Rebuild lean-bench: pages in, verified indexed Lean out

Replaces the previous tree entirely. The pipeline is four separable pieces, each
testable on its own:

1. leanbench/llm.py      provider-neutral OpenAI-compatible connector, stdlib only,
                        with retries, JSON coercion and a scripted client so the
                        rest of the code is testable without a network.
2. leanbench/detect.py   per-page detection of formalizable mathematics. Case 1 is
                        mathematics asserted as fact (definition/theorem/lemma/...,
                        deliberately not sub-classified); case 2 is a problem left
                        open to the reader. Hits come back as spans -- start page
                        and index, end page and index -- so several per page is
                        normal. A hit cut off by the page end makes the detector
                        re-read that page together with the next, repeatedly, so an
                        item spread over three pages is found whole.
                        Offsets come from verbatim quotes resolved by
                        leanbench/anchors.py (exact -> whitespace-insensitive ->
                        fuzzy), because models quote well and count badly.
3. leanbench/formalize.py + leanbench/verify.py
                        each span becomes one Lean 4 declaration, judged by the real
                        compiler: full elaboration for case 1, statement legality
                        only for case 2, which has no proof to check. Lean's own
                        diagnostics feed back for a repair attempt. "verified" (Lean
                        accepted it) and "proved" (accepted with no sorry) are kept
                        strictly apart.
4. leanbench/db.py       indexed SQLite plus JSONL export. Every item is indexed by
                        the types of its inputs, or by its own type when it is not a
                        proof, and records the source book (sha256) and the page it
                        starts on -- so `drop --source H --pages A-B` followed by a
                        re-ingest redoes exactly those pages and nothing else.

Also: lean/ Lake project pinned to Mathlib, docker/ image carrying Lean 4 and a
prebuilt Mathlib (the Mathlib revision and the toolchain are resolved against each
other at build time rather than both hardcoded), and .gitea/workflows for tests,
image build and push to the Gitea registry, and a manual "submit a book" run.

58 tests; they need neither network nor Lean.

tests/conftest.py

@@ -0,0 +1,79 @@
+from __future__ import annotations
+
+import json
+from pathlib import Path
+
+import pytest
+
+from leanbench.document import Document
+from leanbench.verify import MODE_FULL, VerifyResult
+
+PAGE_ONE = """Chapter 1. Divisibility
+
+1.6 Divisibility in the Integers
+
+Definition 1.6.1. Let a and b be integers. We say a divides b, written a | b,
+if there exists an integer k such that b = a k.
+
+Theorem 1.6.2. Let a, b and c be integers. If a divides b and a divides c,
+then a divides b + c.
+
+Proof. Write b = a k and c = a m. Then b + c = a (k + m). QED
+
+Theorem 1.6.3. Let a and b be nonzero integers. Then the set of common
+"""
+
+PAGE_TWO = """divisors of a and b has a greatest element, the greatest common divisor.
+
+Exercise 1.6.4. Show that if a divides b and b divides a, then a = b or a = -b.
+
+Exercise 1.6.5. Prove that the sum of two odd integers is even.
+"""
+
+
+@pytest.fixture()
+def two_page_book(tmp_path: Path) -> Document:
+    path = tmp_path / "book.txt"
+    path.write_text(PAGE_ONE + "\f" + PAGE_TWO, encoding="utf-8")
+    return Document.load(path, title="Test Book")
+
+
+class FakeChecker:
+    """A Lean stand-in: fails anything containing ``BAD``, otherwise accepts."""
+
+    def __init__(self) -> None:
+        self.calls: list[str] = []
+
+    def available(self) -> bool:
+        return True
+
+    def check(self, code: str, *, mode: str = MODE_FULL, imports=None) -> VerifyResult:
+        self.calls.append(code)
+        if "BAD" in code:
+            return VerifyResult(False, mode, False, "LeanBenchCheck.lean:3:0: error: bad")
+        return VerifyResult(True, mode, "sorry" in code, "")
+
+
+@pytest.fixture()
+def fake_checker() -> FakeChecker:
+    return FakeChecker()
+
+
+def detection_reply(items: list[dict]) -> str:
+    return json.dumps({"items": items})
+
+
+def formalize_reply(**overrides) -> str:
+    payload = {
+        "skip": False,
+        "reason": "",
+        "imports": ["Mathlib"],
+        "name": "test_decl",
+        "lean_code": "theorem test_decl (a b : Int) (h : a ∣ b) : a ∣ b := by\n  sorry",
+        "has_proof": False,
+        "informal": "a divides b",
+        "index_types": ["Int"],
+        "confidence": 0.8,
+    }
+    payload.update(overrides)
+    return json.dumps(payload)

