"""Independent discrete oracle for THEORY_HANDOFF.md (not the missing original).

This module deliberately does not import the production ancestry DP or teacher.
It enumerates a finite birth-cap CTMC, routing boundary births into overflow,
and independently integrates all original outcomes and gap subsequences.
"""
from __future__ import annotations

from dataclasses import dataclass
from itertools import combinations, product
from math import comb, exp, expm1, factorial
from typing import Iterator

import numpy as np
from scipy.special import gammaln, logsumexp


@dataclass(frozen=True)
class State:
    originals: tuple[str, ...]  # U, D, or S:<new type>
    gaps: tuple[tuple[str, ...], ...]


@dataclass(frozen=True)
class Reference:
    source: tuple[str, ...] = ("A", "B", "A")
    alphabet: tuple[str, ...] = ("A", "B")
    protected: tuple[bool, ...] = (False, True, False)
    deletion: tuple[float, ...] = (0.41, 0.0, 0.27)
    substitution: tuple[float, ...] = (0.33, 0.0, 0.52)
    beta: tuple[float, ...] = (0.19, 0.31, 0.23, 0.17)
    pi: tuple[tuple[float, ...], ...] = ((0.7, 0.3), (0.4, 0.6), (0.55, 0.45), (0.25, 0.75))

    def __post_init__(self):
        n = len(self.source)
        if not (len(self.protected) == len(self.deletion) == len(self.substitution) == n):
            raise ValueError("Original-parameter sizes differ")
        if len(self.beta) != n + 1 or len(self.pi) != n + 1:
            raise ValueError("Gap-parameter sizes differ")
        for row in self.pi:
            if len(row) != len(self.alphabet) or min(row) < 0 or not np.isclose(sum(row), 1):
                raise ValueError("Invalid normalized AA distribution")
        if min((*self.deletion, *self.substitution, *self.beta)) < 0:
            raise ValueError("Negative reference rate")
        for i, flag in enumerate(self.protected):
            if flag and (self.deletion[i] or self.substitution[i]):
                raise ValueError("Protected original has a nonzero edit rate")

    @property
    def n(self):
        return len(self.source)

    @property
    def initial(self):
        return State(("U",) * self.n, ((),) * (self.n + 1))

    def type_probability(self, g, aa):
        return self.pi[g][self.alphabet.index(aa)] if aa in self.alphabet else 0.0

    def substitution_rate(self, i, aa):
        if aa == self.source[i] or aa not in self.alphabet:
            return 0.0
        return self.substitution[i] / (len(self.alphabet) - 1)


Token = tuple[str, int | None]  # AA, explicit protected source identity
Target = tuple[Token, ...]


def observable(ref: Reference, state: State) -> Target:
    out = []
    for g in range(ref.n + 1):
        out.extend((aa, None) for aa in state.gaps[g])
        if g < ref.n and state.originals[g] != "D":
            aa = ref.source[g] if state.originals[g] == "U" else state.originals[g][2:]
            out.append((aa, g if ref.protected[g] else None))
    return tuple(out)


def _compositions(total: int, count: int):
    if count == 1:
        yield (total,)
    else:
        for k in range(total + 1):
            for tail in _compositions(total - k, count - 1):
                yield (k,) + tail


def enumerate_states(ref: Reference, birth_cap: int = 2):
    options = [(("U",) if ref.protected[i] else ("U", "D") + tuple("S:" + a for a in ref.alphabet if a != ref.source[i])) for i in range(ref.n)]
    gap_options = []
    for total in range(birth_cap + 1):
        for sizes in _compositions(total, ref.n + 1):
            for word in product(ref.alphabet, repeat=total):
                start, gaps = 0, []
                for size in sizes:
                    gaps.append(tuple(word[start:start + size]))
                    start += size
                gap_options.append(tuple(gaps))
    states = [State(tuple(o), g) for o in product(*options) for g in gap_options]
    states.append(None)  # absorbing overflow, including all boundary birth mass
    return states


