#!/usr/bin/env python3 """Certified generative pruning (CGP), a bounded symbolic self-improver. Only the finite candidate-generator automaton is rewritten. Primitive task semantics, proof checking, objectives, and evaluator are outside that interface. Python 3.10+; standard library only. No network, subprocess, eval, or exec. """ from __future__ import annotations from collections import deque from dataclasses import dataclass import hashlib, json, random, time Word = tuple[int, ...] Map = tuple[int, ...] def family(seed: int, n: int = 8) -> tuple[Map, ...]: """Cycle, its inverse, and two adjacent transpositions in a random cycle. The alphabet order varies by seed. These generate S_n; no laws are seeded. """ rng = random.Random(seed) order = list(range(n)); rng.shuffle(order) cycle = list(range(n)) for i in range(n): cycle[order[i]] = order[(i+1) % n] inverse = [0]*n for i,j in enumerate(cycle): inverse[j] = i swaps = [] for i in rng.sample(range(n), 2): p = list(range(n)); a,b = order[i],order[(i+1)%n] p[a],p[b] = p[b],p[a]; swaps.append(tuple(p)) gs = [tuple(cycle),tuple(inverse),*swaps]; rng.shuffle(gs) return tuple(gs) def ref_eval(word: Word, generators: tuple[Map,...]) -> Map: """Independent exact checker: run every boundary input instruction by instruction.""" n = len(generators[0]); out = [] for initial in range(n): x = initial for symbol in word: if type(symbol) is not int or not 0 <= symbol < len(generators): raise ValueError('invalid instruction') x = generators[symbol][x] out.append(x) return tuple(out) def shortlex(w: Word) -> tuple: return len(w), w @dataclass(frozen=True) class Rule: lhs: Word rhs: Word def export(self) -> dict: return {'lhs':list(self.lhs),'rhs':list(self.rhs)} def check_rule(rule: Rule, generators: tuple[Map,...]) -> bool: if not rule.lhs or shortlex(rule.rhs) >= shortlex(rule.lhs): return False try: return ref_eval(rule.lhs,generators) == ref_eval(rule.rhs,generators) except (ValueError, IndexError, TypeError): return False class Guard: """Aho-Corasick automaton rejecting any certified left-hand-side factor.""" def __init__(self, forbidden: list[Word], alphabet: int): self.alphabet = alphabet edges = [{}]; terminal = [False]; self.prefixes = [()] for word in forbidden: state = 0 for symbol in word: if symbol not in edges[state]: edges[state][symbol] = len(edges) edges.append({}); terminal.append(False) self.prefixes.append(self.prefixes[state]+(symbol,)) state = edges[state][symbol] terminal[state] = True self.next = [[0]*alphabet for _ in edges] fail = [0]*len(edges) q = deque() for symbol,state in edges[0].items(): self.next[0][symbol] = state; q.append(state) while q: state=q.popleft(); terminal[state] |= terminal[fail[state]] for symbol in range(alphabet): if symbol in edges[state]: child=edges[state][symbol] fail[child]=self.next[fail[state]][symbol] self.next[state][symbol]=child; q.append(child) else: self.next[state][symbol]=self.next[fail[state]][symbol] self.bad = terminal def scan(self, word: Word) -> int | None: state=0 for symbol in word: state=self.next[state][symbol] if self.bad[state]: return None return state def digest(self) -> str: raw=json.dumps([self.next,self.bad],separators=(',',':')).encode() return hashlib.sha256(raw).hexdigest() class Improver: def __init__(self, generators: tuple[Map,...], rules: list[Rule] | None=None, semantic_dedup: bool=False): if not generators or len({len(g) for g in generators}) != 1: raise ValueError('incompatible primitive maps') n=len(generators[0]) if any(any(type(x) is not int or not 0 <= x < n for x in g) for g in generators): raise ValueError('map outside finite domain') self.generators=generators self.rules=list(rules or []) if not all(check_rule(r,generators) for r in self.rules): raise ValueError('unverified