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holo-program
============
A memory where programs are first-class items, membranes are nested
regions, and writes can be cryptographically keyed.
Three layers, one substrate:
Program layer Operations are stored as key-value pairs:
key = random vector derived from (op, in)
value = bind(out, out_val)
Execution is unbind-then-classify. Chaining is
composition.
Membrane layer Regions have parents. Reads inherit from child
to parent. Writes isolate to the innermost
membrane. Dissolution merges a child into its
parent (P-systems operation). Movement transfers
an object between membranes.
Cryptographic layer
Item vectors are derived from a key. Without
the key, a trace is noise. A commitment scheme
lets a store prove that an item was written
without revealing the item.
Everything is addressable through `ask()`.
Requires: numpy.
"""
from __future__ import annotations
import argparse
import json
import os
import zlib
from typing import Any, Dict, List, Optional, Tuple
import numpy as np
D_DEFAULT = 2048
# ============================================================
# Primitives
# ============================================================
def rvec(seed: int, d: int = D_DEFAULT) -> np.ndarray:
r = np.random.default_rng(seed)
return np.exp(1j * r.uniform(0, 2 * np.pi, d))
def povec(seed: int, d: int = D_DEFAULT) -> np.ndarray:
v = rvec(seed, d)
F = np.fft.fft(v)
return np.fft.ifft(F / np.abs(F))
def bind(a: np.ndarray, b: np.ndarray) -> np.ndarray:
return np.fft.ifft(np.fft.fft(a) * np.fft.fft(b))
def unbind(a: np.ndarray, c: np.ndarray) -> np.ndarray:
return np.fft.ifft(np.fft.fft(c) * np.conj(np.fft.fft(a)))
def norm(v: np.ndarray) -> np.ndarray:
F = np.fft.fft(v)
return np.fft.ifft(F / (np.abs(F) + 1e-12))
def cos(a: np.ndarray, b: np.ndarray) -> float:
na = np.linalg.norm(a)
nb = np.linalg.norm(b)
if na < 1e-12 or nb < 1e-12:
return 0.0
return float(np.real(np.vdot(a, b)) / (na * nb))
def project(u: np.ndarray, v: np.ndarray) -> float:
nv2 = float(np.real(np.vdot(v, v)))
if nv2 < 1e-12:
return 0.0
return float(np.real(np.vdot(u, v)) / nv2)
def cos_batch(u: np.ndarray, X: np.ndarray) -> np.ndarray:
X = X.reshape(len(X), -1)
u = u.ravel()
return np.real(X @ np.conj(u)) / (
np.linalg.norm(X, axis=1) * np.linalg.norm(u) + 1e-12)
# ============================================================
# Cryptographic layer
# ============================================================
def keyed_seed(key: Optional[str], label: str) -> int:
s = f"{key}::{label}" if key is not None else f"_::{label}"
return zlib.crc32(s.encode()) & 0xffffffff
def make_vector(key: Optional[str], label: str, d: int) -> np.ndarray:
return povec(keyed_seed(key, label), d)
# ============================================================
# Global role vectors (cached per dimension)
# ============================================================
_ROLES_CACHE: Dict[int, Dict[str, np.ndarray]] = {}
def get_roles(d: int) -> Dict[str, np.ndarray]:
if d not in _ROLES_CACHE:
_ROLES_CACHE[d] = {
"op": povec(1000, d),
"in": povec(1001, d),
"out": povec(1002, d),
"salt": povec(1003, d),
}
return _ROLES_CACHE[d]
# ============================================================
# Membrane
# ============================================================
class Membrane:
"""
A region of the substrate with an optional parent.
"""
def __init__(self, name: str, d: int, key: Optional[str] = None,
parent: Optional["Membrane"] = None,
threshold: float = 0.05):
self.name = name
self.d = d
self.key = key
self.parent = parent
self.threshold = threshold
self.roles = get_roles(d)
self.trace = np.zeros(d, dtype=complex)
self.ops_trace = np.zeros(d, dtype=complex)
self.weights: Dict[str, float] = {}
self.labels: set = set()
self.operations: List[Tuple[str, str, str]] = []
def _vec(self, label: str) -> np.ndarray:
return make_vector(self.key, label, self.d)
def _op_key(self, op_name: str, in_val: str) -> np.ndarray:
"""
Random key for an operation, derived from the pair.
