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Expression Tree

SRToolkit.utils.expression_tree

Binary expression tree (Node) and conversion utilities between token lists, trees, and LaTeX strings.

Node 

Node(symbol: str, right: Optional[Node] = None, left: Optional[Node] = None)

A node in a binary expression tree.

  • Binary operators ("op") set both left and right.
  • Unary functions ("fn") set only left; right is None.
  • Leaves (variables, constants, literals, numeric values) have both children as None.

Examples:

>>> node = Node("+", Node("x"), Node("1"))
>>> len(node)
3

Parameters:

Name Type Description Default
symbol str

Token string stored at this node.

 required
right Optional[Node]

Right operand (binary operators only).

 None
left Optional[Node]

Left operand (operators and unary functions).

 None
Source code in SRToolkit/utils/expression_tree.py 
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def __init__(self, symbol: str, right: Optional["Node"] = None, left: Optional["Node"] = None) -> None:
    """
    A node in a binary expression tree.

    - Binary operators (``"op"``) set both ``left`` and ``right``.
    - Unary functions (``"fn"``) set only ``left``; ``right`` is ``None``.
    - Leaves (variables, constants, literals, numeric values) have both children as ``None``.

    Examples:
        >>> node = Node("+", Node("x"), Node("1"))
        >>> len(node)
        3

    Args:
        symbol: Token string stored at this node.
        right: Right operand (binary operators only).
        left: Left operand (operators and unary functions).
    """
    self.symbol = symbol
    self.right = right
    self.left = left

to_list 

to_list(
    symbol_library: Optional[SymbolLibrary] = None, notation: str = "infix"
) -> List[str]

Transforms the tree rooted at this node into a list of tokens.

Examples:

>>> node = Node("+", Node("X_0"), Node("1"))
>>> node.to_list(symbol_library=SymbolLibrary.default_symbols())
['1', '+', 'X_0']
>>> node.to_list(notation="postfix")
['1', 'X_0', '+']
>>> node.to_list(notation="prefix")
['+', '1', 'X_0']
>>> node = Node("+", Node("*", Node("X_0"), Node("X_1")), Node("1"))
>>> node.to_list(symbol_library=SymbolLibrary.default_symbols())
['1', '+', 'X_1', '*', 'X_0']
>>> node.to_list(notation="infix")
['1', '+', '(', 'X_1', '*', 'X_0', ')']
>>> node = Node("sin", None, Node("X_0"))
>>> node.to_list(symbol_library=SymbolLibrary.default_symbols())
['sin', '(', 'X_0', ')']
>>> node = Node("^2", None, Node("X_0"))
>>> node.to_list(symbol_library=SymbolLibrary.default_symbols())
['X_0', '^2']
>>> node.to_list()
['(', 'X_0', ')', '^2']
>>> node = Node("*", Node("*", Node("X_0"), Node("X_0")),  Node("X_0"))
>>> node.to_list(symbol_library=SymbolLibrary.default_symbols(),notation="infix")
['X_0', '*', '(', 'X_0', '*', 'X_0', ')']

Parameters:

Name Type Description Default
symbol_library Optional[SymbolLibrary]

Symbol library used to determine token types and precedences during infix reconstruction. If None with "infix" notation, the output may contain redundant parentheses.

 None
notation str

Output notation: "infix", "prefix", or "postfix". Default "infix".

 'infix'

Returns:

Type Description
List[str]

Token list representing the subtree rooted at this node.

Raises:

Type Description
Exception

If notation is not one of the accepted values, or if a token's type cannot be resolved during infix reconstruction.
Source code in SRToolkit/utils/expression_tree.py 
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def to_list(self, symbol_library: Optional[SymbolLibrary] = None, notation: str = "infix") -> List[str]:
    """
    Transforms the tree rooted at this node into a list of tokens.