initial rule') self.guard=Guard([r.lhs for r in self.rules],len(generators)) ident=tuple(range(n)) self.frontier=deque([((),ident,0)]) self.best={ident:()} self.seen_for_queue={ident} self.pending: dict[Word,Rule]={} self.semantic_dedup=semantic_dedup self.stats={'popped':0,'semantic_products':0,'guard_probes':0, 'guard_rejections':0,'queue_filtered':0,'rules_checked':0, 'checker_instruction_steps':0,'rebuild_scan_steps':0, 'peak_queue':1,'installations':0,'independent_checks':0} def advance(self, expansions: int, product_budget: int | None=None) -> dict: before=len(self.best); p0=self.stats['popped']; t=time.perf_counter() g=self.guard; gs=self.generators product_start=self.stats['semantic_products'] for _ in range(expansions): if not self.frontier: break if product_budget is not None and self.stats['semantic_products']-product_start >= product_budget: break word,signature,state=self.frontier.popleft(); self.stats['popped']+=1 for symbol,primitive in enumerate(gs): self.stats['guard_probes']+=1 ns=g.next[state][symbol] if g.bad[ns]: self.stats['guard_rejections']+=1; continue child=word+(symbol,) value=tuple(primitive[x] for x in signature) self.stats['semantic_products']+=1 previous=self.best.get(value) if previous is None: self.best[value]=child elif shortlex(child) < shortlex(previous): self.best[value]=child self.pending.setdefault(previous,Rule(previous,child)) elif child != previous: self.pending.setdefault(child,Rule(child,previous)) if self.semantic_dedup: if value in self.seen_for_queue: continue self.seen_for_queue.add(value) self.frontier.append((child,value,ns)) self.stats['peak_queue']=max(self.stats['peak_queue'],len(self.frontier)) return {'new_semantics':len(self.best)-before, 'expansions':self.stats['popped']-p0, 'wall_seconds':time.perf_counter()-t, 'known_semantics':len(self.best),'queue':len(self.frontier), 'semantic_products':self.stats['semantic_products']-product_start} def install(self, max_rules: int=600) -> dict: """Select sound shortest obstructions; rebuild and replace search-control code. Selection is data-driven, deterministic. No hardcoded semantic identities. Old forbidden languages are retained; this gives monotone pruning. """ start=time.perf_counter(); old=self.guard.digest(); accepted=[] room=max_rules-len(self.rules) # Pending laws with a previously forbidden factor cannot add pruning. pending=sorted(self.pending.values(),key=lambda r:shortlex(r.lhs)) self.pending={} trial_lhs=[r.lhs for r in self.rules] trial=self.guard new_lefts=set() for rule in pending: if len(accepted)>=room: break if self.guard.scan(rule.lhs) is None: continue if any(rule.lhs[i:j] in new_lefts for i in range(len(rule.lhs)) for j in range(i+1,len(rule.lhs)+1)): continue self.stats['rules_checked']+=1 self.stats['checker_instruction_steps']+=len(self.generators[0])*(len(rule.lhs)+len(rule.rhs)) if not check_rule(rule,self.generators): raise AssertionError('untrusted proposal failed verification') accepted.append(rule); trial_lhs.append(rule.lhs); new_lefts.add(rule.lhs) if accepted: self.rules.extend(accepted) trial=Guard(trial_lhs,len(self.generators)) from verifier import verify candidate={'generators':self.generators, 'rules':[r.export() for r in self.rules], 'guard':{'transition':trial.next,'reject':trial.bad, 'prefixes':trial.prefixes,'sha256':trial.digest()}} receipt=verify(candidate) if not receipt['accepted']: self.rules=self.rules[:-len(accepted)] raise AssertionError('independent checker rejected update: '+str(receipt)) self.stats['independent_checks']+=1 self.guard=trial filtered=deque() for word,value,_ in self.frontier: self.stats['rebuild_scan_steps']+=len(word) ns=trial.scan(word) if ns is not None: filtered.append((word,value,ns)) else: self.stats['queue_filtered']+=1 