Fully random: no two distinct pairs share a component, so
cross-talk between operations with the same op name is
negligible. Same computation in add_op and apply.
"""
pair_id = f"__op__{op_name}::{in_val}"
return self._vec(pair_id)
# ---------------- items ----------------
def store(self, label: str, weight: float = 1.0) -> None:
v = self._vec(label)
self.trace += weight * bind(v, v)
self.weights[label] = self.weights.get(label, 0.0) + weight
self.labels.add(label)
def similarity(self, label: str) -> float:
v = self._vec(label)
u = unbind(v, self.trace)
return project(u, v)
def query_inherited(self, label: str) -> float:
sim = self.similarity(label)
if sim >= self.threshold:
return sim
if self.parent is not None:
return self.parent.query_inherited(label)
return sim
# ---------------- operations ----------------
def add_op(self, op_name: str, in_val: str, out_val: str) -> None:
key = self._op_key(op_name, in_val)
value = bind(self.roles["out"], self._vec(out_val))
self.ops_trace += bind(key, value)
self.operations.append((op_name, in_val, out_val))
def apply(self, op_name: str, in_val: str) -> Optional[str]:
if not self.operations:
return None
key = self._op_key(op_name, in_val)
u = unbind(key, self.ops_trace)
out = unbind(self.roles["out"], u)
candidates = sorted({o[2] for o in self.operations})
stack = np.stack([self._vec(c) for c in candidates])
sims = np.abs(cos_batch(out, stack))
best = int(np.argmax(sims))
if sims[best] < self.threshold:
return None
return candidates[best]
def find_applicable(self, in_val: str
) -> List[Tuple[str, str, float]]:
hits: List[Tuple[str, str, float]] = []
for op_name, in_v, out_v in self.operations:
if in_v != in_val:
continue
key = self._op_key(op_name, in_val)
u = unbind(key, self.ops_trace)
out = unbind(self.roles["out"], u)
sim = project(out, self._vec(out_v))
if sim >= self.threshold:
hits.append((op_name, out_v, float(sim)))
hits.sort(key=lambda h: -h[2])
return hits
# ---------------- cryptographic ----------------
def commit(self, label: str, salt: str) -> np.ndarray:
v_label = self._vec(label)
v_salt = self._vec(salt)
return bind(v_label, v_salt)
def verify(self, label: str, salt: str,
commitment: np.ndarray) -> bool:
expected = self.commit(label, salt)
return cos(commitment, expected) > 0.99
# ---------------- diagnostics ----------------
def stats(self) -> Dict:
return {
"name": self.name,
"d": self.d,
"has_key": self.key is not None,
"n_labels": len(self.labels),
"n_operations": len(self.operations),
"trace_magnitude": float(np.linalg.norm(self.trace)),
"ops_magnitude": float(np.linalg.norm(self.ops_trace)),
}
# ============================================================
# HoloProgram
# ============================================================
class HoloProgram:
def __init__(self, d: int = D_DEFAULT,
key: Optional[str] = None,
threshold: float = 0.05):
self.d = d
self.key = key
self.threshold = threshold
self.membranes: Dict[str, Membrane] = {}
self.add_membrane("root", parent=None)
def add_membrane(self, name: str,
parent: Optional[str] = "root") -> None:
if name in self.membranes:
return
parent_m = self.membranes.get(parent) if parent else None
self.membranes[name] = Membrane(
name=name, d=self.d, key=self.key,
parent=parent_m, threshold=self.threshold,
)
def store(self, membrane: str, label: str,
weight: float = 1.0) -> None:
self.membranes[membrane].store(label, weight=weight)
def add_op(self, membrane: str, op_name: str,
in_val: str, out_val: str) -> None:
self.membranes[membrane].add_op(op_name, in_val, out_val)
def query(self, membrane: str, label: str) -> float:
