scan: lean4 — 7 defect tickets (4x MOAD-0001, 2x MOAD-0005, 1x MOAD-0003)
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# lean4-0001: guardCycle() O(N²) — List.contains on call stack in topological build traversal
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**Target:** leanprover/lean4
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**Severity:** HIGH
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**CWE:** CWE-407 (Inefficient Algorithmic Complexity)
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**MOAD:** MOAD-0001 (A Sedimentary Defect)
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**File:** `src/lake/Lake/Util/Cycle.lean:83`, `src/lake/Lake/Build/Topological.lean:98`
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**Language:** Lean 4
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**Status:** open
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## Description
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`guardCycle` uses `List.contains` for cycle detection inside Lake's topological
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dependency resolver. Every module build traversal calls `guardCycle` once per
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node, each time scanning the entire ancestor call stack linearly. For a project
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with N modules in a linear dependency chain, total cost reaches O(N²).
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## Root Cause
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```lean
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-- Lake/Util/Cycle.lean:14
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public abbrev CallStack κ := List κ -- plain List, no hash index
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-- Lake/Util/Cycle.lean:79–86
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@[inline] public def guardCycle
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[BEq κ] [Monad m] [MonadCycle κ m] (key : κ) (act : m α)
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: m α := do
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let parents ← getCallStack
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if parents.contains key then -- O(N) scan every call
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throwCycle <| key :: (parents.partition (· != key)).1 ++ [key]
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else
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withCallStack (key :: parents) act -- prepend: stack grows to depth D
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```
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Called from `recFetchAcyclic` at `Lake/Build/Topological.lean:98` for every
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node in the module dependency graph during a build.
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With a linear chain A → B → C → … → Z (N modules):
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- node 1: scan depth 0
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- node 2: scan depth 1
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- node N: scan depth N-1
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- **Total: O(N²/2) comparisons**
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## Complexity
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| N modules (linear chain) | guardCycle calls | comparisons |
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|--------------------------|-----------------|-------------|
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| 100 | 100 | ~5,000 |
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| 500 | 500 | ~125,000 |
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| 1000 | 1000 | ~500,000 |
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Real projects (Mathlib4: ~2000 files) hit this on dependency-heavy subgraphs.
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## Fix
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Carry a parallel `HashSet` (or `NameHashSet` / `Std.HashSet`) for O(1)
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membership test. Keep the `List` only for cycle path reporting.
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```lean
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-- Proposed: pair (HashSet for O(1) contains, List for cycle reporting)
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public abbrev CallStack κ := Std.HashSet κ × List κ
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@[inline] public def guardCycle
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[BEq κ] [Hashable κ] [Monad m] [MonadCycle κ m] (key : κ) (act : m α)
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: m α := do
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let (set, list) ← getCallStack
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if set.contains key then -- O(1)
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throwCycle <| key :: (list.partition (· != key)).1 ++ [key]
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else
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withCallStack (set.insert key, key :: list) act
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```
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## Speedup Estimate
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Linear chain N=1000: O(N²) → O(N). ~1000× faster at that scale.
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Typical projects (N=50–200 in hot subgraphs): 50–200× faster.
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# lean4-0002: kernel/inductive.cpp O(K×N) — std::find in nested loop for inductive type validation
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**Target:** leanprover/lean4
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**Severity:** MEDIUM
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**CWE:** CWE-407 (Inefficient Algorithmic Complexity)
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**MOAD:** MOAD-0001 (A Sedimentary Defect)
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**File:** `src/kernel/inductive.cpp:529–532`
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**Language:** C++
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**Status:** open
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## Description
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Inside the kernel's inductive type validator, `std::find` on a plain `buffer<expr>`
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runs inside a `for` loop over another buffer. For a constructor with K type-former
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arguments and N result arguments, cost reaches O(K×N).
