mathjs-to-func

A tiny Python library that compiles serialized math.js expression trees into fast, reusable Python callables. The generated function respects dependency ordering, validates inputs, and mirrors a subset of math.js operators (+, -, *, /, ^, %, unary plus/minus) and functions (min, max, sum, ifnull).

Key Features

• Execute without reparsing or repeatedly walking the JSON graph.
• Detect dependency cycles and missing identifiers early.
• Keep execution sandboxed by compiling a controlled Python AST.
• Work well with scalars or NumPy arrays for vectorised workloads.

Installation

The project uses uv for dependency and virtualenv management. From the repository root:

uv add mathjs-to-func

An optional parse extra installs a JSON-to-math.js parser powered by Pydantic:

uv add mathjs-to-func --extra parse

Compiling A Function

from mathjs_to_func import build_evaluator

def main():
    mathjs_payload = {
        "expressions": {
            # z = (x + y) / 2
            "sum_xy": {
                "type": "OperatorNode",
                "fn": "add",
                "args": [
                    {"type": "SymbolNode", "name": "x"},
                    {"type": "SymbolNode", "name": "y"},
                ],
            },
            "mean": {
                "type": "OperatorNode",
                "fn": "divide",
                "args": [
                    {"type": "SymbolNode", "name": "sum_xy"},
                    {"type": "ConstantNode", "value": "2", "valueType": "number"},
                ],
            },
        },
        "inputs": ["x", "y"],
        "target": "mean",
    }

    evaluator = build_evaluator(**mathjs_payload, include_source=True)

    result = evaluator({"x": 10, "y": 6})
    print(result)  # -> 8.0

    # Introspection helpers
    print(evaluator.__mathjs_required_inputs__)     # ('x', 'y')
    print(evaluator.__mathjs_evaluation_order__)    # ('sum_xy', 'mean')
    print(evaluator.__mathjs_source__)              # Generated Python source

Parameters

build_evaluator accepts keyword parameters (or a single payload mapping containing the same keys):

Argument	Type	Description
expressions	Mapping[str, Mapping[str, Any]]	math.js AST JSON keyed by expression id. Each id becomes a local variable in the compiled function.
inputs	Iterable[str]	Whitelisted identifiers that may be supplied when the function is invoked.
target	str	Name of the expression whose computed value should be returned.
include_source	bool (optional)	Attach the generated Python source code as __mathjs_source__ on the returned callable.

The returned callable always expects a single mapping argument with the provided inputs. It returns the evaluated target value and may be reused across invocations.

Supported math.js nodes

Node	Notes
ConstantNode	numeric (number), boolean, or null literals
SymbolNode	validated identifiers; must be alphanumeric/underscore, starting with a letter/underscore
OperatorNode	add, subtract, multiply, divide, pow, mod, unary unaryPlus, unaryMinus
FunctionNode	min, max, sum, ifnull
ParenthesisNode	forwards to the wrapped expression
ArrayNode	materialised to Python lists/NumPy arrays

Unknown node types, invalid identifiers, or disallowed functions raise InvalidNodeError during compilation.

Error handling

• ExpressionError: base class for configuration mistakes.
• MissingTargetError: requested target id does not exist.
• UnknownIdentifierError: an expression references a symbol that is neither an input nor another expression.
• CircularDependencyError: dependency graph contains a cycle.
• InvalidNodeError: AST contains unsupported structures or invalid literals.
• InputValidationError: the compiled function received inputs that are missing, unexpected, or not a mapping.

All exceptions provide enough context (expression name, offending identifier, cycle list, etc.) to surface descriptive UI errors.

Parsing math.js JSON

With the extra installed you can turn serialized math.js nodes into evaluator-ready mappings:

from mathjs_to_func import build_evaluator
from mathjs_to_func.parse import parse

expression = parse(
    """{
    "type": "OperatorNode",
    "fn": "add",
    "args": [
        {"type": "SymbolNode", "name": "x"},
        {"type": "ConstantNode", "value": "2", "valueType": "number"}
    ]
}"""
)

evaluator = build_evaluator(
    expressions={"total": expression},
    inputs=["x"],
    target="total",
)

result = evaluator({"x": 40})  # -> 42

All examples below assume commands are wrapped with uv run ... to execute inside the managed environment.

Implementation Notes

1. AST translation – MathJsAstBuilder walks the math.js JSON and emits Python ast.AST nodes. Identifiers are validated via a strict regex to prevent sneaky names like __import__.
2. Dependency graph – A topological sorter (graphlib.TopologicalSorter) runs over expression references to produce a safe evaluation order while catching cycles and missing references upfront.
3. Code generation – The generated function validates the provided scope, binds required inputs to local variables, evaluates expressions in order, and returns the target. Intermediate values are stored as local variables named after their expression id.
4. Execution sandbox – The compiled module is executed with a tightly scoped globals dictionary: helper math functions, NumPy, and a few safe built-ins only. There is no ambient __builtins__ exposure.
5. Helper functions – math.js functions map onto small Python helpers (_mj_min, _mj_max, _mj_sum, _mj_ifnull) that understand scalars and NumPy arrays.

Testing

Run the full suite (178 tests) with:

uv run pytest

The tests cover operator translation, helper semantics, dependency validation, error conditions, numpy-friendly behaviour, and public API ergonomics.

Project Structure

src/mathjs_to_func/
├── __init__.py          # build_evaluator public API and export list
├── ast_builder.py       # math.js JSON → Python AST translation
├── compiler.py          # dependency graph, code generation, compilation
├── errors.py            # structured exception hierarchy
├── helpers.py           # runtime helpers for min/max/sum/ifnull
└── py.typed             # PEP 561 marker for type-aware consumers

Additional documentation lives in docs/api_design.md, outlining the initial design considerations.

Limitations & Future Work

• Only a subset of math.js functions/operators are implemented today.
• Units, user-defined functions, and incremental recomputation are intentionally out of scope for this milestone.
• Arrays are handled via NumPy; if you need bigints, complex numbers, or matrices, the helper layer will require extension.

Contributions and bug reports are welcome!