    Examples:
        >>> node = Node("+", Node("X_0"), Node("1"))
        >>> node.to_list(symbol_library=SymbolLibrary.default_symbols())
        ['1', '+', 'X_0']
        >>> node.to_list(notation="postfix")
        ['1', 'X_0', '+']
        >>> node.to_list(notation="prefix")
        ['+', '1', 'X_0']
        >>> node = Node("+", Node("*", Node("X_0"), Node("X_1")), Node("1"))
        >>> node.to_list(symbol_library=SymbolLibrary.default_symbols())
        ['1', '+', 'X_1', '*', 'X_0']
        >>> node.to_list(notation="infix")
        ['1', '+', '(', 'X_1', '*', 'X_0', ')']
        >>> node = Node("sin", None, Node("X_0"))
        >>> node.to_list(symbol_library=SymbolLibrary.default_symbols())
        ['sin', '(', 'X_0', ')']
        >>> node = Node("^2", None, Node("X_0"))
        >>> node.to_list(symbol_library=SymbolLibrary.default_symbols())
        ['X_0', '^2']
        >>> node.to_list()
        ['(', 'X_0', ')', '^2']
        >>> node = Node("*", Node("*", Node("X_0"), Node("X_0")),  Node("X_0"))
        >>> node.to_list(symbol_library=SymbolLibrary.default_symbols(),notation="infix")
        ['X_0', '*', '(', 'X_0', '*', 'X_0', ')']

    Args:
        symbol_library: Symbol library used to determine token types and precedences
            during infix reconstruction. If ``None`` with ``"infix"`` notation, the
            output may contain redundant parentheses.
        notation: Output notation: ``"infix"``, ``"prefix"``, or ``"postfix"``.
            Default ``"infix"``.

    Returns:
        Token list representing the subtree rooted at this node.

    Raises:
        Exception: If ``notation`` is not one of the accepted values, or if a token's
            type cannot be resolved during infix reconstruction.
    """
    # if symbol_library is None:
    #     symbol_library = SymbolLibrary.default_symbols()

    left = [] if self.left is None else self.left.to_list(symbol_library, notation)
    right = [] if self.right is None else self.right.to_list(symbol_library, notation)

    if notation == "prefix":
        return [self.symbol] + left + right

    elif notation == "postfix":
        return left + right + [self.symbol]

    elif notation == "infix" and symbol_library is None:
        warnings.warn(
            "Symbol library not provided. Generated expression may contain unnecessary parentheses and"
            " have other issues."
        )
        if self.left is None and self.right is None:
            return [self.symbol]
        if self.right is None and self.left is not None:
            if self.symbol[0] == "^":
                return ["("] + left + [")", self.symbol]
            else:
                return [self.symbol, "("] + left + [")"]
        else:
            if len(left) > 1:
                left = ["("] + left + [")"]
            if len(right) > 1:
                right = ["("] + right + [")"]
            return left + [self.symbol] + right

    elif notation == "infix":
        assert symbol_library is not None, "[Node.to_list] parameter symbol_library should be of type SymbolLibrary"
        if is_float(self.symbol):
            return [self.symbol]
        if symbol_library.get_type(self.symbol) in ["var", "const", "lit"]:
            return [self.symbol]
        elif symbol_library.get_type(self.symbol) == "fn":
            if symbol_library.get_precedence(self.symbol) > 0:
                return [self.symbol, "("] + left + [")"]
            else:
                if len(left) > 1:
                    left = ["("] + left + [")"]
                return left + [self.symbol]
        elif symbol_library.get_type(self.symbol) == "op":
            if (
                self.left is not None
                and not is_float(self.left.symbol)
                and -1
                < symbol_library.get_precedence(self.left.symbol)
                <= symbol_library.get_precedence(self.symbol)
            ):
                left = ["("] + left + [")"]
            if (
                self.right is not None
                and not is_float(self.right.symbol)
                and -1
                < symbol_library.get_precedence(self.right.symbol)
                <= symbol_library.get_precedence(self.symbol)
            ):
                right = ["("] + right + [")"]
            return left + [self.symbol] + right
        else:
            raise Exception(f"Invalid symbol type for symbol {self.symbol}.")
    else:
        raise Exception(
            "Invalid notation selected. Use 'infix', 'prefix', 'postfix', or leave blank (defaults to 'infix')."
        )

to_latex 

to_latex(symbol_library: SymbolLibrary) -> str

Transforms the tree rooted at this node into a LaTeX expression.