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## Root Cause
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```cpp
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// inductive.cpp:526–532
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buffer<expr> result_args;
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get_app_args(type, result_args);
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/* Check condition 2: every argument in to_check must occur in result_args */
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for (expr const & arg : to_check) { // O(K) outer
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if (std::find(result_args.begin(), result_args.end(), arg) == result_args.end()) // O(N) inner
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return true; /* Condition 2 failed */
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}
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```
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`to_check` holds type-former arguments; `result_args` holds application
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arguments from the return type. Both grow with constructor arity.
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## Fix
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Use `std::unordered_set<expr>` (or Lean's `expr_set`) for `result_args`:
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```cpp
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expr_set result_set(result_args.begin(), result_args.end()); // O(N) build
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for (expr const & arg : to_check) {
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if (result_set.find(arg) == result_set.end()) // O(1) lookup
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return true;
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}
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```
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## Related
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`inductive.cpp:543` — same `std::find` pattern for fresh universe param name
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generation (while loop scanning `m_lparams`). Low severity in practice since
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universe parameter counts stay small, but structurally identical defect.
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# lean4-0003: library/util.cpp + kernel/inductive.cpp — O(N²) fresh name generation via std::find in while loop
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**Target:** leanprover/lean4
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**Severity:** LOW-MEDIUM
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**CWE:** CWE-407 (Inefficient Algorithmic Complexity)
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**MOAD:** MOAD-0001 (A Sedimentary Defect)
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**Files:** `src/library/util.cpp:69–72`, `src/kernel/inductive.cpp:543–546`
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**Language:** C++
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**Status:** open
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## Description
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Two identical patterns: a `while` loop generates fresh names by appending
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an incrementing index, checking for collisions via `std::find` on a plain
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vector each iteration. Cost is O(N²) if N existing names must be checked
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before a fresh one is found.
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## Root Cause
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```cpp
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// library/util.cpp:69–72
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while (std::find(lp_names.begin(), lp_names.end(), l) != lp_names.end()) {
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l = name("l").append_after(i);
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i++;
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}
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// kernel/inductive.cpp:543–546
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while (std::find(m_lparams.begin(), m_lparams.end(), u) != m_lparams.end()) {
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u = name("u").append_after(i);
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i++;
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}
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```
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Both scan the full list per attempt. With N existing names: O(N²) to find
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a free slot at position N.
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## Fix
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Convert to `std::unordered_set<name>` (or `name_set`) before the loop:
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```cpp
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name_set existing(lp_names.begin(), lp_names.end());
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while (existing.count(l)) {
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l = name("l").append_after(i++);
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}
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```
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## Severity Note
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Universe parameter counts are typically < 10 in practice. Performance
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impact is negligible today but the pattern is structurally a sedimentary
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defect and will bite as Lean handles larger polymorphic libraries.
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# lean4-0004: ir_interpreter.cpp — double-checked locking without memory barrier in symbol lookup
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**Target:** leanprover/lean4
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**Severity:** HIGH
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**CWE:** CWE-362 (Concurrent Execution Using Shared Resource with Improper Synchronization)
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**MOAD:** MOAD-0005 (A Thundering Herd)
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**File:** `src/library/ir_interpreter.cpp:828–869`
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**Language:** C++
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**Status:** open
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## Description
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`lookup_symbol` in the IR interpreter uses a double-checked locking pattern
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without memory barriers. A first check on `m_symbol_cache` runs without any
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lock. A second check on `g_native_symbol_cache` runs under shared lock.
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Between the two, the lock is released and re-acquired as exclusive. On
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weakly-ordered architectures, two concurrent threads can both pass the
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unguarded first check, both acquire exclusive lock in sequence, and insert
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duplicate entries — or worse, observe partially-constructed cache entries.