self.frontier=filtered; self.stats['installations']+=1 return {'accepted':len(accepted),'rules_total':len(self.rules), 'automaton_states':len(self.guard.next),'before_hash':old, 'after_hash':self.guard.digest(), 'wall_seconds':time.perf_counter()-start} def export(self) -> dict: return {'generators':[list(x) for x in self.generators], 'rules':[r.export() for r in self.rules], 'guard':{'transition':self.guard.next,'reject':self.guard.bad, 'prefixes':[list(p) for p in self.guard.prefixes], 'sha256':self.guard.digest()}, 'stats':self.stats.copy(),'known_semantics':len(self.best)} def train(seed: int, n: int=8, rounds: int=8, batch: int=300, mode: str='recursive', max_rules: int=600, product_batches: bool=False) -> tuple[Improver,list[dict]]: if mode not in {'recursive','frozen','oneshot','semantic_bfs','recursive_bfs','oneshot_bfs'}: raise ValueError('unknown mode') engine=Improver(family(seed,n),semantic_dedup=(mode in {'semantic_bfs','recursive_bfs','oneshot_bfs'})) records=[] for generation in range(rounds): growth=engine.advance(100000,product_budget=batch) if product_batches else engine.advance(batch) if mode in {'recursive','recursive_bfs'} or (mode in {'oneshot','oneshot_bfs'} and generation==0): upgrade=engine.install(max_rules) else: # Pending rules may be kept as data in a frozen control; they do not # change the generator. Clear to avoid irrelevant memory accumulation. engine.pending={}; upgrade={'accepted':0,'wall_seconds':0.0, 'rules_total':len(engine.rules)} records.append({'generation':generation+1,'growth':growth,'upgrade':upgrade}) return engine,records if __name__=='__main__': for mode in ['frozen','oneshot','recursive','semantic_bfs']: t=time.perf_counter(); e,h=train(7101,mode=mode) print(mode,round(time.perf_counter()-t,4),len(e.best),len(e.rules), [r['growth']['known_semantics'] for r in h], [r['upgrade']['accepted'] for r in h]) def cold_search(generators: tuple[Map,...], rules: list[Rule], expansions: int, dedup: bool=False, product_budget: int | None=None, wall_budget: float | None=None) -> dict: """Task deployment: no proof mining or pending-law overhead in either control. For dedup=True this is conventional semantic BFS with an optimized inner loop, not a deliberately slowed variant of the self-improver. Construction of the supplied automaton is included in measured deployment time. """ t=time.perf_counter(); ident=tuple(range(len(generators[0]))) best={ident:()}; products=0; probes=0; popped=0; peak=1 if dedup and not rules: todo=deque([(ident,())]) while todo and popped < expansions: if product_budget is not None and products>=product_budget: break if wall_budget is not None and time.perf_counter()-t>=wall_budget: break signature,word=todo.popleft(); popped+=1 for a,g in enumerate(generators): value=tuple(g[x] for x in signature); products+=1 if value not in best: child=word+(a,);best[value]=child;todo.append((value,child)) peak=max(peak,len(todo)) states=0 else: guard=Guard([r.lhs for r in rules],len(generators)); states=len(guard.next) todo=deque([(ident,(),0)]) while todo and popped < expansions: if product_budget is not None and products>=product_budget: break if wall_budget is not None and time.perf_counter()-t>=wall_budget: break signature,word,state=todo.popleft(); popped+=1 for a,g in enumerate(generators): probes+=1; ns=guard.next[state][a] if guard.bad[ns]: continue value=tuple(g[x] for x in signature);products+=1 child=word+(a,) if value not in best: best[value]=child;todo.append((value,child,ns)) elif not dedup:todo.append((value,child,ns)) peak=max(peak,len(todo)) return {'known_semantics':len(best),'semantic_products':products,'popped':popped, 'guard_probes':probes,'automaton_states':states,'peak_queue':peak, 'wall_seconds':time.perf_counter()-t,'best':best}