernel caching; that is the technique used to reach the flaw, not its cause. Exploitation requires running a metaprogram in-process, for example by building a project or importing a malicious Lake dependency.
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Analysis
by VulDB Data Team • 08/20/2026
The vulnerability identified involves critical failures within the Lean 4 proof assistant's kernel and environment management systems, specifically concerning type checking during the registration of nested inductive types. The core technical flaw stems from two distinct but related oversights: first, the kernel fails to verify that the structure named in a projection expression matches the actual type of the value being projected; second, the function responsible for adding inductive definitions did not perform adequate type checking on nested inductive applications that are replaced by auxiliary types. This lack of verification allows parametric arguments associated with these nested structures to escape standard validation processes entirely. Consequently, an attacker can craft a metaprogram running within the Lean process environment to register an ill-typed nested inductive definition where a constructor applies a projection operation to a value belonging to an unrelated type.
This architectural weakness enables a severe type confusion scenario that compromises the logical integrity of the system. Because the kernel admits such declarations through its standard checked declaration path at maximum checking levels, it does not require workarounds typically associated with bypassing security controls, such as using sorry blocks, unsafe casts, debug skips, or modified object files. The immediate operational impact is catastrophic for a proof assistant: an attacker can construct a valid-looking proof of False that carries no axioms and relies solely on the flawed type system logic. In formal verification contexts where logical consistency is paramount, deriving False allows any proposition to be derived via ex falso quodlibet, effectively rendering all previous proofs within that session or context invalid and untrustworthy.
From a threat modeling perspective, this vulnerability aligns with CWE-843, which relates to the access of resources using incorrect types, leading to type confusion attacks. The exploitation vector is classified under MITRE ATT&CK technique T1059, specifically Command and Scripting Interpreter subcategories involving metaprogramming capabilities inherent to the language environment. While the published proof of concept utilizes a side-channel attack by padding expressions to cause hash collisions in kernel caching mechanisms as a delivery method, this cache collision is merely an enabler for reaching the flawed code path rather than the root cause itself. The fundamental issue remains the insufficient type checking during the registration of complex nested structures within the environment layer.
Mitigation strategies must focus on strengthening the validation logic within the kernel's inductive handling routines. Developers need to implement rigorous cross-referencing between projection expressions and their target value types before admitting declarations into the global context. Additionally, enhancing the type checker for auxiliary types generated during nested inductive application processing is essential to prevent parametric arguments from bypassing scrutiny. Until a patch is deployed, users should exercise extreme caution when importing external Lake dependencies or executing untrusted metaprograms within Lean sessions, as these represent the primary vectors for triggering this vulnerability through in-process execution.