Examples:

>>> node = Node("+", Node("X_0"), Node("1"))
>>> node.to_latex(symbol_library=SymbolLibrary.default_symbols())
'$1 + X_{0}$'
>>> node = Node("+", Node("*", Node("X_0"), Node("X_1")), Node("1"))
>>> print(node.to_latex(symbol_library=SymbolLibrary.default_symbols()))
$1 + X_{1} \cdot X_{0}$
>>> node = Node("sin", None, Node("X_0"))
>>> print(node.to_latex(symbol_library=SymbolLibrary.default_symbols()))
$\sin X_{0}$
>>> node = Node("+", Node("*", Node("X_0"), Node("C")), Node("C"))
>>> print(node.to_latex(symbol_library=SymbolLibrary.default_symbols()))
$C_{0} + C_{1} \cdot X_{0}$

Parameters:

Name Type Description Default
symbol_library SymbolLibrary

Symbol library providing the LaTeX template for each token.

 required

Returns:

Type Description
str

A LaTeX string of the form $...$.

Raises:

Type Description
Exception

If the tree contains a token whose type cannot be resolved in symbol_library.
Source code in SRToolkit/utils/expression_tree.py 
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def to_latex(self, symbol_library: SymbolLibrary) -> str:
    r"""
    Transforms the tree rooted at this node into a LaTeX expression.

    Examples:
        >>> node = Node("+", Node("X_0"), Node("1"))
        >>> node.to_latex(symbol_library=SymbolLibrary.default_symbols())
        '$1 + X_{0}$'
        >>> node = Node("+", Node("*", Node("X_0"), Node("X_1")), Node("1"))
        >>> print(node.to_latex(symbol_library=SymbolLibrary.default_symbols()))
        $1 + X_{1} \cdot X_{0}$
        >>> node = Node("sin", None, Node("X_0"))
        >>> print(node.to_latex(symbol_library=SymbolLibrary.default_symbols()))
        $\sin X_{0}$
        >>> node = Node("+", Node("*", Node("X_0"), Node("C")), Node("C"))
        >>> print(node.to_latex(symbol_library=SymbolLibrary.default_symbols()))
        $C_{0} + C_{1} \cdot X_{0}$

    Args:
        symbol_library: Symbol library providing the LaTeX template for each token.

    Returns:
        A LaTeX string of the form ``$...$``.

    Raises:
        Exception: If the tree contains a token whose type cannot be resolved in
            ``symbol_library``.
    """
    assert symbol_library is not None, "[Node.to_latex] parameter symbol_library should be of type SymbolLibrary"
    return f"${self.__to_latex_rec(symbol_library)[0]}$"

height 

height() -> int

Return the height of the subtree rooted at this node.

A single-node tree has height 1.

Examples:

>>> node = Node("+", Node("x"), Node("1"))
>>> node.height()
2

Returns:

Type Description
int

Height of the subtree.
Source code in SRToolkit/utils/expression_tree.py 
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def height(self) -> int:
    """
    Return the height of the subtree rooted at this node.

    A single-node tree has height 1.

    Examples:
        >>> node = Node("+", Node("x"), Node("1"))
        >>> node.height()
        2

    Returns:
        Height of the subtree.
    """
    return 1 + max(
        (self.left.height() if self.left is not None else 0),
        (self.right.height() if self.right is not None else 0),
    )

__len__ 

__len__() -> int

Return the number of nodes in the subtree rooted at this node.

Examples:

>>> node = Node("+", Node("x"), Node("1"))
>>> len(node)
3

Returns:

Type Description
int

Total node count of the subtree.
Source code in SRToolkit/utils/expression_tree.py 
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def __len__(self) -> int:
    """
    Return the number of nodes in the subtree rooted at this node.

    Examples:
        >>> node = Node("+", Node("x"), Node("1"))
        >>> len(node)
        3

    Returns:
        Total node count of the subtree.
    """
    return 1 + (len(self.left) if self.left is not None else 0) + (len(self.right) if self.right is not None else 0)

__str__ 

__str__() -> str

Return the expression as a concatenated string using default infix notation that may contain redundant parentheses.

