epathtools.py

"""Tools for manipulation of expressions using paths. """

from sympy.core import Basic

class EPath(object):
    r"""
    Manipulate expressions using paths.

    EPath grammar in EBNF notation::

        literal   ::= /[A-Za-z_][A-Za-z_0-9]*/
        number    ::= /-?\d+/
        type      ::= literal
        attribute ::= literal "?"
        all       ::= "*"
        slice     ::= "[" number? (":" number? (":" number?)?)? "]"
        range     ::= all | slice
        query     ::= (type | attribute) ("|" (type | attribute))*
        selector  ::= range | query range?
        path      ::= "/" selector ("/" selector)*

    See the docstring of the epath() function.

    """

    __slots__ = ["_path", "_epath"]

    def __new__(cls, path):
        """Construct new EPath. """
        if isinstance(path, EPath):
            return path

        if not path:
            raise ValueError("empty EPath")

        _path = path

        if path[0] == '/':
            path = path[1:]
        else:
            raise NotImplementedError("non-root EPath")

        epath = []

        for selector in path.split('/'):
            selector = selector.strip()

            if not selector:
                raise ValueError("empty selector")

            index = 0

            for c in selector:
                if c.isalnum() or c == '_' or c == '|' or c == '?':
                    index += 1
                else:
                    break

            attrs = []
            types = []

            if index:
                elements = selector[:index]
                selector = selector[index:]

                for element in elements.split('|'):
                    element = element.strip()

                    if not element:
                        raise ValueError("empty element")

                    if element.endswith('?'):
                        attrs.append(element[:-1])
                    else:
                        types.append(element)

            span = None

            if selector == '*':
                pass
            else:
                if selector.startswith('['):
                    try:
                        i = selector.index(']')
                    except ValueError:
                        raise ValueError("expected ']', got EOL")

                    _span, span = selector[1:i], []

                    if ':' not in _span:
                        span = int(_span)
                    else:
                        for elt in _span.split(':', 3):
                            if not elt:
                                span.append(None)
                            else:
                                span.append(int(elt))

                        span = slice(*span)

                    selector = selector[i+1:]

                if selector:
                    raise ValueError("trailing characters in selector")

            epath.append((attrs, types, span))

        obj = object.__new__(cls)

        obj._path = _path
        obj._epath = epath

        return obj

    def __repr__(self):
        return "%s(%r)" % (self.__class__.__name__, self._path)

    def _get_ordered_args(self, expr):
        """Sort ``expr.args`` using printing order. """
        if expr.is_Add:
            return expr.as_ordered_terms()
        elif expr.is_Mul:
            return expr.as_ordered_factors()
        else:
            return expr.args

    def _hasattrs(self, expr, attrs):
        """Check if ``expr`` has any of ``attrs``. """
        for attr in attrs:
            if not hasattr(expr, attr):
                return False

        return True

    def _hastypes(self, expr, types):
        """Check if ``expr`` is any of ``types``. """
        _types = [ cls.__name__ for cls in expr.__class__.mro() ]
        return bool(set(_types).intersection(types))

    def _has(self, expr, attrs, types):
        """Apply ``_hasattrs`` and ``_hastypes`` to ``expr``. """
        if not (attrs or types):
            return True

        if attrs and self._hasattrs(expr, attrs):
            return True

        if types and self._hastypes(expr, types):
            return True

        return False

    def apply(self, expr, func, args=None, kwargs=None):
        """
        Modify parts of an expression selected by a path.

        Examples
        ========

        >>> from sympy.simplify.epathtools import EPath
        >>> from sympy import sin, cos, E
        >>> from sympy.abc import x, y, z, t

        >>> path = EPath("/*/[0]/Symbol")
        >>> expr = [((x, 1), 2), ((3, y), z)]

        >>> path.apply(expr, lambda expr: expr**2)
        [((x**2, 1), 2), ((3, y**2), z)]

        >>> path = EPath("/*/*/Symbol")
        >>> expr = t + sin(x + 1) + cos(x + y + E)

        >>> path.apply(expr, lambda expr: 2*expr)
        t + sin(2*x + 1) + cos(2*x + 2*y + E)