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## Root Cause
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```cpp
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// ir_interpreter.cpp:828–869 (simplified)
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auto e = m_symbol_cache.find(fn); // (1) unguarded check
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if (e != m_symbol_cache.end()) {
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return e->second;
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}
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std::shared_lock<std::shared_mutex> lock(*g_native_symbol_cache_mutex);
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auto ne = g_native_symbol_cache->find(fn); // (2) shared-locked check
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if (ne != g_native_symbol_cache->end()) {
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m_symbol_cache.insert({ fn, e_new }); // inserts without exclusive lock
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return e_new;
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}
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lock.unlock();
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std::unique_lock<std::shared_mutex> unique_lock(*g_native_symbol_cache_mutex);
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ne = g_native_symbol_cache->find(fn); // (3) double-check under exclusive lock
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if (ne == g_native_symbol_cache->end()) {
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// ... compute ...
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g_native_symbol_cache->insert({ fn, e_new.m_native });
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}
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```
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Step (1) reads `m_symbol_cache` without synchronization. On x86 this is
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generally safe due to TSO, but on ARM/RISC-V reordering can expose
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partially-initialized entries from another thread's prior insert.
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## Fix
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Use `std::atomic<bool>` or ensure `m_symbol_cache` access is guarded by
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the same mutex. Alternatively, use a single-phase double-check under the
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exclusive lock:
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```cpp
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{
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std::shared_lock lock(*g_native_symbol_cache_mutex);
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auto e = m_symbol_cache.find(fn);
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if (e != m_symbol_cache.end()) return e->second;
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}
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std::unique_lock lock(*g_native_symbol_cache_mutex);
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// recheck under exclusive lock, then compute+insert
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```
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# lean4-0005: Lake/Build/Run.lean — concurrent job registration races on JobQueue IO.Ref
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**Target:** leanprover/lean4
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**Severity:** HIGH
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**CWE:** CWE-362 (Concurrent Execution Using Shared Resource with Improper Synchronization)
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**MOAD:** MOAD-0005 (A Thundering Herd)
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**Files:** `src/lake/Lake/Build/Job/Register.lean:43`, `src/lake/Lake/Build/Run.lean:157`
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**Language:** Lean 4
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**Status:** open
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## Description
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Multiple async build tasks call `registerJob` concurrently. Each calls
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`registeredJobs.modify (·.push job)` on a shared `IO.Ref (Array OpaqueJob)`
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without a mutex. Lean's `IO.Ref.modify` is not atomic with respect to
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concurrent tasks — two tasks can both read the same array, both push their
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job, and one registration gets lost.
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## Root Cause
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```lean
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-- Lake/Build/Context.lean:42
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public def JobQueue := IO.Ref (Array OpaqueJob)
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-- Lake/Build/Job/Register.lean:43
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(← getBuildContext).registeredJobs.modify (·.push job)
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-- ↑ read-modify-write on shared IO.Ref, no mutex
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```
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Concurrently spawned tasks (via `Job.async`) all share the same
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`BuildContext.registeredJobs`. Each calls `.modify` independently:
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- Task A reads array [j1, j2]
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- Task B reads array [j1, j2]
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- Task A writes [j1, j2, jA]
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- Task B writes [j1, j2, jB] ← overwrites Task A's registration
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- jA is lost from the monitor
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```lean
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-- Lake/Build/Run.lean:157 — monitor reads the same ref
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let newJobs ← (← read).jobs.modifyGet ((·, #[]))
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```
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The monitor drain races with concurrent registrations.
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## Fix
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Wrap `JobQueue` with a `Mutex` or use `IO.Mutex`:
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```lean
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public def JobQueue := IO.Mutex (Array OpaqueJob)
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-- register:
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(← getBuildContext).registeredJobs.atomically (·.push job)
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-- poll:
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let newJobs ← (← read).jobs.atomically (fun arr => (arr, #[]))
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```
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Or use a `Channel`/`Queue` abstraction that is safe for concurrent push
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from producers and drain from the monitor consumer.