def transitions(ref: Reference, state: State, birth_cap: int | None = None):
    """Physical channel rates, including multiplicities giving identical states."""
    for i, status in enumerate(state.originals):
        if status != "U" or ref.protected[i]:
            continue
        new = list(state.originals)
        new[i] = "D"
        yield ("D", i), State(tuple(new), state.gaps), ref.deletion[i]
        for aa in ref.alphabet:
            rate = ref.substitution_rate(i, aa)
            if rate:
                new[i] = "S:" + aa
                yield ("S", i, aa), State(tuple(new), state.gaps), rate
    total = sum(map(len, state.gaps))
    for g, gap in enumerate(state.gaps):
        for r in range(len(gap) + 1):
            for aa in ref.alphabet:
                rate = ref.beta[g] / (len(gap) + 1) * ref.type_probability(g, aa)
                gaps = list(state.gaps)
                gaps[g] = gap[:r] + (aa,) + gap[r:]
                nxt = None if birth_cap is not None and total >= birth_cap else State(state.originals, tuple(gaps))
                yield ("I", g, r, aa), nxt, rate


def generator(ref: Reference, birth_cap: int = 2):
    states = enumerate_states(ref, birth_cap)
    index = {state: i for i, state in enumerate(states)}
    q = np.zeros((len(states), len(states)))
    for i, state in enumerate(states[:-1]):
        for _, nxt, rate in transitions(ref, state, birth_cap):
            q[i, index[nxt]] += rate
            q[i, i] -= rate
    return states, index, q


def gap_kernel(ref: Reference, g: int, current: tuple[str, ...], target: Target, delta: float, *, omit_binomial=False):
    """Uniform existing-subsequence embeddings, independent of the CTMC matrix."""
    k, K = len(current), len(target)
    if k > K or delta < 0:
        return 0.0
    ell = K - k
    poisson = exp(-ref.beta[g] * delta) * (ref.beta[g] * delta) ** ell / factorial(ell)
    total = 0.0
    for positions in combinations(range(K), k):
        if any(target[j] != (aa, None) for aa, j in zip(current, positions)):
            continue
        selected = set(positions)
        weight = 1.0
        for j, (aa, label) in enumerate(target):
            if j not in selected:
                weight *= ref.type_probability(g, aa) if label is None else 0.0
        total += weight
    return poisson * total / (1 if omit_binomial else comb(K, k))


def gap_remaining_loglik(log_current, log_birth, beta: float, delta: float):
    """Generic independent continuous/discrete gap oracle, enumerating embeddings.

    log_current[r,j] is the transition log density from current born residue r
    to target j; log_birth[j] is its *terminal* entrance/type log density. All
    normalized densities must already include any type/protection zero support.
    Cost is binomial(K,k); use only for tiny validation cases.
    """
    lc, lb = np.asarray(log_current, float), np.asarray(log_birth, float)
    if lc.ndim != 2 or lb.ndim != 1 or lc.shape[1] != len(lb):
        raise ValueError("Expected log_current[k,K], log_birth[K]")
    if beta < 0 or delta < 0:
        raise ValueError("Negative rate or remaining horizon")
    k, K = lc.shape
    ell = K - k
    if ell < 0 or ((beta == 0 or delta == 0) and ell):
        return -np.inf
    log_poisson = -beta * delta + (ell * np.log(beta * delta) if ell else 0.0) - gammaln(ell + 1)
    log_embeddings = []
    for positions in combinations(range(K), k):
        chosen = set(positions)
        terms = [lc[r, j] for r, j in enumerate(positions)]
        terms.extend(lb[j] for j in range(K) if j not in chosen)
        log_embeddings.append(sum(terms))
    log_binomial = gammaln(K + 1) - gammaln(k + 1) - gammaln(K - k + 1)
    return float(log_poisson - log_binomial + logsumexp(log_embeddings))


def original_weights(ref: Reference, state: State, i: int, token: Token | None, delta: float):
    status = state.originals[i]
    if status == "D":
        return float(token is None)
    if token is not None:
        aa, label = token
        expected = i if ref.protected[i] else None
        if label != expected:
            return 0.0
    if status.startswith("S:"):
        return float(token is not None and token[0] == status[2:])
    q = ref.deletion[i] + ref.substitution[i]
    event_integral = -expm1(-q * delta) / q if q else delta
    if token is None:
        return ref.deletion[i] * event_integral
    if token[0] == ref.source[i]:
        return exp(-q * delta)
    return ref.substitution_rate(i, token[0]) * event_integral


def remaining_likelihood(ref: Reference, state: State | None, target: Target, delta: float):
    """Brute recursive sum over target blocks; no production recurrence imported."""
    if state is None:
        return 0.0
    def visit(g, j):
        value = 0.0
        for stop in range(j, len(target) + 1):
            gap = gap_kernel(ref, g, state.gaps[g], target[j:stop], delta)
            if not gap:
                continue
            if g == ref.n:
                value += gap * float(stop == len(target))
            else:
                value += gap * original_weights(ref, state, g, None, delta) * visit(g + 1, stop)
                if stop < len(target):
                    value += gap * original_weights(ref, state, g, target[stop], delta) * visit(g + 1, stop + 1)
        return value
    return visit(0, 0)