tests/test_anchors.py

@@ -0,0 +1,54 @@
+from __future__ import annotations
+
+from leanbench.anchors import find, resolve_span
+
+TEXT = (
+    "Theorem 1.6.2. Let a, b and c be integers. If a divides b and a divides c,\n"
+    "then a divides b + c.\n\nProof. Write b = a k."
+)
+
+
+def test_exact_match() -> None:
+    match = find(TEXT, "Theorem 1.6.2.")
+    assert match is not None and match.method == "exact"
+    assert TEXT[match.start : match.end] == "Theorem 1.6.2."
+
+
+def test_whitespace_insensitive_match_across_a_line_break() -> None:
+    match = find(TEXT, "a divides c, then a divides b + c.")
+    assert match is not None
+    assert match.method == "whitespace"
+    assert TEXT[match.start : match.end].replace("\n", " ") == "a divides c, then a divides b + c."
+
+
+def test_fuzzy_match_survives_a_typo() -> None:
+    match = find(TEXT, "Let a, b and c be integres. If a divides b")
+    assert match is not None
+    assert match.method == "fuzzy"
+    assert "integers" in TEXT[match.start : match.end]
+
+
+def test_missing_anchor_is_reported_not_guessed() -> None:
+    assert find(TEXT, "nothing like this appears anywhere in the page") is None
+
+
+def test_resolve_span_covers_start_to_end() -> None:
+    span = resolve_span(TEXT, "Theorem 1.6.2.", "a divides b + c.")
+    assert span is not None and span.resolved
+    assert TEXT[span.start : span.end].startswith("Theorem 1.6.2.")
+    assert TEXT[span.start : span.end].endswith("a divides b + c.")
+
+
+def test_resolve_span_falls_back_when_the_end_quote_is_wrong() -> None:
+    span = resolve_span(TEXT, "Theorem 1.6.2.", "this ending was invented", fallback_length=40)
+    assert span is not None
+    assert "truncated" in span.method
+    assert span.end - span.start == 40
+
+
+def test_resolve_span_searches_forward_from_the_cursor() -> None:
+    text = "alpha beta alpha gamma"
+    first = resolve_span(text, "alpha", "beta")
+    assert first is not None and first.start == 0
+    second = resolve_span(text, "alpha", "gamma", search_from=first.end)
+    assert second is not None and second.start == text.rindex("alpha")