Examples:

>>> node = Node("+", Node("x"), Node("1"))
>>> str(node)
'1+x'

Returns:

Type Description
str

Concatenated token string with no spaces.
Source code in SRToolkit/utils/expression_tree.py 
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def __str__(self) -> str:
    """
    Return the expression as a concatenated string using default infix notation that may contain redundant parentheses.

    Examples:
        >>> node = Node("+", Node("x"), Node("1"))
        >>> str(node)
        '1+x'

    Returns:
        Concatenated token string with no spaces.
    """
    return "".join(self.to_list())

__copy__ 

__copy__() -> Node

Return a deep copy of the subtree rooted at this node.

Examples:

>>> node = Node("+", Node("X_0"), Node("1"))
>>> new_node = copy(node)
>>> node.to_list(symbol_library=SymbolLibrary.default_symbols())
['1', '+', 'X_0']
>>> new_node.to_list(symbol_library=SymbolLibrary.default_symbols())
['1', '+', 'X_0']
>>> node == node
True
>>> node == new_node
False

Returns:

Type Description
Node

An independent copy of the subtree.
Source code in SRToolkit/utils/expression_tree.py 
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def __copy__(self) -> "Node":
    """
    Return a deep copy of the subtree rooted at this node.

    Examples:
        >>> node = Node("+", Node("X_0"), Node("1"))
        >>> new_node = copy(node)
        >>> node.to_list(symbol_library=SymbolLibrary.default_symbols())
        ['1', '+', 'X_0']
        >>> new_node.to_list(symbol_library=SymbolLibrary.default_symbols())
        ['1', '+', 'X_0']
        >>> node == node
        True
        >>> node == new_node
        False

    Returns:
        An independent copy of the subtree.
    """
    if self.left is not None:
        left = copy(self.left)
    else:
        left = None
    if self.right is not None:
        right = copy(self.right)
    else:
        right = None
    return Node(copy(self.symbol), left=left, right=right)

is_float 

is_float(element: Any) -> bool

Return True if element can be interpreted as a floating-point number.

Examples:

>>> is_float(1.0)
True
>>> is_float("1.0")
True
>>> is_float("1")
True
>>> is_float(None)
False

Parameters:

Name Type Description Default
element Any

Value to test.

 required

Returns:

Type Description
bool

True if float(element) succeeds, False otherwise (including None).
Source code in SRToolkit/utils/expression_tree.py 
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def is_float(element: Any) -> bool:
    """
    Return ``True`` if ``element`` can be interpreted as a floating-point number.

    Examples:
        >>> is_float(1.0)
        True
        >>> is_float("1.0")
        True
        >>> is_float("1")
        True
        >>> is_float(None)
        False

    Args:
        element: Value to test.

    Returns:
        ``True`` if ``float(element)`` succeeds, ``False`` otherwise (including ``None``).
    """
    if element is None:
        return False
    try:
        float(element)
        return True
    except ValueError:
        return False

tokens_to_tree 

tokens_to_tree(tokens: List[str], sl: SymbolLibrary) -> Node

Parse a token list into an expression tree using the shunting-yard algorithm.

Examples:

>>> tree = tokens_to_tree(["(", "X_0", "+", "X_1", ")"], SymbolLibrary.default_symbols())
>>> len(tree)
3

Parameters:

Name Type Description Default
tokens List[str]

Token list in infix notation.

 required
sl SymbolLibrary

Symbol library used to resolve token types and precedences.

 required

Returns:

Type Description
Node

Root Node of the parsed expression tree.

Raises:

Type Description
Exception

If a token is absent from sl, or if the expression is syntactically invalid.
Source code in SRToolkit/utils/expression_tree.py 
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def tokens_to_tree(tokens: List[str], sl: SymbolLibrary) -> Node:
    """
    Parse a token list into an expression tree using the shunting-yard algorithm.

    Examples:
        >>> tree = tokens_to_tree(["(", "X_0", "+", "X_1", ")"], SymbolLibrary.default_symbols())
        >>> len(tree)
        3

    Args:
        tokens: Token list in infix notation.
        sl: Symbol library used to resolve token types and precedences.

    Returns:
        Root [Node][SRToolkit.utils.expression_tree.Node] of the parsed expression tree.

