Snippet to convert between Unicode and LaTeX representations of logical propositions.

unicode_logic_to_latex.py

import re

_LATEX_POST_ENTITY = "{}"

# Mapping of Unicode characters to LaTeX expressions
MAPPING = {
    "∀": "\\forall",
    "∃": "\\exists",
    "→": "\\rightarrow",
    "↔": "\\leftrightarrow",
    "¬": "\\neg",
    "∧": "\\land",
    "∨": "\\lor",
    # Add more mappings if needed
}

def to_latex(expression: str) -> str:
    """
    Convert a logical expression with Unicode characters into its LaTeX representation.
    
    Parameters:
    - expression (str): The logical expression containing Unicode characters.
    
    Returns:
    - str: The LaTeX representation of the given expression.
    
    Example:
    >>> to_latex("∀x∀y(Congruent(x,y) → SameArea(x,y))")
    '\\forall{}x\\forall{}y(Congruent(x,y) \\rightarrow SameArea(x,y))'
    """
    
    for char, latex in MAPPING.items():
        expression = expression.replace(char, latex + _LATEX_POST_ENTITY)

    # Convert predicates to \text{\textsc{Predicate}} format
    expression = re.sub(r'([A-Za-z]+)\(', r'\\text{\\textsc{\1}}(', expression)

    return expression

def from_latex(expression: str) -> str:
    """
    Convert a LaTeX logical expression into its Unicode representation.
    
    Parameters:
    - expression (str): The LaTeX representation of a logical expression.
    
    Returns:
    - str: The logical expression with Unicode characters.
    
    Example:
    >>> from_latex('\\forall{}x\\forall{}y(Congruent(x,y) \\rightarrow SameArea(x,y))')
    '∀x∀y(Congruent(x,y) → SameArea(x,y))'
    """
    
    reversed_mapping = {latex: char for char, latex in MAPPING.items()}

    for latex, char in reversed_mapping.items():
        expression = expression.replace(latex, char)

    # Remove \s*{\s*}\s* from from expression using re
    expression = re.sub(r'\\s*\{\s*\}\s*', '', expression)

    # Convert \text{\textsc{Predicate}} format to predicates
    expression = re.sub(r'\\text{\\textsc{([A-Za-z]+)}}\(', r'\1(', expression)

    return expression

if __name__ == "__main__":
    # Test
    options = [
        "∀x∀y(Congruent(x,y) → SameArea(x,y))",
        "∀x∀y(Congruent(x,y) ↔ SameArea(x,y))",
        # ... (rest of the options)
    ]

    latex_options = [to_latex(option) for option in options]
    for option in latex_options:
        print(option)

    print("\nInverse conversion:")
    for option in latex_options:
        print(from_latex(option))