multilingual-gsm-symbolic 0.1.0

A package for generating multilingual symbolic GSM math problems

multilingual-gsm-symbolic

A Python package for generating synthetic multilingual math problems from symbolic templates. See the Data section for available languages.

Installation

pip install multilingual-gsm-symbolic

Quickstart

from multilingual_gsm_symbolic import load_data, load_replacements, available_languages

# see possible languages
languages = available_languages()

lang = "eng"
print(languages[lang])
# {"number of samples": 100}

# Load English templates (default)
templates = load_data(lang)

# Load language-specific replacement values (used in some templates)
replacements = load_replacements(lang)

# Generate concrete questions from a template
template = templates[0]
questions = template.generate_questions(n=10, language="eng", replacements=replacements)

for q in questions:
    print(q.question)
    print(q.answer)
    print()

Template format

Templates are JSON files with four fields:

Field	Description
question	Concrete question (the original example)
answer	Concrete answer with calculation steps
question_annotated	Template with variable placeholders and #init / #conditions / #answer sections
answer_annotated	Answer template with inline expressions

Annotated question syntax

{variable, default_value}   — placeholder in the question text
#init:
- $var = range(low, high)   — variable sampled from a range
- $var = sample([a, b, c])  — variable sampled from a list
#conditions:
- is_int(x / y)             — constraint that must hold for a combination to be valid
#answer: x * y + z          — Python expression evaluated to produce the numeric answer

Example: fog bank problem

{
  "question": "A fog bank rolls in over a city at 3 miles/hour. The city is 42 miles wide. How many hours will it take for the fog bank to cover the city?",
  "question_annotated": "A fog bank rolls in over a city at {speed,3} miles/hour. The city is {width,42} miles wide. How many hours will it take for the fog bank to cover the city?\n#init:\n- $speed = range(1, 20)\n- $width = range(2, 100)\n#conditions:\n- is_int(width / speed)\n#answer: width // speed",
  "answer": "At 3 miles/hour, it will take 42/3=14 hours for the fog to cover the city.",
  "answer_annotated": "At {speed} miles/hour, it will take {width}/{speed}={width//speed} hours for the fog to cover the city."
}

Example: shopping problem

{
  "question": "A store sells apples for $2 each and oranges for $3 each. If you buy 4 apples and 5 oranges, how much do you spend?",
  "question_annotated": "A store sells apples for ${apple_price,2} each and oranges for ${orange_price,3} each. If you buy {n_apples,4} apples and {n_oranges,5} oranges, how much do you spend?\n#init:\n- $apple_price = range(1, 10)\n- $orange_price = range(1, 10)\n- $n_apples = range(1, 20)\n- $n_oranges = range(1, 20)\n#conditions:\n- True\n#answer: apple_price * n_apples + orange_price * n_oranges",
  "answer": "You spend 4*2 + 5*3 = 8 + 15 = $23.",
  "answer_annotated": "You spend {n_apples}*{apple_price} + {n_oranges}*{orange_price} = {n_apples*apple_price} + {n_oranges*orange_price} = ${apple_price*n_apples + orange_price*n_oranges}."
}

Available helper functions

Function	Description
range(start, end[, step])	All integers in [start, end)
sample([a, b, c])	One value from the list
range_sample(start, end, step)	Uniform sample from a range
sample_sequential(items, n)	n consecutive items from a list
arange_sample(start, end, step)	Sample from np.arange(start, end, step)
is_int(x)	True if x is an integer
divides(a, b)	True if a divides b
frac_format(x)	Format x as a fraction string

📖 API reference

load_data(language="eng", directory=None) → list[AnnotatedQuestion]

Load symbolic templates.

• language — "eng" (default) or "dan", or any language code for which a template folder exists
• directory — override the bundled data; load templates from this path instead

load_replacements(language="eng") → dict

Load language-specific named values (e.g. lists of names, places) used inside templates.

load_gsm(language="eng", directory=None) → list[GSMProblem]

Load the bundled concrete problems for a given language.

AnnotatedQuestion

Core class. Constructed from a JSON template file via AnnotatedQuestion.from_json(path).

Key methods:

Method	Description
generate_questions(n, language, replacements)	Generate n concrete Question instances
get_default_assignments(replacements)	Extract the example variable values from the template
format_question(assignments, language)	Render the question text for a given assignment
format_answer(assignments, language)	Render the answer text for a given assignment

Question

Dataclass holding a single generated problem: question, answer, id_orig, id_shuffled.

GSMProblem

Pydantic model for a concrete problem loaded from disk: question, answer, id_orig, filepath.

Data

The English templates are derived from Apple's GSM-Symbolic paper. The Danish templates are manual translations and localizations of the English set, validated both computationally and manually. The original concrete problems are from GSM8k.

Language	Code	Templates
English	eng	100
Danish	dan	100

Acknowledgement

The symbolic template engine and the danish subset were originally developed as part of the m-gsm-symbolic project at the Centre for Humanities Computing by:

• Kenneth Enevoldsen
• Simon Mosegaard
• Enniw

The initial template format was derived from Apple's GSM-Symbolic paper and the original concrete problems are from GSM8k.