return self.membranes[membrane].query_inherited(label)
def apply(self, membrane: str, op_name: str,
in_val: str) -> Optional[str]:
return self.membranes[membrane].apply(op_name, in_val)
def run_chain(self, membrane: str, ops: List[str],
start: str) -> Dict:
cur = start
path = [cur]
for op in ops:
nxt = self.apply(membrane, op, cur)
if nxt is None:
return {"path": path, "ok": False, "failed_at": op}
path.append(nxt)
cur = nxt
return {"path": path, "ok": True}
def run_data_driven(self, membrane: str, start: str,
max_steps: int = 20) -> Dict:
cur = start
path = [cur]
for _ in range(max_steps):
hits = self.membranes[membrane].find_applicable(cur)
if not hits:
break
op_name, out_val, sim = hits[0]
path.append(out_val)
cur = out_val
return {"path": path, "steps": len(path) - 1}
def commit(self, membrane: str, label: str,
salt: str) -> np.ndarray:
return self.membranes[membrane].commit(label, salt)
def verify(self, membrane: str, label: str, salt: str,
commitment: np.ndarray) -> bool:
return self.membranes[membrane].verify(label, salt, commitment)
def move(self, label: str, src: str, dst: str) -> bool:
s = self.membranes[src]
d = self.membranes[dst]
if label not in s.labels:
return False
w = s.weights.get(label, 1.0)
if w <= 0:
return False
v = s._vec(label)
s.trace -= w * bind(v, v)
s.weights[label] = 0.0
s.labels.discard(label)
d.store(label, weight=w)
return True
def dissolve(self, child: str, into: str) -> None:
c = self.membranes[child]
t = self.membranes[into]
t.trace = t.trace + c.trace
t.ops_trace = t.ops_trace + c.ops_trace
for lbl, w in c.weights.items():
t.weights[lbl] = t.weights.get(lbl, 0.0) + w
t.labels.add(lbl)
t.operations.extend(c.operations)
for m in self.membranes.values():
if m.parent is c:
m.parent = t
del self.membranes[child]
def ask(self, query: str, top_k: int = 8) -> List[Dict]:
hits: List[Dict] = []
for m_name, mem in self.membranes.items():
if query in mem.labels:
sim = mem.query_inherited(query)
hits.append({
"type": "item",
"membrane": m_name,
"label": query,
"similarity": sim,
})
for m_name, mem in self.membranes.items():
for op_name, in_v, out_v in mem.operations:
if query in (op_name, in_v, out_v):
role = ("op" if query == op_name else
"in" if query == in_v else "out")
hits.append({
"type": "operation",
"membrane": m_name,
"role": role,
"op": op_name,
"in": in_v,
"out": out_v,
})
if query in self.membranes:
hits.append({
"type": "membrane",
"membrane": query,
})
def sort_key(h):
if h["type"] == "item":
return (0, -h["similarity"])
return (1, 0)
hits.sort(key=sort_key)
return hits[:top_k]
def stats(self) -> Dict:
return {
"d": self.d,
"has_key": self.key is not None,
"threshold": self.threshold,
"n_membranes": len(self.membranes),
"membranes": {n: m.stats()
for n, m in self.membranes.items()},
}
def save_json(self, path: str) -> None:
out = self.stats()
out["membrane_detail"] = {
n: {
"labels": sorted(m.labels),
"operations": [
{"op": o, "in": i, "out": r}
for o, i, r in m.operations
],
"parent": m.parent.name if m.parent else None,
}
for n, m in self.membranes.items()
}
with open(path, "w") as f:
json.dump(out, f, indent=2)
print(f" saved: {path}")
# ============================================================
# Helpers
# ============================================================
def section(title: str) -> None:
print()
print("=" * 78)
print(title)
print("=" * 78)
def self_test() -> bool:
print(" self-test:")
d = 2048
a = povec(1, d)
b = povec(2, d)
ok1 = cos(unbind(a, bind(a, b)), b) > 0.99
print(f" bind/unbind identity: {'PASS' if ok1 else 'FAIL'}")