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# lean4-0006: kernel/trace.cpp — LEAN_THREAD_PTR(g_opts) leaks trace options across tasks on thread pool reuse
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**Target:** leanprover/lean4
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**Severity:** MEDIUM
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**CWE:** CWE-668 (Exposure of Resource to Wrong Sphere)
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**MOAD:** MOAD-0003 (A Leaked Context)
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**File:** `src/kernel/trace.cpp:16`
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**Language:** C++
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**Status:** open
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## Description
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`g_opts` — the trace options pointer — is stored as a thread-local variable
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via `LEAN_THREAD_PTR`. Lean's async task system uses a thread pool. When a
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thread finishes one elaboration task and picks up a new one, the thread-local
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`g_opts` from the previous task remains set. The new task inherits the old
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trace configuration, causing incorrect trace output (silence when tracing
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expected, or noise when silence expected).
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## Root Cause
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```cpp
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// kernel/trace.cpp:16
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LEAN_THREAD_PTR(const options, g_opts);
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// kernel/trace.cpp:25
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bool is_trace_class_enabled(name const & n) {
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if (!g_opts) return false;
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return is_trace_class_enabled_core(*g_opts, n);
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}
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```
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`g_opts` is set per-elaboration invocation but never explicitly cleared on
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task completion. Thread pool threads reuse their `g_opts` across tasks.
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## Fix
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Reset `g_opts` to `nullptr` at task boundaries (on task start/end in the
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thread pool scheduler), or pass options explicitly via context rather than
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thread-local. The pattern of setting thread-locals before a task and
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clearing after is already used in other parts of the runtime
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(`reset_thread_local()`). Apply the same discipline here.
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# lean4-0007: runtime/process.cpp — O(N²) Windows environment variable inheritance
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**Target:** leanprover/lean4
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**Severity:** LOW-MEDIUM
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**CWE:** CWE-407 (Inefficient Algorithmic Complexity)
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**MOAD:** MOAD-0001 (A Sedimentary Defect)
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**File:** `src/runtime/process.cpp:247–254`
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**Language:** C++
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**Platform:** Windows only
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**Status:** open
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## Description
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When spawning child processes on Windows with `inherit_env=true`, the runtime
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iterates all inherited environment variable keys and checks each against
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`new_env_vars` (an `unordered_map`) using `.count({key_begin, key_end})`.
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This constructs a temporary `std::string` from a char range per iteration.
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With N environment variables and M override vars, cost is O(N × M) due to
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repeated string construction and hash lookup inside the loop.
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## Root Cause
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```cpp
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// runtime/process.cpp:237–254
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std::unordered_map<std::string, option_ref<string_ref>> new_env_vars;
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// ... populate new_env_vars from explicit overrides ...
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while (*key_begin) {
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char *key_end = strchr(key_begin, '=');
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char *entry_end = key_end + strlen(key_end);
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if (!new_env_vars.count({key_begin, key_end})) { // constructs std::string each iteration
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new_envp = std::copy(key_begin, entry_end + 1, new_envp);
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}
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key_begin = entry_end + 1;
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}
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```
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`.count({key_begin, key_end})` constructs a `std::string` on each of N
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iterations. The map itself is O(1) per lookup, but string construction
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is non-trivial. On systems with 200–500 env vars, this is measurable.
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## Fix
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Use `std::string_view` for the key lookup (C++17), or pre-build a
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`std::unordered_set<std::string>` from `new_env_vars` keys before the loop
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and use `.count()` on it with a string_view. The `std::string` allocation
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per iteration is the waste to eliminate.
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```cpp
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// Build key set once, outside loop
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std::unordered_set<std::string> override_keys;
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for (auto const & kv : new_env_vars) override_keys.insert(kv.first);
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while (*key_begin) {
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char *key_end = strchr(key_begin, '=');
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std::string_view key(key_begin, key_end - key_begin);
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if (!override_keys.count(std::string(key))) { // still O(1), one alloc per lookup
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...
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}
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}
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```
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## Severity Note
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Windows-only code path. Environment variable counts rarely exceed 500.
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Impact is real but not critical. Low priority compared to lean4-0001 and lean4-0004.
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