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from __future__ import annotations
from dataclasses import dataclass
from typing import Any, Iterable, Mapping
from .canonical import attach_hash
from .expression import affine_coefficients, evaluate_dual_interval, evaluate_point
from .interval import ClosedInterval
from .model import IntervalWorld, Relation
from .rational import Q
@dataclass(frozen=True, slots=True)
class CrossingResult:
relation: Relation
accepted: bool
status: str
exact_root: Q | None
bracket: ClosedInterval
certificate: Mapping[str, Any]
def qrecord(value: Q | None) -> dict[str, int] | None:
return None if value is None else value.to_record()
def state_record(state: Mapping[str, Q]) -> dict[str, dict[str, int]]:
return {name: value.to_record() for name, value in sorted(state.items())}
def _opposite_sign(a: Q, b: Q) -> bool:
return a.sign() * b.sign() < 0
def certify_crossing(
world: IntervalWorld,
relation: Relation,
bracket: ClosedInterval,
*,
refine_steps: int | None = None,
) -> CrossingResult:
trajectory = world.trajectory
active = relation.active_time.intersection(bracket)
if active is None or active != bracket:
record = attach_hash({
"schema": "TOM-CERTIFIED-CROSSING-0.3",
"world_hash": world.content_hash,
"relation_id": relation.id,
"relation_hash": relation.content_hash,
"status": "outside-active-time",
"accepted": False,
"bracket": bracket.to_record(),
})
return CrossingResult(relation, False, "outside-active-time", None, bracket, record)
steps = int(world.solver.get("refine_steps", 24) if refine_steps is None else refine_steps)
max_steps = int(world.solver.get("max_refine_steps", 128))
if steps < 0 or steps > max_steps:
raise ValueError(f"refine_steps {steps} outside 0..{max_steps}")
f0 = evaluate_point(relation.expression, trajectory, bracket.lower)
f1 = evaluate_point(relation.expression, trajectory, bracket.upper)
dual = evaluate_dual_interval(relation.expression, trajectory, bracket)
affine = affine_coefficients(relation.expression, trajectory)
exact_root: Q | None = None
existence = False
root_kind = "none"
if f0 == Q(0):
exact_root = bracket.lower
existence = True
root_kind = "left-endpoint"
elif f1 == Q(0):
exact_root = bracket.upper
existence = True
root_kind = "right-endpoint"
elif _opposite_sign(f0, f1):
existence = True
root_kind = "sign-change"
if affine is not None and affine[0] != Q(0):
candidate = -affine[1] / affine[0]
if bracket.contains(candidate):
exact_root = candidate
root_kind = "exact-affine"
refined = bracket
rf0, rf1 = f0, f1
bisections = 0
if existence and exact_root is None and _opposite_sign(f0, f1):
lo, hi = bracket.lower, bracket.upper
flo, fhi = f0, f1
for _ in range(steps):
mid = (lo + hi) / 2
fm = evaluate_point(relation.expression, trajectory, mid)
bisections += 1
if fm == Q(0):
exact_root = mid
lo = hi = mid
flo = fhi = fm
root_kind = "exact-bisection"
break
if _opposite_sign(flo, fm):
hi, fhi = mid, fm
else:
lo, flo = mid, fm
refined = ClosedInterval(lo, hi)
rf0, rf1 = flo, fhi
derivative_excludes_zero = dual.derivative.excludes_zero()
unique = existence and derivative_excludes_zero
root_state: dict[str, Q] | None = None
support_ok = False
compatibility_ok = False
if exact_root is not None:
root_state = trajectory.state_at(exact_root)
support_ok = world.supports[relation.support_id].accepts_point(root_state)
compatibility_ok = world.compatibilities[relation.compatibility_id].accepts(root_state)
elif existence:
root_state_interval = trajectory.state_interval(refined)
support_ok = world.supports[relation.support_id].contains_interval(root_state_interval)