v1 = make_vector("key1", "label", d)
v2 = make_vector("key2", "label", d)
ok2 = cos(v1, v2) < 0.1
print(f" keys separate vectors: {'PASS' if ok2 else 'FAIL'}")
bb = 0.7 * bind(a, a)
recovered = project(unbind(a, bb), a)
ok3 = abs(recovered - 0.7) < 0.02
print(f" raw projection: {'PASS' if ok3 else 'FAIL'}")
# Fully random key-value storage: many pairs sharing nothing
r = get_roles(d)
trace = np.zeros(d, dtype=complex)
pairs = []
for i in range(50):
key = norm(bind(r["op"], povec(2000 + i, d)))
val = povec(3000 + i, d)
trace += bind(key, val)
pairs.append((key, val))
correct = 0
for key, val in pairs:
rec = unbind(key, trace)
if cos(rec, val) > cos(rec, pairs[0][1]):
correct += 1
ok4 = correct >= 48
print(f" random-key key-value: "
f"{'PASS' if ok4 else 'FAIL'} ({correct}/50)")
return ok1 and ok2 and ok3 and ok4
# ============================================================
# DEMO 1. Program execution (chains)
# ============================================================
def demo_program_chains():
section("DEMO 1. PROGRAM EXECUTION — chained operations")
prog = HoloProgram(d=2048)
for i in range(20):
prog.add_op("root", "inc", str(i), str(i + 1))
for i in range(20):
prog.add_op("root", "double", str(i), str(2 * i))
for i in range(10):
prog.add_op("root", "square", str(i), str(i * i))
print(" stored: 20 inc, 20 double, 10 square operations")
print()
chains = [
(["inc", "inc", "double"], "3"),
(["square", "inc"], "4"),
(["double", "inc", "inc"], "5"),
(["inc", "square"], "2"),
]
for ops, start in chains:
result = prog.run_chain("root", ops, start)
path_str = " -> ".join(result["path"])
ok = "OK" if result["ok"] else f"FAILED at {result['failed_at']}"
print(f" [{', '.join(ops)}] from '{start}': {path_str} {ok}")
print()
print(" single apply:")
for op_name, in_val in [("inc", "7"), ("double", "7"), ("square", "7")]:
out = prog.apply("root", op_name, in_val)
print(f" {op_name}({in_val}) -> {out}")
# ============================================================
# DEMO 2. Data-driven execution
# ============================================================
def demo_data_driven():
section("DEMO 2. DATA-DRIVEN EXECUTION — apply any applicable op")
prog = HoloProgram(d=2048)
transitions = [
("t1", "cold", "warm"),
("t2", "warm", "hot"),
("t3", "hot", "boiling"),
("t4", "boiling", "evaporated"),
]
for op, src, dst in transitions:
prog.add_op("root", op, src, dst)
result = prog.run_data_driven("root", "cold", max_steps=10)
print(f" start at 'cold', walk using whichever op matches:")
print(f" {' -> '.join(result['path'])}")
print(f" steps: {result['steps']}")
print()
result = prog.run_data_driven("root", "evaporated", max_steps=5)
print(f" start at 'evaporated' (no matching op):")
print(f" {' -> '.join(result['path'])}")
print(f" steps: {result['steps']}")
# ============================================================
# DEMO 3. Membranes with inheritance
# ============================================================
def demo_membranes():
section("DEMO 3. MEMBRANES — nested regions with inheritance")
prog = HoloProgram(d=2048)
prog.add_membrane("alice", parent="root")
prog.add_membrane("alice_kitchen", parent="alice")
prog.store("root", "earth_round")
prog.store("root", "water_wet")
prog.store("alice", "alice_lives_in_paris")
prog.store("alice", "alice_works_at_cafe")
prog.store("alice_kitchen", "kitchen_floor_5")
prog.store("alice_kitchen", "manager_is_bob")
print(" membranes: root <- alice <- alice_kitchen")
print()
print(f" {'query':>24} {'root':>8} {'alice':>8} {'kitchen':>8}")
for q in ["earth_round", "alice_lives_in_paris",
