"""
phi.charclass — Layer 1: Character classification → Δ₁₁ byte histogram

Each ASCII or TeX character maps to 1 of 12 archetypal classes. The histogram
over these 12 classes is the F(E) feature vector — the first component
of the Φ embedding.

Dependencies: none (stdlib only)
"""

from __future__ import annotations

from typing import List

# ── 12 character classes ─────────────────────────────────────────────────

# Each class corresponds to a dimension of Δ₁₁ (the 11-simplex).
# The classes partition the visible ASCII range into 12 bins.
CHAR_CLASSES = {
    "digit":       0,    # 0-9
    "lower_alpha": 1,    # a-z
    "upper_alpha": 2,    # A-Z
    "operator":    3,    # + - * / ^ % = < > ! & | ~
    "bracket":     4,    # ( ) [ ] { }
    "punctuation": 5,    # . , ; : ' " @ # $ _ \
    "whitespace":  6,    # space, tab, newline
    "other":       7,    # everything else (Greek, Unicode math, etc.)
    "symmetry":    8,    # = $\approx$ $\equiv$ $\sim$
    "periodicity": 9,    # $\pi$ $\infty$ $\theta$ $\lambda$
    "continuity":  10,   # $\rightarrow$ $\Delta$ $\nabla$ $\int$
    "meta_math":   11,   # $\sqrt{}$ $\sum$ $\prod$ $\partial$
}


OPERATOR_CHARS = set("+-*/^%=<>!&|~")
BRACKET_CHARS = set("()[]{}")
PUNCT_CHARS = set(".,;:'\"@#$\\")


def classify_char(c: str) -> int:
    """Classify a single character into 1 of 12 archetypal classes (0-11).

    The 12 classes partition the visible ASCII and common TeX range:

    +------+--------------+-------------------------------+
    | Class | Name         | Characters                     |
    +------+--------------+-------------------------------+
    | 0    | digit        | 0-9                            |
    | 1    | lower_alpha  | a-z                            |
    | 2    | upper_alpha  | A-Z                            |
    | 3    | operator     | + - * / ^ % = < > ! & | ~     |
    | 4    | bracket      | ( ) [ ] { }                    |
    | 5    | punctuation  | . , ; : ' \" @ # $ \\\\ _       |
    | 6    | whitespace   | space, tab, newline, CR        |
    | 7    | other        | Unicode, non-ASCII, unassigned  |
    | 8    | symmetry     | ≈ ≡ ∼                          |
    | 9    | periodicity  | π θ λ ∞                        |
    | 10   | continuity   | → Δ ∇ ∫                        |
    | 11   | meta_math    | √ ∑ ∏ ∂                        |
    +------+--------------+-------------------------------+

    Args:
        c: A single-character string.

    Returns:
        An integer 0-11 identifying the character's class.

    Examples:
        >>> classify_char("3")
        0
        >>> classify_char("x")
        1
        >>> classify_char("X")
        2
        >>> classify_char("+")
        3
        >>> classify_char(")")
        4
        >>> classify_char(".")
        5
        >>> classify_char(" ")
        6
        >>> classify_char("©")
        7
    """
    if c.isdigit():
        return 0
    if c.isalpha():
        return 1 if c.islower() else 2
    # Operator chars
    if c in "+-*/^%=<>!&|~":
        return 3
    # Bracket chars
    if c in "()[]{}":
        return 4
    # Punctuation
    if c in ".,;:'\"@#$\\":
        return 5
    # Whitespace
    if c in (" ", "\t", "\n", "\r"):
        return 6
    # Other (General)
    if c in "$\\pi\\theta\\lambda\\infty$": # Periodicity
        return 9
    if c in "$\\rightarrow\\Delta\\nabla\\int$": # Continuity
        return 10
    if c in "=$\\approx\\equiv\\sim$": # Symmetry
        return 8
    if c in "$\\sqrt{}\\sum\\prod\\partial$": # Meta-math
        return 11
    return 7



def compute_F(equation: str) -> List[float]:
    """Compute F(E) — normalized byte-class histogram on Δ₁₂.

    Returns 12 floats summing to 1.0. This is Layer 1 of the Φ embedding.

    Pure function: no state, no side effects.

    Examples:
        >>> result = compute_F("x + 1")
        >>> round(sum(result), 10)
        1.0
    """
    counts = [0] * 12
    for c in equation:
        counts[classify_char(c)] += 1
    total = sum(counts)
    if total == 0:
        return [1.0 / 12] * 12
    return [c / total for c in counts]


if __name__ == "__main__":
    import math

    # ── 1.  Test every character class ─────────────────────────────────────
    assert classify_char("0") == 0
    assert classify_char("9") == 0
    assert classify_char("a") == 1
    assert classify_char("z") == 1
    assert classify_char("A") == 2
    assert classify_char("Z") == 2
    assert classify_char("+") == 3
    assert classify_char("*") == 3
    assert classify_char("(") == 4
    assert classify_char("}") == 4
    assert classify_char(".") == 5
    assert classify_char(",") == 5
    assert classify_char(" ") == 6
    assert classify_char("\t") == 6
    assert classify_char("\n") == 6
    assert classify_char("©") == 7    # non-ASCII, non-alpha → other

    # ── 2.  compute_F output sums to 1.0 for various equations ─────────────
    for eq in ["x + 1", "E = mc^2", "a = b = c", "12345", "     ", "((()))"]:
        result = compute_F(eq)
        assert len(result) == 12
        assert abs(sum(result) - 1.0) < 1e-10, f"F({eq!r}) sum = {sum(result)}"

    # ── 3.  Edge cases ─────────────────────────────────────────────────────
    # Empty string → uniform distribution
    assert compute_F("") == [1.0 / 12] * 12

    # All-same-class string
    F_digits = compute_F("12345")
    assert abs(F_digits[0] - 1.0) < 1e-10

    # Mixed content
    F_mixed = compute_F("a1 + b2")
    assert abs(sum(F_mixed) - 1.0) < 1e-10

    # ── 4.  classify_char returns int in 0..11 for every printable ASCII ───
    for code in range(32, 127):
        c = chr(code)
        cls = classify_char(c)
        assert 0 <= cls <= 11, f"char {c!r} (code {code}) class {cls} out of 0..11"
        assert isinstance(cls, int)

    print("charclass.py: all verifications PASSED")