tests/test_db.py

@@ -0,0 +1,133 @@
+from __future__ import annotations
+
+import json
+from pathlib import Path
+
+import pytest
+
+from leanbench.db import Database, ItemRow, item_id
+
+
+def row(**overrides) -> ItemRow:
+    data = dict(
+        id="",
+        source_hash="book-hash-a",
+        kind="statement",
+        label="Theorem 1.6.2",
+        summary="divisibility is additive",
+        informal="a | b and a | c implies a | b + c",
+        start_page=12,
+        start_index=100,
+        end_page=12,
+        end_index=260,
+        page_checksum="abc",
+        source_text="Theorem 1.6.2 ...",
+        lean_name="dvd_add'",
+        lean_code="theorem dvd_add' (a b c : Int) : True := trivial",
+        imports=["Mathlib"],
+        has_proof=True,
+        verified=True,
+        proved=True,
+        verify_mode="full",
+        diagnostics="",
+        confidence=0.9,
+        match_method="exact",
+        match_score=1.0,
+        truncated=False,
+        types=[("Int", "input")],
+    )
+    data.update(overrides)
+    if not data["id"]:
+        data["id"] = item_id(data["source_hash"], data["start_page"], data["start_index"],
+                             data["end_page"], data["end_index"])
+    return ItemRow(**data)
+
+
+@pytest.fixture()
+def database(tmp_path: Path) -> Database:
+    db = Database(tmp_path / "test.sqlite")
+    db.upsert_source("book-hash-a", title="Algebra", path="a.pdf", pages=400)
+    yield db
+    db.close()
+
+
+def test_item_id_is_stable_for_the_same_span() -> None:
+    first = item_id("h", 1, 2, 3, 4)
+    assert first == item_id("h", 1, 2, 3, 4)
+    assert first != item_id("h", 1, 2, 3, 5)
+
+
+def test_store_and_read_back(database: Database) -> None:
+    identifier = database.upsert_item(row())
+    stored = database.get(identifier)
+    assert stored is not None
+    assert stored["imports"] == ["Mathlib"]
+    assert stored["types"] == [{"name": "Int", "role": "input"}]
+
+
+def test_reingesting_the_same_span_updates_rather_than_duplicates(database: Database) -> None:
+    database.upsert_item(row())
+    database.upsert_item(row(lean_name="renamed", types=[("Nat", "input")]))
+    assert database.stats()["items"] == 1
+    stored = database.get(item_id("book-hash-a", 12, 100, 12, 260))
+    assert stored is not None and stored["lean_name"] == "renamed"
+    assert stored["types"] == [{"name": "Nat", "role": "input"}], "stale types are dropped"
+
+
+def test_search_by_type_is_the_point(database: Database) -> None:
+    database.upsert_item(row(types=[("Int", "input")]))
+    database.upsert_item(row(start_index=500, end_index=700, kind="problem",
+                             types=[("Polynomial", "input"), ("Int", "input")]))
+    assert len(database.search(types=["Int"])) == 2
+    assert len(database.search(types=["Polynomial"])) == 1
+    assert len(database.search(types=["Int", "Polynomial"], match_all_types=True)) == 1
+    assert len(database.search(types=["Int"], kind="problem")) == 1
+
+
+def test_search_by_role_separates_definitions_from_theorems(database: Database) -> None:
+    database.upsert_item(row(types=[("Ideal", "own")]))
+    database.upsert_item(row(start_index=900, end_index=950, types=[("Ideal", "input")]))
+    assert len(database.search(types=["Ideal"], roles=["own"])) == 1
+    assert len(database.search(types=["Ideal"], roles=["input"])) == 1
+
+
+def test_search_by_page_finds_items_spanning_it(database: Database) -> None:
+    database.upsert_item(row(start_page=12, end_page=14))
+    assert len(database.search(page=13)) == 1
+    assert len(database.search(page=20)) == 0
+
+
+def test_dropping_a_page_range_lets_you_redo_part_of_a_book(database: Database) -> None:
+    database.upsert_item(row(start_page=12))
+    database.upsert_item(row(start_page=40, start_index=1, end_page=40, end_index=50))
+    removed = database.delete_pages("book-hash-a", 10, 20)
+    assert removed == 1
+    assert database.stats()["items"] == 1
+    assert database.search(page=40)
+
+
+def test_dropping_a_source_takes_its_items_with_it(database: Database) -> None:
+    database.upsert_item(row())
+    database.delete_source("book-hash-a")
+    assert database.stats()["items"] == 0
+    assert database.sources() == []
+
+
+def test_export_jsonl_leaves_out_bulk_by_default(database: Database, tmp_path: Path) -> None:
+    database.upsert_item(row())
+    out = tmp_path / "items.jsonl"
+    assert database.export_jsonl(out) == 1
+    record = json.loads(out.read_text(encoding="utf-8").splitlines()[0])
+    assert "source_text" not in record and "diagnostics" not in record
+    assert record["types"] == [{"name": "Int", "role": "input"}]
+    assert database.export_jsonl(out, include_source_text=True) == 1
+    assert "source_text" in json.loads(out.read_text(encoding="utf-8").splitlines()[0])
+
+
+def test_stats_counts_the_things_that_matter(database: Database) -> None:
+    database.upsert_item(row())
+    database.upsert_item(row(start_index=2, kind="problem", proved=False, verified=True))
+    stats = database.stats()
+    assert stats["items"] == 2 and stats["statements"] == 1 and stats["problems"] == 1
+    assert stats["verified"] == 2 and stats["proved"] == 1
+    assert database.type_counts()[0]["name"] == "Int"

