Formula Engine Deep-Dive¶

# src/calculations/parser/tokenizer.py
class TokenType(Enum):
    """Token types for Excel formula lexer."""

    # Literals
    NUMBER = auto()      # 42, 3.14, 1.5E10
    STRING = auto()      # "Hello", 'World'
    BOOLEAN = auto()     # TRUE, FALSE
    ERROR = auto()       # #DIV/0!, #N/A

    # References
    CELL_REF = auto()    # A1, $A$1
    RANGE_REF = auto()   # A1:B10
    COLUMN_REF = auto()  # A:A
    ROW_REF = auto()     # 1:1
    SHEET_REF = auto()   # Sheet1!

    # Structured References
    STRUCTURED_REF = auto()  # [@[Column Name]]
    TABLE_REF = auto()       # Table1[Column]

    # Operators
    PLUS = auto()        # +
    MINUS = auto()       # -
    MULTIPLY = auto()    # *
    DIVIDE = auto()      # /
    POWER = auto()       # ^
    CONCAT = auto()      # &

    # Comparators
    EQ = auto()          # =
    NE = auto()          # <>
    LT = auto()          # <
    GT = auto()          # >
    LE = auto()          # <=
    GE = auto()          # >=

    # Functions
    FUNCTION = auto()    # SUM, IF, XLOOKUP

# Input formula
formula = "=IF(A1>0, SUM(B1:B10)*2, 0)"

# Tokenization result
tokens = [
    Token(FUNCTION, "IF", pos=1),
    Token(LPAREN, "(", pos=3),
    Token(CELL_REF, "A1", pos=4),
    Token(GT, ">", pos=6),
    Token(NUMBER, "0", pos=7),
    Token(COMMA, ",", pos=8),
    Token(FUNCTION, "SUM", pos=10),
    Token(LPAREN, "(", pos=13),
    Token(RANGE_REF, "B1:B10", pos=14),
    Token(RPAREN, ")", pos=20),
    Token(MULTIPLY, "*", pos=21),
    Token(NUMBER, "2", pos=22),
    Token(COMMA, ",", pos=23),
    Token(NUMBER, "0", pos=25),
    Token(RPAREN, ")", pos=26),
    Token(EOF, "", pos=27),
]

# src/calculations/parser/ast_nodes.py
class ASTVisitor(ABC):
    """Base visitor for AST traversal."""

    @abstractmethod
    def visit_number(self, node: NumberNode) -> Any: pass

    @abstractmethod
    def visit_cell_ref(self, node: CellRefNode) -> Any: pass

    @abstractmethod
    def visit_function(self, node: FunctionNode) -> Any: pass

    @abstractmethod
    def visit_binary_op(self, node: BinaryOpNode) -> Any: pass
    # ... other visit methods

class DependencyExtractor(DefaultASTVisitor):
    """Extract cell references from a formula."""

    def __init__(self):
        self.dependencies: set[str] = set()

    def visit_cell_ref(self, node: CellRefNode) -> None:
        self.dependencies.add(node.address)

    def visit_range_ref(self, node: RangeRefNode) -> None:
        # Expand range to individual cells
        for cell in expand_range(node):
            self.dependencies.add(cell)

# src/calculations/safe_evaluator.py
class SafeExpressionEvaluator:
    """Safe expression evaluator - NO dynamic code execution."""

    # Maximum expression length
    MAX_EXPRESSION_LENGTH = 10000

    # Maximum recursion depth
    MAX_DEPTH = 50

    # Dangerous patterns - BLOCKED
    DANGEROUS_PATTERNS = [
        r'__\w+__',      # Dunder methods
        r'\bimport\b',   # Import statements
        r'\bexec\b',     # Dynamic execution
        r'\bcompile\b',  # Code compilation
        r'\bopen\b',     # File operations
        r'\bgetattr\b',  # Attribute access
        r'\bglobals\b',  # Globals access
        r'\blocals\b',   # Locals access
        r'\bos\.\w+',    # OS module
        r'\bsys\.\w+',   # Sys module
    ]

    # Whitelisted functions ONLY
    SAFE_FUNCTIONS = {
        'abs': abs,
        'round': round,
        'min': min,
        'max': max,
        'sum': sum,
        'SUM': lambda *args: sum(args),
        'AVERAGE': lambda *args: sum(args) / len(args),
        'SQRT': math.sqrt,
        # ... other safe functions
    }

# src/calculations/functions/vectorized.py

def vectorized_if(
    condition: pd.Series,
    value_if_true: Any,
    value_if_false: Any
) -> pd.Series:
    """Vectorized IF - processes entire column at once."""
    return np.where(condition, value_if_true, value_if_false)

def vectorized_xlookup(
    lookup_values: pd.Series,
    lookup_dict: dict,
    default: Any = None
) -> pd.Series:
    """Vectorized XLOOKUP using dictionary mapping."""
    return lookup_values.map(lookup_dict).fillna(default)

def vectorized_sumifs(
    sum_range: pd.Series,
    *criteria_pairs  # (range, criteria, range, criteria, ...)
) -> float:
    """Vectorized SUMIFS with multiple criteria."""
    mask = pd.Series([True] * len(sum_range))
    for i in range(0, len(criteria_pairs), 2):
        criteria_range = criteria_pairs[i]
        criteria = criteria_pairs[i + 1]
        mask &= (criteria_range == criteria)
    return sum_range[mask].sum()

# src/calculations/types.py
from decimal import Decimal, ROUND_HALF_UP

class Money:
    """Money type with 2 decimal place precision."""
    PRECISION = Decimal("0.01")

    def __init__(self, value: Union[int, float, Decimal], currency: str = "USD"):
        self.value = Decimal(str(value)).quantize(
            self.PRECISION,
            rounding=ROUND_HALF_UP
        )
        self.currency = currency

class FinancialRate:
    """Financial rate with 6 decimal place precision."""
    PRECISION = Decimal("0.000001")

    def __init__(self, value: Union[int, float, Decimal]):
        self.value = Decimal(str(value)).quantize(
            self.PRECISION,
            rounding=ROUND_HALF_UP
        )

# Error types
class FormulaError(Enum):
    DIV_ZERO = "#DIV/0!"
    VALUE = "#VALUE!"
    REF = "#REF!"
    NAME = "#NAME?"
    NA = "#N/A"
    NUM = "#NUM!"

# Error propagation
def handle_division(numerator: Any, denominator: Any) -> Any:
    if denominator == 0:
        return FormulaError.DIV_ZERO
    return numerator / denominator

def handle_lookup_miss(lookup_value: Any, found: bool) -> Any:
    if not found:
        return FormulaError.NA
    return lookup_value

# 1. Define the function
def custom_function(arg1: Any, arg2: Any) -> Any:
    """Custom Excel function implementation."""
    return arg1 + arg2

# 2. Register in SAFE_FUNCTIONS
SAFE_FUNCTIONS["CUSTOM"] = custom_function

# 3. Add to tokenizer FUNCTIONS set
FUNCTIONS.add("CUSTOM")

# 1. Add token type
class TokenType(Enum):
    CUSTOM_OP = auto()

# 2. Add to tokenizer patterns
PATTERNS.append((r'\$\$', TokenType.CUSTOM_OP))

# 3. Add to binary ops
BINARY_OPS[ast.CustomOp] = lambda a, b: custom_operation(a, b)