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CVE-2026-72711— Lean 4 before 4.32.2 Kernel Accepts Opaque Declaration With an Unbound Free Variable

Quick assessment

Affected
leanprover lean4
Exploitation
No confirmed in-the-wild exploitation; assess based on exposure
Recommended action
Check the vendor advisory and references for a fixed version. If immediate upgrade is impossible, restrict exposure and increase monitoring.

Lean 4 内核未检查不透明声明（opaque declaration）的主体是否已闭合（closed）。 跳过了 和 路径中所执行的 检查，因此，若一个值包含自由变量（free variable）但该变量不在局部上下文（local context）中，内核不会直接拒绝它。 元程序（metaprogram）可以首先导致内核创建一个类型为 的临时局部变量，并将其类型记录在类型检查器的推理缓存（inference cache）中；随后，在该缓存条目仍驻留在同一类型检查器实例上期间，恢复局部上下文；最后提交一个不透明声

CVSS 6.3 · Medium EPSS 0.12% · P2

Affected Version Matrix 1

VendorProduct Version RangeStatus
leanprover lean4 < 4.32.2 affected
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I. Basic Information for CVE-2026-72711

Vulnerability Information
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Vulnerability Title
Lean 4 before 4.32.2 Kernel Accepts Opaque Declaration With an Unbound Free Variable
Source: CVE Program / CVE List V5
Vulnerability Description
The Lean 4 kernel does not check that the body of an opaque declaration is closed. environment::add_opaque omits the check_no_metavar_no_fvar call that the definition and theorem paths perform, so a value containing a free variable that is absent from the local context is not rejected outright. A metaprogram can first cause the kernel to create a temporary local of type False and record its type in the type checker's inference cache, then restore the local context while that cache entry persists on the same type checker instance, and finally submit an opaque declaration whose value is the now-unbound variable. The cache lookup answers before the branch that would test membership of the local context, so the kernel infers the cached type and admits an opaque constant of type False, from which any proposition follows. The declaration is accepted through the ordinary checked path at maximum kernel checking, without sorry, unsafeCast, debug.skipKernelTC, addDeclWithoutChecking, foreign code or a modified .olean file, and the result carries no axioms. Fixed in 4.32.2 by adding the missing closure check.
Source: CVE Program / CVE List V5
CVSS Information
CVSS:3.1/AV:L/AC:L/PR:N/UI:R/S:C/C:N/I:H/A:N
Source: CVE Program / CVE List V5
Vulnerability Type
输入验证不恰当
Source: CVE Program / CVE List V5

Affected Products

Vendor Product Affected Versions CPE Subscribe
leanprover lean4 0 ~ 4.32.2 -

II. Public POCs for CVE-2026-72711

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III. Intelligence Information for CVE-2026-72711

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Patches & Fixes for CVE-2026-72711 (1)

Vendor Advisories for CVE-2026-72711 (1)

Proof of Concept for CVE-2026-72711 (2)

IV. Related Vulnerabilities

Same product: lean4
Same vendor: leanprover
Same weakness: CWE-20

V. Comments for CVE-2026-72711

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