tests/test_detect.py

@@ -0,0 +1,133 @@
+from __future__ import annotations
+
+from leanbench.detect import KIND_PROBLEM, KIND_STATEMENT, detect_document
+from leanbench.document import Document
+from leanbench.llm import ScriptedClient
+
+from .conftest import detection_reply
+
+
+def test_single_page_detection_reports_page_and_index(two_page_book: Document) -> None:
+    client = ScriptedClient(
+        [
+            detection_reply(
+                [
+                    {
+                        "kind": "statement",
+                        "label": "Definition 1.6.1",
+                        "summary": "divisibility",
+                        "start_quote": "Definition 1.6.1. Let a and b be integers.",
+                        "end_quote": "b = a k.",
+                        "continues_past_end": False,
+                    }
+                ]
+            ),
+            detection_reply([]),
+        ]
+    )
+    report = detect_document(client, two_page_book, max_window_pages=3)
+    assert len(report.detections) == 1
+    found = report.detections[0]
+    assert found.kind == KIND_STATEMENT
+    assert found.start_page == 1 and found.end_page == 1
+    page = two_page_book.page(1).text
+    assert page[found.start_index : found.end_index].startswith("Definition 1.6.1")
+    assert page[found.start_index : found.end_index].endswith("b = a k.")
+
+
+def test_item_running_off_the_page_triggers_a_second_page(two_page_book: Document) -> None:
+    truncated = detection_reply(
+        [
+            {
+                "kind": "statement",
+                "label": "Theorem 1.6.3",
+                "summary": "gcd exists",
+                "start_quote": "Theorem 1.6.3. Let a and b be nonzero integers.",
+                "end_quote": "the set of common",
+                "continues_past_end": True,
+            }
+        ]
+    )
+    whole = detection_reply(
+        [
+            {
+                "kind": "statement",
+                "label": "Theorem 1.6.3",
+                "summary": "gcd exists",
+                "start_quote": "Theorem 1.6.3. Let a and b be nonzero integers.",
+                "end_quote": "the greatest common divisor.",
+                "continues_past_end": False,
+            },
+            {
+                "kind": "problem",
+                "label": "Exercise 1.6.5",
+                "summary": "odd + odd is even",
+                "start_quote": "Exercise 1.6.5. Prove that the sum of two odd",
+                "end_quote": "odd integers is even.",
+                "continues_past_end": False,
+            },
+        ]
+    )
+    client = ScriptedClient([truncated, whole])
+    report = detect_document(client, two_page_book, max_window_pages=3)
+
+    assert len(client.calls) == 2, "the page should be re-read with its successor"
+    theorem = report.detections[0]
+    assert theorem.start_page == 1
+    assert theorem.end_page == 2, "the span must cross the page boundary"
+    assert theorem.spans_pages == 2
+    assert not theorem.truncated
+    assert two_page_book.page(2).text[: theorem.end_index].endswith("greatest common divisor.")
+
+    exercise = report.detections[1]
+    assert exercise.kind == KIND_PROBLEM
+    assert exercise.start_page == 2
+
+
+def test_window_stops_growing_at_the_limit_and_says_so(two_page_book: Document) -> None:
+    always_truncated = detection_reply(
+        [
+            {
+                "kind": "statement",
+                "label": "",
+                "summary": "",
+                "start_quote": "Definition 1.6.1. Let a and b be integers.",
+                "end_quote": "b = a k.",
+                "continues_past_end": True,
+            }
+        ]
+    )
+    client = ScriptedClient([always_truncated] * 4)
+    report = detect_document(client, two_page_book, max_window_pages=2)
+    assert len(client.calls) == 2
+    assert report.detections[0].truncated is True
+
+
+def test_unresolvable_quotes_are_recorded_not_invented(two_page_book: Document) -> None:
+    client = ScriptedClient(
+        [
+            detection_reply(
+                [
+                    {
+                        "kind": "statement",
+                        "label": "Hallucination 9",
+                        "summary": "not in the book",
+                        "start_quote": "Theorem 9.9.9 about topological quantum widgets",
+                        "end_quote": "which is absurd.",
+                        "continues_past_end": False,
+                    }
+                ]
+            ),
+            detection_reply([]),
+        ]
+    )
+    report = detect_document(client, two_page_book)
+    assert report.detections == []
+    assert len(report.unresolved) == 1
+
+
+def test_a_failing_page_does_not_kill_the_run(two_page_book: Document) -> None:
+    client = ScriptedClient(["not json at all", detection_reply([])])
+    report = detect_document(client, two_page_book)
+    assert report.pages_scanned == 2
+    assert any("detector failed" in u.get("reason", "") for u in report.unresolved)

