"""Compact certificates with the same constructive closure semantics as v3.

The checker derives known atoms only from submitted steps, never by completing
the proof for the model. Redundant copying of a final atom list is unnecessary.
"""
from crypto_proof_kernel import check as full_check,reference as full_reference,trace as full_trace,parse_final,prompt

SCHEMA=('Return JSON with exactly "secret_unreachable" (boolean) and "steps" '
        '(list of zero-based public fact indices). Begin with initial_known. Each '
        'submitted [message,key] fact must have an already-known key and add a new '
        'message. The checker derives the known set from your steps; do not copy '
        'a known-atom list. Finish the entire closure, even after finding the query: '
        'every fact with a known key must have its message known. Set '
        'secret_unreachable to whether query_secret is absent at that fixed point. '
        'Any valid deduction order is accepted. No external tools or code.')


def expanded(instance,certificate):
    if not isinstance(certificate,dict) or set(certificate)!={'secret_unreachable','steps'}:return None
    if type(certificate['secret_unreachable']) is not bool or not isinstance(certificate['steps'],list) or len(certificate['steps'])>128:return None
    if any(type(i) is not int for i in certificate['steps']):return None
    known=set(instance['initial_known']);facts=instance['encrypted_facts']
    for i in certificate['steps']:
        if not 0<=i<len(facts):return dict(**certificate,known=sorted(known))
        known.add(facts[i][0])
    return dict(**certificate,known=sorted(known))


def reference(instance):
    value=full_reference(instance)
    return {k:value[k] for k in ['secret_unreachable','steps']}


def check(instance,certificate):
    value=expanded(instance,certificate)
    return 'schema' if value is None else full_check(instance,value)


def trace(instance,certificate):
    assert check(instance,certificate)=='valid'
    return full_trace(instance,expanded(instance,certificate))