# Equality compatibility over a nonpoint bracket is certified only when
# each constrained field interval is the required point.
compatibility = world.compatibilities[relation.compatibility_id]
compatibility_ok = all(
name in root_state_interval
and root_state_interval[name].is_point()
and root_state_interval[name].lower == expected
for name, expected in compatibility.equals.items()
)
accepted = existence and support_ok and compatibility_ok
if not existence:
status = "no-certified-crossing"
elif not support_ok:
status = "outside-support"
elif not compatibility_ok:
status = "incompatible"
elif exact_root is None:
status = "accepted-bracket"
else:
status = "accepted-exact-root"
record: dict[str, Any] = {
"schema": "TOM-CERTIFIED-CROSSING-0.3",
"world_hash": world.content_hash,
"trajectory_id": trajectory.id,
"trajectory_hash": trajectory.content_hash,
"relation_id": relation.id,
"relation_hash": relation.content_hash,
"event_id": relation.event_id,
"priority": relation.priority,
"status": status,
"accepted": accepted,
"continuity_basis": "finite expression over exact rational affine fields using +,-,*",
"original_bracket": bracket.to_record(),
"original_endpoint_residuals": {
"lower": f0.to_record(),
"upper": f1.to_record(),
},
"original_residual_interval": dual.value.to_record(),
"derivative_interval": dual.derivative.to_record(),
"derivative_excludes_zero": derivative_excludes_zero,
"existence_certified_by_sign_change_or_exact_endpoint": existence,
"uniqueness_certified_by_monotonic_derivative": unique,
"root_kind": root_kind,
"exact_root_time": qrecord(exact_root),
"refined_bracket": refined.to_record(),
"refined_endpoint_residuals": {
"lower": rf0.to_record(),
"upper": rf1.to_record(),
},
"bisections": bisections,
"support_id": relation.support_id,
"support_ok": support_ok,
"compatibility_id": relation.compatibility_id,
"compatibility_ok": compatibility_ok,
"root_state": None if root_state is None else state_record(root_state),
"ordering_key": None if exact_root is None else [
exact_root.to_record(), relation.priority, relation.id,
relation.event_id, relation.content_hash,
],
}
record = attach_hash(record)
return CrossingResult(relation, accepted, status, exact_root, refined, record)
def certified_events(
world: IntervalWorld,
start: Any,
end: Any,
*,
refine_steps: int | None = None,
) -> list[CrossingResult]:
start_q = Q.from_value(start)
end_q = Q.from_value(end)
if end_q < start_q:
raise ValueError("event interval end is before start")
if not world.trajectory.domain.contains(start_q) or not world.trajectory.domain.contains(end_q):
raise ValueError("event interval lies outside trajectory domain")
results: list[CrossingResult] = []
seen: set[tuple[str, str]] = set()
for tick in range(start_q.floor(), end_q.ceil()):
bracket = ClosedInterval(max(start_q, Q(tick)), min(end_q, Q(tick + 1)))
if bracket.upper < bracket.lower:
continue
for relation in world.relations:
result = certify_crossing(world, relation, bracket, refine_steps=refine_steps)
if not result.accepted:
continue
root_key = result.exact_root.to_text() if result.exact_root is not None else result.bracket.to_text()
key = (relation.id, root_key)
if key in seen:
continue
seen.add(key)
results.append(result)
results.sort(key=event_order_key)
return results
def event_order_key(result: CrossingResult) -> tuple[Any, ...]:
if result.exact_root is None:
time_key = (1, result.bracket.lower.as_fraction(), result.bracket.upper.as_fraction())
else:
time_key = (0, result.exact_root.as_fraction(), result.exact_root.as_fraction())
relation = result.relation
return (*time_key, relation.priority, relation.id, relation.event_id, relation.content_hash)
def next_event_set(
world: IntervalWorld,
after: Any,
before: Any,
*,
include_after: bool = False,
refine_steps: int | None = None,
) -> dict[str, Any]:
after_q = Q.from_value(after)
results = certified_events(world, after_q, before, refine_steps=refine_steps)
results = [
result for result in results
if result.exact_root is not None
and (result.exact_root >= after_q if include_after else result.exact_root > after_q)
]
if not results:
return attach_hash({
"schema": "TOM-NEXT-EVENT-SET-0.3",
"world_hash": world.content_hash,
"after": after_q.to_record(),
"before": Q.from_value(before).to_record(),
"status": "none",
"events": [],
})
earliest = results[0].exact_root
assert earliest is not None
simultaneous = [result for result in results if result.exact_root == earliest]
simultaneous.sort(key=event_order_key)
record = {
"schema": "TOM-NEXT-EVENT-SET-0.3",
"world_hash": world.content_hash,
"trajectory_id": world.trajectory.id,
"after": after_q.to_record(),
"before": Q.from_value(before).to_record(),
"include_after": include_after,
"status": "accepted",
"event_time": earliest.to_record(),
"simultaneity_basis": "exact equal canonical rational root time",
"event_count": len(simultaneous),
"event_order": [result.relation.event_id for result in simultaneous],
"relation_order": [result.relation.id for result in simultaneous],
"ordering_rule": ["root_time", "priority", "relation_id", "event_id", "relation_hash"],
"events": [dict(result.certificate) for result in simultaneous],
}
return attach_hash(record)
def events_certificate(
world: IntervalWorld,
start: Any,
end: Any,
*,
refine_steps: int | None = None,
) -> dict[str, Any]:
results = certified_events(world, start, end, refine_steps=refine_steps)
return attach_hash({
"schema": "TOM-CERTIFIED-EVENTS-IN-SUPPORT-0.3",
"world_hash": world.content_hash,
"start": Q.from_value(start).to_record(),
"end": Q.from_value(end).to_record(),
"event_count": len(results),
"ordering_rule": ["root_time", "priority", "relation_id", "event_id", "relation_hash"],
"events": [dict(result.certificate) for result in results],
})
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