features.py

"""Feature extraction for separating linguistic vs mathematical difficulty in MWPs.

Two orthogonal feature blocks per problem:
  LING  - readability formulas, lexical (CEFR), syntactic (parse depth, dependency length)
  MATH  - solution-step count, operation count/type, equation/number complexity
"""
import re
import numpy as np
import textstat
import spacy
from cefrpy import CEFRAnalyzer

_NLP = spacy.load("en_core_web_sm")
_CEFR = CEFRAnalyzer()
_CEFR_NUM = {"A1": 1, "A2": 2, "B1": 3, "B2": 4, "C1": 5, "C2": 6}

# Protected Common-Core / NCTM math terms - never count as "hard language"
MATH_TERMS = {
    "area", "perimeter", "volume", "ratio", "proportion", "fraction", "decimal",
    "percent", "percentage", "median", "mean", "mode", "average", "sum", "difference",
    "product", "quotient", "divide", "multiply", "add", "subtract", "equation",
    "angle", "triangle", "rectangle", "square", "circle", "diameter", "radius",
    "numerator", "denominator", "integer", "remainder", "factor", "multiple",
}


def _cefr_features(tokens):
    levels = []
    above_b1 = 0
    for t in tokens:
        w = t.lower()
        if w in MATH_TERMS:
            continue
        lvl = _CEFR.get_average_word_level_CEFR(w)
        if lvl is not None:
            n = int(lvl.value)  # CEFRLevel enum -> 1..6
            levels.append(n)
            if n >= 3:  # B1 or above
                above_b1 += 1
    if not levels:
        return 0.0, 0.0, 0.0
    return float(np.mean(levels)), float(np.max(levels)), above_b1 / max(len(levels), 1)


def _syntactic_features(doc):
    # parse-tree depth (max distance to root), mean dependency length
    depths, dep_lens = [], []
    n_clauses = 0
    n_subord = 0
    for sent in doc.sents:
        for tok in sent:
            # depth: walk up to root
            d, cur = 0, tok
            while cur.head != cur:
                cur = cur.head
                d += 1
                if d > 50:
                    break
            depths.append(d)
            dep_lens.append(abs(tok.i - tok.head.i))
            if tok.dep_ in ("ccomp", "advcl", "relcl", "acl", "xcomp"):
                n_clauses += 1
            if tok.dep_ == "mark" or tok.tag_ == "IN" and tok.dep_ == "mark":
                n_subord += 1
    return (
        float(np.max(depths)) if depths else 0.0,
        float(np.mean(dep_lens)) if dep_lens else 0.0,
        float(n_clauses),
    )


def linguistic_features(text):
    doc = _NLP(text)
    tokens = [t.text for t in doc if t.is_alpha]
    fk = textstat.flesch_kincaid_grade(text)
    fre = textstat.flesch_reading_ease(text)
    dc = textstat.dale_chall_readability_score(text)
    n_words = len(tokens)
    n_sents = max(len(list(doc.sents)), 1)
    mean_word_len = float(np.mean([len(t) for t in tokens])) if tokens else 0.0
    cefr_mean, cefr_max, cefr_above_b1 = _cefr_features(tokens)
    parse_depth, mean_dep_len, n_clauses = _syntactic_features(doc)
    return {
        "ling_fk_grade": fk,
        "ling_flesch_ease": fre,
        "ling_dale_chall": dc,
        "ling_n_words": n_words,
        "ling_words_per_sent": n_words / n_sents,
        "ling_mean_word_len": mean_word_len,
        "ling_cefr_mean": cefr_mean,
        "ling_cefr_max": cefr_max,
        "ling_cefr_above_b1": cefr_above_b1,
        "ling_parse_depth": parse_depth,
        "ling_mean_dep_len": mean_dep_len,
        "ling_n_clauses": n_clauses,
    }


_OPS = re.compile(r"[+\-*/]")


def math_features_from_chain(chain):
    """ASDiv: count <gadget> calculator steps and operators."""
    n_steps = chain.count("<gadget")
    # only look at expressions inside gadget tags to avoid counting tag slashes
    exprs = " ".join(re.findall(r'<gadget[^>]*>(.*?)</gadget>', chain, flags=re.S))
    ops = _OPS.findall(exprs)
    nums = re.findall(r"\d+\.?\d*", exprs)
    max_num = max([float(n) for n in nums], default=0.0)
    has_frac = 1.0 if "/" in exprs else 0.0
    has_dec = 1.0 if any("." in n for n in nums) else 0.0
    return {
        "math_n_steps": float(max(n_steps, 1)),
        "math_n_ops": float(len(ops)),
        "math_max_num": max_num,
        "math_has_frac": has_frac,
        "math_has_decimal": has_dec,
    }


def math_features_from_equation(eq):
    """SVAMP: parse the Equation string."""
    ops = _OPS.findall(eq)
    nums = re.findall(r"\d+\.?\d*", eq)
    max_num = max([float(n) for n in nums], default=0.0)
    depth = 0
    cur = 0
    for ch in eq:
        if ch == "(":
            cur += 1
            depth = max(depth, cur)
        elif ch == ")":
            cur -= 1
    return {
        "math_n_ops": float(len(ops)),
        "math_max_num": max_num,
        "math_paren_depth": float(depth),
        "math_has_decimal": 1.0 if any("." in n and float(n) != int(float(n)) for n in nums) else 0.0,
    }


if __name__ == "__main__":
    t = "Ellen has six more balls than Marin. Marin has nine balls. How many balls does Ellen have?"
    print(linguistic_features(t))
    print(math_features_from_chain('<gadget id="calculator">6 + 9</gadget>'))