tests/test_document.py

@@ -0,0 +1,46 @@
+from __future__ import annotations
+
+from leanbench.document import Document, Page, PageWindow, normalise_page_text
+
+
+def test_pages_are_numbered_from_one(two_page_book: Document) -> None:
+    assert len(two_page_book) == 2
+    assert [p.number for p in two_page_book.pages] == [1, 2]
+    assert two_page_book.page(1).text.startswith("Chapter 1")
+
+
+def test_window_locate_maps_back_to_the_right_page() -> None:
+    window = PageWindow([Page(7, "abcdef"), Page(8, "ghij")])
+    assert window.text == "abcdef\nghij"
+    assert window.locate(0) == (7, 0)
+    assert window.locate(5) == (7, 5)
+    assert window.locate(6) == (7, 6)      # end of page 7
+    assert window.locate(7) == (8, 0)      # first char of page 8
+    assert window.locate(10) == (8, 3)
+    assert window.locate(999) == (8, 4)    # clamped
+
+
+def test_window_globalise_is_the_inverse() -> None:
+    window = PageWindow([Page(1, "hello"), Page(2, "world")])
+    for page, offset in [(1, 0), (1, 4), (2, 0), (2, 4)]:
+        assert window.locate(window.globalise(page, offset)) == (page, offset)
+
+
+def test_document_slice_reconstructs_a_cross_page_span(two_page_book: Document) -> None:
+    page_one = two_page_book.page(1).text
+    start = page_one.index("Theorem 1.6.3")
+    end = two_page_book.page(2).text.index("has a greatest")
+    text = two_page_book.slice(1, start, 2, end)
+    assert text.startswith("Theorem 1.6.3")
+    assert text.rstrip().endswith("divisors of a and b")
+
+
+def test_normalisation_is_stable_and_gentle() -> None:
+    text = "first line   \nsecond"
+    assert normalise_page_text(text) == "first line\nsecond"
+    assert normalise_page_text(normalise_page_text(text)) == normalise_page_text(text)
+
+
+def test_page_checksum_changes_with_content() -> None:
+    assert Page(1, "a").checksum != Page(1, "b").checksum
+    assert Page(1, "a").checksum == Page(9, "a").checksum