@dataclass(frozen=True)
class Ancestry:
    source_to_target: tuple[int, ...]
    gaps: tuple[tuple[int, ...], ...]
    weight: float


def enumerate_ancestries(ref: Reference, target: Target, horizon=1.0):
    """Unnormalized endpoint histories by explicit recursion (tiny cases only)."""
    histories = []
    def visit(g, j, origins, gaps, weight):
        for stop in range(j, len(target) + 1):
            bw = gap_kernel(ref, g, (), target[j:stop], horizon)
            if not bw:
                continue
            newg = gaps + (tuple(range(j, stop)),)
            if g == ref.n:
                if stop == len(target):
                    histories.append(Ancestry(origins, newg, weight * bw))
                continue
            dw = original_weights(ref, ref.initial, g, None, horizon)
            if dw:
                visit(g + 1, stop, origins + (-1,), newg, weight * bw * dw)
            if stop < len(target):
                mw = original_weights(ref, ref.initial, g, target[stop], horizon)
                if mw:
                    visit(g + 1, stop + 1, origins + (stop,), newg, weight * bw * mw)
    visit(0, 0, (), (), 1.0)
    return histories


def direct_components(ref: Reference, target: Target, ancestry: Ancestry, t: float, horizon=1.0):
    """Enumerate random-time latent Bernoullis and their complete jump labels."""
    if not 0 <= t < horizon:
        raise ValueError("Require 0 <= t < horizon")
    original_options = []
    for i, j in enumerate(ancestry.source_to_target):
        outcome = "D" if j < 0 else ("U" if target[j][0] == ref.source[i] else "S:" + target[j][0])
        if outcome == "U":
            original_options.append((("U", 1.0, None),))
        else:
            q = ref.deletion[i] + ref.substitution[i]
            normalizer = -expm1(-q * horizon)
            p = -expm1(-q * t) / normalizer
            # Avoid subtracting p from one near T: flux multiplies this tiny
            # pending probability by the diverging conditioned edit hazard.
            pending_p = exp(-q * t) * -expm1(-q * (horizon - t)) / normalizer
            original_options.append((("U", pending_p, outcome), (outcome, p, None)))
    births = [(g, j) for g, js in enumerate(ancestry.gaps) for j in js]
    for originals in product(*original_options):
        for present in product((False, True), repeat=len(births)):
            probability = float(np.prod([x[1] for x in originals]))
            probability *= (t / horizon) ** sum(present) * (1 - t / horizon) ** (len(births) - sum(present))
            gaps = tuple(tuple(target[j][0] for (gg, j), yes in zip(births, present) if gg == g and yes) for g in range(ref.n + 1))
            state = State(tuple(x[0] for x in originals), gaps)
            jumps = []
            for i, (_, _, pending) in enumerate(originals):
                if pending is not None:
                    q = ref.deletion[i] + ref.substitution[i]
                    rate = q / -expm1(-q * (horizon - t))
                    altered = list(state.originals)
                    altered[i] = pending
                    jumps.append((State(tuple(altered), state.gaps), rate))
            for (g, j), yes in zip(births, present):
                if not yes:
                    rank = sum(yes2 and gg == g and jj < j for (gg, jj), yes2 in zip(births, present))
                    altered = list(gaps)
                    altered[g] = gaps[g][:rank] + (target[j][0],) + gaps[g][rank:]
                    jumps.append((State(state.originals, tuple(altered)), 1 / (horizon - t)))
            yield state, probability, jumps


def direct_marginal_flux(ref: Reference, target: Target, states, index, t, horizon=1.0):
    histories = enumerate_ancestries(ref, target, horizon)
    z = sum(a.weight for a in histories)
    if z <= 0:
        raise ValueError("Unreachable endpoint")
    marginal = np.zeros(len(states))
    flux = np.zeros((len(states), len(states)))
    for ancestry in histories:
        for state, probability, jumps in direct_components(ref, target, ancestry, t, horizon):
            mass = ancestry.weight / z * probability
            i = index[state]
            marginal[i] += mass
            for nxt, rate in jumps:
                flux[i, index[nxt]] += mass * rate
    return marginal, flux