"kitchen_floor_5", "manager_is_bob"]:
r_root = prog.query("root", q)
r_alice = prog.query("alice", q)
r_kit = prog.query("alice_kitchen", q)
print(f" {q:>24} {r_root:>+8.3f} {r_alice:>+8.3f} {r_kit:>+8.3f}")
# ============================================================
# DEMO 4. Communication and dissolution
# ============================================================
def demo_communication():
section("DEMO 4. COMMUNICATION AND DISSOLUTION")
prog = HoloProgram(d=2048)
prog.add_membrane("inner", parent="root")
prog.store("root", "common_knowledge")
prog.store("inner", "private_note")
print(" before move:")
print(f" root sees private_note: {prog.query('root', 'private_note'):+.4f}")
print(f" inner sees private_note: {prog.query('inner', 'private_note'):+.4f}")
prog.move("private_note", "inner", "root")
print()
print(" after move (inner -> root):")
print(f" root sees private_note: {prog.query('root', 'private_note'):+.4f}")
print(f" inner sees private_note: {prog.query('inner', 'private_note'):+.4f}")
prog.add_membrane("middle", parent="root")
prog.store("middle", "middle_fact")
print()
print(" before dissolution:")
print(f" root sees middle_fact: {prog.query('root', 'middle_fact'):+.4f}")
print(f" middle sees middle_fact: {prog.query('middle', 'middle_fact'):+.4f}")
prog.dissolve("middle", "root")
print()
print(" after dissolution (middle -> root):")
print(f" root sees middle_fact: {prog.query('root', 'middle_fact'):+.4f}")
print(f" membranes remaining: {list(prog.membranes.keys())}")
# ============================================================
# DEMO 5. Cryptographic layer
# ============================================================
def demo_crypto():
section("DEMO 5. CRYPTOGRAPHIC LAYER — keyed codebook")
print(" Store items with key 'secret_A'. Copy the trace to two")
print(" other programs: one with the same key, one with a wrong")
print(" key. Query both.")
print()
p_correct = HoloProgram(d=2048, key="secret_A")
p_correct.store("root", "classified_meeting_place")
p_correct.store("root", "classified_meeting_time")
p_wrong = HoloProgram(d=2048, key="wrong_key")
p_wrong.membranes["root"].trace = \
p_correct.membranes["root"].trace.copy()
candidates = ["classified_meeting_place", "classified_meeting_time",
"paris", "3pm", "unrelated_word"]
print(f" {'candidate':>30} {'correct key':>14} {'wrong key':>12}")
for c in candidates:
sim_c = p_correct.query("root", c)
sim_w = p_wrong.query("root", c)
print(f" {c:>30} {sim_c:>+14.4f} {sim_w:>+12.4f}")
# ============================================================
# DEMO 6. Commitment scheme
# ============================================================
def demo_commit():
section("DEMO 6. COMMITMENT SCHEME")
prog = HoloProgram(d=2048, key="K")
prog.store("root", "secret_value")
commitment = prog.commit("root", "secret_value", salt="random_salt_123")
print(f" commitment vector shape: {commitment.shape}")
print(f" commitment magnitude: {np.linalg.norm(commitment):.4f}")
print()
print(" verification:")
ok1 = prog.verify("root", "secret_value", "random_salt_123", commitment)
ok2 = prog.verify("root", "secret_value", "wrong_salt", commitment)
ok3 = prog.verify("root", "different_value", "random_salt_123", commitment)
print(f" correct (label, salt): {ok1}")
print(f" wrong salt: {ok2}")
print(f" wrong label: {ok3}")
# ============================================================
# DEMO 7. Unified ask()
# ============================================================
def demo_ask():
section("DEMO 7. UNIFIED ask() — non-flat interface")
prog = HoloProgram(d=2048)