tests/test_formalize.py

@@ -0,0 +1,90 @@
+from __future__ import annotations
+
+from leanbench.detect import KIND_PROBLEM, KIND_STATEMENT, Detection
+from leanbench.formalize import formalize, formalize_all, verification_mode
+from leanbench.llm import ScriptedClient
+from leanbench.verify import MODE_FULL, MODE_STATEMENT
+
+from .conftest import formalize_reply
+
+
+def make_detection(kind: str = KIND_STATEMENT) -> Detection:
+    return Detection(
+        kind=kind,
+        label="Theorem 1.6.2",
+        summary="divisibility is additive",
+        start_page=12,
+        start_index=100,
+        end_page=12,
+        end_index=260,
+        text="Theorem 1.6.2. If a divides b and a divides c then a divides b + c.",
+    )
+
+
+def test_open_problems_are_only_checked_as_statements() -> None:
+    assert verification_mode(make_detection(KIND_PROBLEM)) == MODE_STATEMENT
+    assert verification_mode(make_detection(KIND_STATEMENT)) == MODE_FULL
+
+
+def test_formalize_produces_verified_code_and_types(fake_checker) -> None:
+    client = ScriptedClient([formalize_reply()])
+    result = formalize(client, make_detection(), checker=fake_checker)
+    assert result.lean_code.startswith("theorem test_decl")
+    assert result.verified
+    assert not result.proved, "a sorry in the code means it is not proved"
+    assert ("Int", "input") in result.index_types
+
+
+def test_a_real_proof_counts_as_proved(fake_checker) -> None:
+    client = ScriptedClient(
+        [formalize_reply(lean_code="theorem t (n : Nat) : n = n := rfl", has_proof=True)]
+    )
+    result = formalize(client, make_detection(), checker=fake_checker)
+    assert result.has_proof and result.proved
+
+
+def test_lean_diagnostics_drive_a_repair_attempt(fake_checker) -> None:
+    client = ScriptedClient(
+        [
+            formalize_reply(lean_code="theorem t : BAD := by sorry"),
+            formalize_reply(lean_code="theorem t (n : Nat) : n = n := rfl", has_proof=True),
+        ]
+    )
+    result = formalize(client, make_detection(), checker=fake_checker, repair_attempts=1)
+    assert result.attempts == 2
+    assert result.verified
+    assert len(client.calls) == 2
+    repair_prompt = client.calls[1][-1]["content"]
+    assert "error: bad" in repair_prompt, "the compiler's own words go back to the model"
+
+
+def test_repair_gives_up_after_the_budget(fake_checker) -> None:
+    client = ScriptedClient([formalize_reply(lean_code="theorem t : BAD := by sorry")] * 3)
+    result = formalize(client, make_detection(), checker=fake_checker, repair_attempts=1)
+    assert result.attempts == 2
+    assert not result.verified
+
+
+def test_model_may_decline_an_unformalizable_passage(fake_checker) -> None:
+    client = ScriptedClient(['{"skip": true, "reason": "prose only"}'])
+    result = formalize(client, make_detection(), checker=fake_checker)
+    assert result.skipped and result.skip_reason == "prose only"
+    assert fake_checker.calls == []
+
+
+def test_imports_inside_the_body_are_stripped(fake_checker) -> None:
+    client = ScriptedClient(
+        [formalize_reply(lean_code="import Mathlib\ntheorem t (n : Nat) : n = n := rfl")]
+    )
+    result = formalize(client, make_detection(), checker=fake_checker)
+    assert "import" not in result.lean_code
+
+
+def test_one_bad_item_does_not_stop_the_batch(fake_checker) -> None:
+    client = ScriptedClient(["garbage, not json", formalize_reply()])
+    results = formalize_all(
+        client, [make_detection(), make_detection(KIND_PROBLEM)], checker=fake_checker
+    )
+    assert len(results) == 2
+    assert results[0].skipped and "formalizer failed" in results[0].skip_reason
+    assert results[1].verified

tests/test_llm.py

@@ -0,0 +1,38 @@
+from __future__ import annotations
+
+import pytest
+
+from leanbench.llm import LLMError, ScriptedClient, extract_code, parse_json
+
+
+def test_parse_json_plain() -> None:
+    assert parse_json('{"a": 1}') == {"a": 1}
+
+
+def test_parse_json_through_a_fence() -> None:
+    assert parse_json('```json\n{"a": [1, 2]}\n```') == {"a": [1, 2]}
+
+
+def test_parse_json_with_chatter_around_it() -> None:
+    assert parse_json('Sure!\n{"ok": true}\nHope that helps.') == {"ok": True}
+
+
+def test_parse_json_raises_when_there_is_none() -> None:
+    with pytest.raises(ValueError):
+        parse_json("no json here")
+
+
+def test_extract_code_pulls_the_lean_block() -> None:
+    raw = "Here you go:\n```lean4\ntheorem t : True := trivial\n```\nDone."
+    assert extract_code(raw) == "theorem t : True := trivial"
+
+
+def test_extract_code_passes_bare_code_through() -> None:
+    assert extract_code("theorem t : True := trivial") == "theorem t : True := trivial"
+
+
+def test_scripted_client_runs_out_loudly() -> None:
+    client = ScriptedClient(["one"])
+    assert client.complete([]) == "one"
+    with pytest.raises(LLMError):
+        client.complete([])

