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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
Warning

The second positional argument is right, not left. When passing children positionally (e.g. Node("+", Node("a"), Node("b"))), Node("a") becomes the right child and Node("b") the left. Use keyword arguments to avoid confusion: Node("+", right=Node("a"), left=Node("b")).

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

    Warning:
        The second positional argument is ``right``, not ``left``. When passing
        children positionally (e.g. ``Node("+", Node("a"), Node("b"))``),
        ``Node("a")`` becomes the ``right`` child and ``Node("b")`` the ``left``.
        Use keyword arguments to avoid confusion: ``Node("+", right=Node("a"), left=Node("b"))``.

    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, a UserWarning is issued and 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.
Exception

If symbol_library is provided and 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, a
            ``UserWarning`` is issued and 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.
        Exception: If ``symbol_library`` is provided and 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:
        try:
            symbol_library = SymbolLibrary.get_active()
        except RuntimeError:
            pass

    if 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

    if 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: Optional[SymbolLibrary] = None) -> str

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

Examples:

>>> node = Node("+", right=Node("X_0"), left=Node("1"))
>>> node.to_latex(symbol_library=SymbolLibrary.default_symbols())
'$1 + X_{0}$'
>>> node = Node("+", right=Node("*", right=Node("X_0"), left=Node("X_1")), left=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("+", right=Node("*", right=Node("X_0"), left=Node("C")), left=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 Optional[SymbolLibrary]

Symbol library providing LaTeX templates for each token. If None, falls back to the currently active library set via 'with SymbolLibrary(...) as sl:'. Defaults to None.

 None

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: Optional[SymbolLibrary] = None) -> str:
    r"""
    Transforms the tree rooted at this node into a LaTeX expression.

    Examples:
        >>> node = Node("+", right=Node("X_0"), left=Node("1"))
        >>> node.to_latex(symbol_library=SymbolLibrary.default_symbols())
        '$1 + X_{0}$'
        >>> node = Node("+", right=Node("*", right=Node("X_0"), left=Node("X_1")), left=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("+", right=Node("*", right=Node("X_0"), left=Node("C")), left=Node("C"))
        >>> print(node.to_latex(symbol_library=SymbolLibrary.default_symbols()))
        $C_{0} + C_{1} \cdot X_{0}$

    Args:
        symbol_library: Symbol library providing LaTeX templates for each token.
            If None, falls back to the currently active library set via
            'with SymbolLibrary(...) as sl:'. Defaults to None.

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

    Raises:
        Exception: If the tree contains a token whose type cannot be resolved in
            ``symbol_library``.
    """
    if symbol_library is None:
        symbol_library = SymbolLibrary.get_active()
    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
>>> is_float("hello")
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
        >>> is_float("hello")
        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: Optional[SymbolLibrary] = None, notation: str = 'infix') -> Node

Parse a token list into an expression tree.

Infix token lists are parsed with the shunting-yard algorithm; prefix and postfix lists are parsed with a single stack pass using the arity implied by each token's type ("op" is binary, "fn" is unary, and variables, constants, literals, and numeric literals are leaves). This is the inverse of Node.to_list, so a tree survives a round trip through any of the three notations.

Examples:

>>> tree = tokens_to_tree(["(", "X_0", "+", "X_1", ")"], SymbolLibrary.default_symbols())
>>> len(tree)
3
>>> tree = tokens_to_tree(["+", "1", "X_0"], SymbolLibrary.default_symbols(), notation="prefix")
>>> tree.to_list(SymbolLibrary.default_symbols())
['1', '+', 'X_0']
>>> tree = tokens_to_tree(["X_0", "X_1", "*", "1", "+"], SymbolLibrary.default_symbols(), notation="postfix")
>>> tree.to_list(SymbolLibrary.default_symbols())
['X_0', '*', 'X_1', '+', '1']
>>> tree = tokens_to_tree(["sin", "X_0"], SymbolLibrary.default_symbols(), notation="prefix")
>>> tree.to_list(SymbolLibrary.default_symbols())
['sin', '(', 'X_0', ')']

Parameters:

Name Type Description Default
tokens List[str]

Token list in the notation given by notation.

 required
sl Optional[SymbolLibrary]

Symbol library used to resolve token types and precedences. If None, falls back to the currently active library set via 'with SymbolLibrary(...) as sl:'. Defaults to None.