    Raises:
        Exception: If a token is absent from ``sl``, or if the expression is
            syntactically invalid.
    """
    num_tokens = len([t for t in tokens if t != "(" and t != ")"])
    expr_str = "".join(tokens)
    tokens = ["("] + tokens + [")"]
    operator_stack = []
    out_stack = []
    for token in tokens:
        if token == "(":
            operator_stack.append(token)
        elif sl.get_type(token) in ["var", "const", "lit"] or is_float(token):
            out_stack.append(Node(token))
        elif sl.get_type(token) == "fn":
            if token[0] == "^":
                out_stack.append(Node(token, left=out_stack.pop()))
            else:
                operator_stack.append(token)
        elif sl.get_type(token) == "op":
            while (
                len(operator_stack) > 0
                and operator_stack[-1] != "("
                and sl.get_precedence(operator_stack[-1]) >= sl.get_precedence(token)
            ):
                if sl.get_type(operator_stack[-1]) == "fn":
                    out_stack.append(Node(operator_stack.pop(), left=out_stack.pop()))
                else:
                    out_stack.append(Node(operator_stack.pop(), out_stack.pop(), out_stack.pop()))
            operator_stack.append(token)
        else:
            if token != ")":
                raise Exception(
                    f'Invalid symbol "{token}" in expression {expr_str}. Did you add token "{token}" to the symbol library?'
                )

            while len(operator_stack) > 0 and operator_stack[-1] != "(":
                if sl.get_type(operator_stack[-1]) == "fn":
                    out_stack.append(Node(operator_stack.pop(), left=out_stack.pop()))
                else:
                    out_stack.append(Node(operator_stack.pop(), out_stack.pop(), out_stack.pop()))
            operator_stack.pop()
            if len(operator_stack) > 0 and sl.get_type(operator_stack[-1]) == "fn":
                out_stack.append(Node(operator_stack.pop(), left=out_stack.pop()))
    if len(out_stack[-1]) == num_tokens:
        return out_stack[-1]
    else:
        raise Exception(f"Error while parsing expression {expr_str}.")

expr_to_latex 

expr_to_latex(
    expr: Union[Node, List[str]], symbol_library: SymbolLibrary
) -> str

Convert an expression to a LaTeX string.

Examples:

>>> expr_to_latex(["(", "X_0", "+", "X_1", ")"], SymbolLibrary.default_symbols())
'$X_{0} + X_{1}$'
>>> expr = Node("+", Node("X_0"), Node("1"))
>>> expr_to_latex(expr, SymbolLibrary.default_symbols())
'$1 + X_{0}$'

Parameters:

Name Type Description Default
expr Union[Node, List[str]]

Expression as a token list or a Node tree.

 required
symbol_library SymbolLibrary

Symbol library providing LaTeX templates.

 required

Returns:

Type Description
str

A LaTeX string of the form $...$, or an empty string if conversion fails.
Source code in SRToolkit/utils/expression_tree.py 
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def expr_to_latex(expr: Union[Node, List[str]], symbol_library: SymbolLibrary) -> str:
    """
    Convert an expression to a LaTeX string.

    Examples:
        >>> expr_to_latex(["(", "X_0", "+", "X_1", ")"], SymbolLibrary.default_symbols())
        '$X_{0} + X_{1}$'
        >>> expr = Node("+", Node("X_0"), Node("1"))
        >>> expr_to_latex(expr, SymbolLibrary.default_symbols())
        '$1 + X_{0}$'

    Args:
        expr: Expression as a token list or a [Node][SRToolkit.utils.expression_tree.Node] tree.
        symbol_library: Symbol library providing LaTeX templates.

    Returns:
        A LaTeX string of the form ``$...$``, or an empty string if conversion fails.
    """
    try:
        if isinstance(expr, Node):
            return expr.to_latex(symbol_library)
        elif isinstance(expr, list):
            return tokens_to_tree(expr, symbol_library).to_latex(symbol_library)
        else:
            raise Exception(
                f"Invalid type for expression {str(expr)}. Should be SRToolkit.utils.Node or a list of tokens."
            )
    except Exception as e:
        print(f"Error while converting expression {str(expr)} to LaTeX: {str(e)}")
        return ""