tests/test_pipeline.py

@@ -0,0 +1,158 @@
+from __future__ import annotations
+
+from pathlib import Path
+
+from leanbench.config import Settings
+from leanbench.db import Database
+from leanbench.document import Document
+from leanbench.llm import ScriptedClient
+from leanbench.pipeline import ingest
+
+from .conftest import detection_reply, formalize_reply
+
+DETECT_PAGE_ONE = detection_reply(
+    [
+        {
+            "kind": "statement",
+            "label": "Definition 1.6.1",
+            "summary": "divisibility",
+            "start_quote": "Definition 1.6.1. Let a and b be integers.",
+            "end_quote": "b = a k.",
+            "continues_past_end": False,
+        },
+        {
+            "kind": "statement",
+            "label": "Theorem 1.6.3",
+            "summary": "gcd exists",
+            "start_quote": "Theorem 1.6.3. Let a and b be nonzero integers.",
+            "end_quote": "the set of common",
+            "continues_past_end": True,
+        },
+    ]
+)
+
+DETECT_BOTH_PAGES = detection_reply(
+    [
+        {
+            "kind": "statement",
+            "label": "Definition 1.6.1",
+            "summary": "divisibility",
+            "start_quote": "Definition 1.6.1. Let a and b be integers.",
+            "end_quote": "b = a k.",
+            "continues_past_end": False,
+        },
+        {
+            "kind": "statement",
+            "label": "Theorem 1.6.3",
+            "summary": "gcd exists",
+            "start_quote": "Theorem 1.6.3. Let a and b be nonzero integers.",
+            "end_quote": "the greatest common divisor.",
+            "continues_past_end": False,
+        },
+        {
+            "kind": "problem",
+            "label": "Exercise 1.6.4",
+            "summary": "mutual divisibility",
+            "start_quote": "Exercise 1.6.4. Show that if a divides b and b divides a",
+            "end_quote": "a = b or a = -b.",
+            "continues_past_end": False,
+        },
+    ]
+)
+
+
+def _settings(tmp_path: Path) -> Settings:
+    settings = Settings.from_env(dotenv=None)
+    settings.database = str(tmp_path / "leanbench.sqlite")
+    settings.repair_attempts = 0
+    return settings
+
+
+def test_end_to_end_run_stores_indexed_items(tmp_path: Path, two_page_book, fake_checker) -> None:
+    client = ScriptedClient(
+        [DETECT_PAGE_ONE, DETECT_BOTH_PAGES]
+        + [
+            formalize_reply(name="divides_def",
+                            lean_code="def divides (a b : Int) : Prop := ∃ k : Int, b = a * k"),
+            formalize_reply(name="gcd_exists",
+                            lean_code="theorem gcd_exists (a b : Int) : True := by\n  sorry"),
+            formalize_reply(name="dvd_antisymm'",
+                            lean_code="theorem dvd_antisymm' (a b : Int) : True := by\n  sorry"),
+        ]
+    )
+    settings = _settings(tmp_path)
+    database = Database(settings.database)
+    result = ingest(
+        two_page_book.path,
+        settings=settings,
+        client=client,
+        database=database,
+        checker=fake_checker,
+        title="Test Book",
+    )
+    summary = result.summary()
+    assert summary["detected"] == 3
+    assert summary["problems"] == 1
+    assert summary["multi_page"] == 1
+    assert summary["stored"] == 3
+    assert summary["verified"] == 3
+
+    assert database.stats()["items"] == 3
+    by_type = database.search(types=["Int"])
+    assert len(by_type) == 3, "every item is reachable through its types"
+    problems = database.search(kind="problem")
+    assert len(problems) == 1 and problems[0]["start_page"] == 2
+    database.close()
+
+
+def test_reingesting_a_page_range_replaces_only_that_range(
+    tmp_path: Path, two_page_book: Document, fake_checker
+) -> None:
+    settings = _settings(tmp_path)
+    database = Database(settings.database)
+
+    first = ScriptedClient([DETECT_PAGE_ONE, DETECT_BOTH_PAGES] + [formalize_reply()] * 3)
+    ingest(two_page_book.path, settings=settings, client=first, database=database,
+           checker=fake_checker)
+    assert database.stats()["items"] == 3
+
+    # redo page 2 only: the page-1 item survives, page-2 items are rebuilt
+    second = ScriptedClient(
+        [
+            detection_reply(
+                [
+                    {
+                        "kind": "problem",
+                        "label": "Exercise 1.6.5",
+                        "summary": "odd plus odd",
+                        "start_quote": "Exercise 1.6.5. Prove that the sum of two odd",
+                        "end_quote": "odd integers is even.",
+                        "continues_past_end": False,
+                    }
+                ]
+            ),
+            formalize_reply(name="odd_add_odd"),
+        ]
+    )
+    ingest(two_page_book.path, settings=settings, client=second, database=database,
+           checker=fake_checker, first_page=2, last_page=2)
+
+    pages = sorted(item["start_page"] for item in database.search(limit=100))
+    assert pages == [1, 1, 2], "page 1 untouched, page 2 replaced by the new run"
+    database.close()
+
+
+def test_a_run_without_lean_stores_items_but_claims_nothing(
+    tmp_path: Path, two_page_book: Document
+) -> None:
+    from leanbench.verify import NullChecker
+
+    client = ScriptedClient([DETECT_PAGE_ONE, DETECT_BOTH_PAGES] + [formalize_reply()] * 3)
+    settings = _settings(tmp_path)
+    database = Database(settings.database)
+    result = ingest(two_page_book.path, settings=settings, client=client, database=database,
+                    checker=NullChecker())
+    assert result.summary()["stored"] == 3
+    assert result.summary()["verified"] == 0
+    assert database.search(verified=True) == []
+    database.close()