prog.add_membrane("alice", parent="root")
prog.add_membrane("alice_kitchen", parent="alice")
prog.store("root", "earth_round")
prog.store("root", "water_wet")
prog.store("alice", "alice_lives_in_paris")
prog.store("alice", "alice_works_at_cafe")
prog.store("alice_kitchen", "kitchen_floor_5")
prog.store("alice_kitchen", "manager_is_bob")
prog.add_op("root", "serve", "customer", "coffee")
prog.add_op("root", "greet", "customer", "hello")
prog.add_op("alice_kitchen", "brew", "coffee", "ready")
for query in ["alice", "alice_lives_in_paris", "coffee",
"alice_kitchen", "manager_is_bob"]:
hits = prog.ask(query, top_k=6)
print(f" ask('{query}'):")
if not hits:
print(f" (no hits)")
for h in hits:
if h["type"] == "item":
print(f" [item] membrane={h['membrane']:<14} "
f"sim={h['similarity']:+.3f}")
elif h["type"] == "operation":
print(f" [operation] membrane={h['membrane']:<14} "
f"role={h['role']:<4} "
f"op={h['op']}({h['in']}) -> {h['out']}")
elif h["type"] == "membrane":
print(f" [membrane] {h['membrane']}")
print()
# ============================================================
# DEMO 8. Programs as items
# ============================================================
def demo_program_as_item():
section("DEMO 8. PROGRAMS AS ITEMS")
prog = HoloProgram(d=2048)
prog.add_op("root", "inc", "1", "2")
prog.add_op("root", "inc", "2", "3")
prog.add_op("root", "double", "3", "6")
print(" The substrate holds operations alongside items.")
print(" Query for 'inc' through ask():")
hits = prog.ask("inc", top_k=10)
for h in hits:
if h["type"] == "operation":
print(f" {h['op']}({h['in']}) -> {h['out']} "
f"(membrane={h['membrane']})")
print()
print(" Query for '3' (input and output of operations):")
hits = prog.ask("3", top_k=10)
for h in hits:
if h["type"] == "operation":
print(f" {h['op']}({h['in']}) -> {h['out']} "
f"role={h['role']}")
# ============================================================
# Main
# ============================================================
def run_all_demos(output_dir: str = "holo_program_out") -> None:
os.makedirs(output_dir, exist_ok=True)
print("=" * 78)
print("HOLO-PROGRAM")
print("Programs as items, membranes as regions, keys as gates.")
print("=" * 78)
demos = [
demo_program_chains,
demo_data_driven,
demo_membranes,
demo_communication,
demo_crypto,
demo_commit,
demo_ask,
demo_program_as_item,
]
for d in demos:
try:
d()
except Exception as e:
print(f" EXCEPTION in {d.__name__}: {e}")
section("OUTPUT")
prog = HoloProgram(d=2048, key="demo_key")
prog.add_membrane("alice", parent="root")
prog.store("root", "earth_round")
prog.store("alice", "alice_lives_in_paris")
prog.add_op("root", "inc", "1", "2")
prog.save_json(os.path.join(output_dir, "state.json"))
print()
print("=" * 78)
print(f"All outputs saved to: {output_dir}/")
print("=" * 78)
def main() -> None:
parser = argparse.ArgumentParser(
description="Programs as items, membranes as regions, "
"keys as gates.",
formatter_class=argparse.RawDescriptionHelpFormatter,
epilog="""
Library usage:
from holo_program import HoloProgram
prog = HoloProgram(d=2048, key=None)
prog.add_membrane("alice", parent="root")
prog.store("root", "apple")
prog.add_op("root", "inc", "0", "1")
prog.run_chain("root", ["inc", "inc"], "0")
""")
parser.add_argument("--output", default="holo_program_out",
help="output directory (default: holo_program_out)")
args = parser.parse_args()
print("=" * 78)
print("SELF-TEST")
print("=" * 78)
if not self_test():
print(" primitive test failed; continuing anyway")
run_all_demos(output_dir=args.output)
if __name__ == "__main__":
main() |