CVE-2026-72844

Lean 4 Kernel Type Checking Bypass via Mismatched Structure Projections

Published Aug 20, 2026 CVSS 4.0 · 6.8 Medium EPSS < 1% KEV · Not listed
Description
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.

Remediation

No solution or workaround provided in the CVE record

Tracking

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Advisories

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History
Type Values Removed Values Added
Metrics ssvc

{'options': {'Automatable': 'no', 'Exploitation': 'poc', 'Technical Impact': 'partial'}, 'version': '2.0.3'}

Type Values Removed Values Added
First Time appeared Leanprover
Leanprover lean4
Vendors & Products Leanprover
Leanprover lean4
Type Values Removed Values Added
Description 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.
Title Lean 4 Kernel Type Checking Bypass via Mismatched Structure Projections
Weaknesses CWE-843
References
Metrics cvssV3_1

{'score': 6.3, 'vector': 'CVSS:3.1/AV:L/AC:L/PR:N/UI:R/S:C/C:N/I:H/A:N'}

cvssV4_0

{'score': 6.8, 'vector': 'CVSS:4.0/AV:L/AC:L/AT:N/PR:N/UI:P/VC:N/VI:H/VA:N/SC:N/SI:N/SA:N'}

Weaknesses

Sources

Status
PUBLISHED
Assigner
VulnCheck
Published
Updated
Nov 8, 2026, 2:08 PM
Reserved
Aug 10, 2026, 3:14 PM
Status
Deferred
Published
Aug 20, 2026, 6:16 PM
Modified
Oct 26, 2026, 2:17 AM