 None
notation str

Notation of tokens: "infix", "prefix", or "postfix". Default "infix".

 'infix'

Returns:

Type Description
Node

Root Node of the parsed expression tree.

Raises:

Type Description
Exception

If notation is not one of the accepted values, if a token is absent from sl, or if the expression is syntactically invalid (e.g. an operator lacks operands or tokens remain unconsumed).
Source code in SRToolkit/utils/expression_tree.py 
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def tokens_to_tree(tokens: List[str], sl: Optional[SymbolLibrary] = None, notation: str = "infix") -> Node:
    """
    Parse a token list into an expression tree.

    Infix token lists are parsed with the shunting-yard algorithm; prefix and
    postfix lists are parsed with a single stack pass using the arity implied by
    each token's type (``"op"`` is binary, ``"fn"`` is unary, and variables,
    constants, literals, and numeric literals are leaves). This is the inverse of
    [Node.to_list][SRToolkit.utils.expression_tree.Node.to_list], so a tree
    survives a round trip through any of the three notations.

    Examples:
        >>> tree = tokens_to_tree(["(", "X_0", "+", "X_1", ")"], SymbolLibrary.default_symbols())
        >>> len(tree)
        3
        >>> tree = tokens_to_tree(["+", "1", "X_0"], SymbolLibrary.default_symbols(), notation="prefix")
        >>> tree.to_list(SymbolLibrary.default_symbols())
        ['1', '+', 'X_0']
        >>> tree = tokens_to_tree(["X_0", "X_1", "*", "1", "+"], SymbolLibrary.default_symbols(), notation="postfix")
        >>> tree.to_list(SymbolLibrary.default_symbols())
        ['X_0', '*', 'X_1', '+', '1']
        >>> tree = tokens_to_tree(["sin", "X_0"], SymbolLibrary.default_symbols(), notation="prefix")
        >>> tree.to_list(SymbolLibrary.default_symbols())
        ['sin', '(', 'X_0', ')']

    Args:
        tokens: Token list in the notation given by ``notation``.
        sl: Symbol library used to resolve token types and precedences. If None,
            falls back to the currently active library set via
            'with SymbolLibrary(...) as sl:'. Defaults to None.
        notation: Notation of ``tokens``: ``"infix"``, ``"prefix"``, or
            ``"postfix"``. Default ``"infix"``.

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

    Raises:
        Exception: If ``notation`` is not one of the accepted values, if a token is
            absent from ``sl``, or if the expression is syntactically invalid (e.g.
            an operator lacks operands or tokens remain unconsumed).
    """
    if sl is None:
        sl = SymbolLibrary.get_active()

    if notation == "infix":
        return _infix_to_tree(tokens, sl)
    elif notation in ("prefix", "postfix"):
        return _prefix_postfix_to_tree(tokens, sl, notation)
    else:
        raise Exception(
            "Invalid notation selected. Use 'infix', 'prefix', 'postfix', or leave blank (defaults to 'infix')."
        )

expr_to_latex 

expr_to_latex(expr: Union[Node, List[str]], symbol_library: Optional[SymbolLibrary] = None) -> 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 Optional[SymbolLibrary]

Symbol library providing LaTeX templates. If None, falls back to the currently active library set via 'with SymbolLibrary(...) as sl:'. Defaults to None.

 None

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: Optional[SymbolLibrary] = None) -> 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. If None, falls
            back to the currently active library set via
            'with SymbolLibrary(...) as sl:'. Defaults to None.

    Returns:
        A LaTeX string of the form ``$...$``, or an empty string if conversion fails.
    """
    if symbol_library is None:
        symbol_library = SymbolLibrary.get_active()
    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 ""