tests/test_typeindex.py

@@ -0,0 +1,81 @@
+from __future__ import annotations
+
+from leanbench.typeindex import ROLE_GOAL, ROLE_INPUT, ROLE_OWN, index_types, parse_signature
+
+
+def test_theorem_is_indexed_by_the_types_of_its_inputs() -> None:
+    code = "theorem add_dvd (a b c : Int) (h : a ∣ b) (k : a ∣ c) : a ∣ b + c := by\n  sorry"
+    signature = parse_signature(code)
+    assert signature is not None
+    assert signature.is_proof
+    assert signature.name == "add_dvd"
+    assert "Int" in signature.inputs
+    pairs = index_types(code)
+    assert ("Int", ROLE_INPUT) in pairs
+
+
+def test_definition_is_indexed_by_its_own_type() -> None:
+    code = "def divides (a b : Int) : Prop := ∃ k : Int, b = a * k"
+    signature = parse_signature(code)
+    assert signature is not None
+    assert not signature.is_proof
+    pairs = index_types(code)
+    assert ("Int", ROLE_INPUT) in pairs
+    assert ("Prop", ROLE_OWN) in pairs, "a predicate's own type is the point of it"
+    assert all(role != ROLE_GOAL for _, role in pairs)
+
+
+def test_a_proof_is_not_indexed_by_Prop() -> None:
+    pairs = index_types("theorem t (n : Nat) : n = n := rfl")
+    assert all(name != "Prop" for name, _ in pairs)
+
+
+def test_definition_of_a_concrete_type_records_it() -> None:
+    pairs = index_types("def double (n : Nat) : Nat := 2 * n")
+    assert ("Nat", ROLE_OWN) in pairs
+
+
+def test_instance_binders_count_as_inputs() -> None:
+    code = "theorem foo {G : Type*} [Group G] (x : G) : x * 1 = x := by simp"
+    signature = parse_signature(code)
+    assert signature is not None
+    assert "Group" in signature.inputs
+
+
+def test_unicode_number_types_are_normalised() -> None:
+    code = "theorem sq_nonneg' (n : ℤ) : 0 ≤ n ^ 2 := by positivity"
+    pairs = dict(index_types(code))
+    assert pairs.get("Int") == ROLE_INPUT
+
+
+def test_structure_records_its_own_type() -> None:
+    code = "structure Monoid' (M : Type) : Type where\n  one : M"
+    signature = parse_signature(code)
+    assert signature is not None
+    assert signature.keyword == "structure"
+    assert signature.own or signature.inputs
+
+
+def test_model_supplied_types_are_merged_without_duplicates() -> None:
+    code = "theorem t (n : Nat) : n = n := rfl"
+    pairs = index_types(code, ["Nat", "Polynomial", "  "])
+    names = [name for name, _ in pairs]
+    assert names.count("Nat") == 1
+    assert "Polynomial" in names
+
+
+def test_comments_do_not_leak_into_the_index() -> None:
+    code = "-- about Matrix stuff\n/- Group -/\ntheorem t (n : Nat) : n = n := rfl"
+    names = [name for name, _ in index_types(code)]
+    assert "Matrix" not in names and "Group" not in names
+
+
+def test_declaration_keyword_detected_after_attributes() -> None:
+    code = "@[simp]\nprivate theorem t (n : Nat) : n = n := rfl"
+    signature = parse_signature(code)
+    assert signature is not None and signature.keyword == "theorem"
+
+
+def test_unparsable_code_yields_nothing_rather_than_nonsense() -> None:
+    assert parse_signature("this is not lean") is None
+    assert index_types("this is not lean") == []