        """
        def _apply(path, expr, func):
            if not path:
                return func(expr)
            else:
                selector, path = path[0], path[1:]
                attrs, types, span = selector

                if isinstance(expr, Basic):
                    if not expr.is_Atom:
                        args, basic = self._get_ordered_args(expr), True
                    else:
                        return expr
                elif hasattr(expr, '__iter__'):
                    args, basic = expr, False
                else:
                    return expr

                args = list(args)

                if span is not None:
                    if type(span) == slice:
                        indices = range(*span.indices(len(args)))
                    else:
                        indices = [span]
                else:
                    indices = xrange(len(args))

                for i in indices:
                    try:
                        arg = args[i]
                    except IndexError:
                        continue

                    if self._has(arg, attrs, types):
                        args[i] = _apply(path, arg, func)

                if basic:
                    return expr.func(*args)
                else:
                    return expr.__class__(args)

        _args, _kwargs = args or (), kwargs or {}
        _func = lambda expr: func(expr, *_args, **_kwargs)

        return _apply(self._epath, expr, _func)

    def select(self, expr):
        """
        Retrieve parts of an expression selected by a path.

        Examples
        ========

        >>> from sympy.simplify.epathtools import EPath
        >>> from sympy import sin, cos, E
        >>> from sympy.abc import x, y, z, t

        >>> path = EPath("/*/[0]/Symbol")
        >>> expr = [((x, 1), 2), ((3, y), z)]

        >>> path.select(expr)
        [x, y]

        >>> path = EPath("/*/*/Symbol")
        >>> expr = t + sin(x + 1) + cos(x + y + E)

        >>> path.select(expr)
        [x, x, y]

        """
        result = []

        def _select(path, expr):
            if not path:
                result.append(expr)
            else:
                selector, path = path[0], path[1:]
                attrs, types, span = selector

                if isinstance(expr, Basic):
                    args = self._get_ordered_args(expr)
                elif hasattr(expr, '__iter__'):
                    args = expr
                else:
                    return

                if span is not None:
                    if type(span) == slice:
                        args = args[span]
                    else:
                        try:
                            args = [args[span]]
                        except IndexError:
                            return

                for arg in args:
                    if self._has(arg, attrs, types):
                        _select(path, arg)

        _select(self._epath, expr)
        return result

def epath(path, expr=None, func=None, args=None, kwargs=None):
    r"""
    Manipulate parts of an expression selected by a path.

    This function allows to manipulate large nested expressions in single
    line of code, utilizing techniques to those applied in XML processing
    standards (e.g. XPath).

    If ``func`` is ``None``, :func:`epath` retrieves elements selected by
    the ``path``. Otherwise it applies ``func`` to each matching element.

    Note that it is more efficient to create an EPath object and use the select
    and apply methods of that object, since this will compile the path string
    only once.  This function should only be used as a convenient shortcut for
    interactive use.

    This is the supported syntax:

    * select all: ``/*``
          Equivalent of ``for arg in args:``.
    * select slice: ``/[0]`` or ``/[1:5]`` or ``/[1:5:2]``
          Supports standard Python's slice syntax.
    * select by type: ``/list`` or ``/list|tuple``
          Emulates :func:`isinstance`.
    * select by attribute: ``/__iter__?``
          Emulates :func:`hasattr`.

    Parameters
    ==========

    path : str | EPath
        A path as a string or a compiled EPath.
    expr : Basic | iterable
        An expression or a container of expressions.
    func : callable (optional)
        A callable that will be applied to matching parts.
    args : tuple (optional)
        Additional positional arguments to ``func``.
    kwargs : dict (optional)
        Additional keyword arguments to ``func``.

    Examples
    ========

    >>> from sympy.simplify.epathtools import epath
    >>> from sympy import sin, cos, E
    >>> from sympy.abc import x, y, z, t

    >>> path = "/*/[0]/Symbol"
    >>> expr = [((x, 1), 2), ((3, y), z)]

    >>> epath(path, expr)
    [x, y]
    >>> epath(path, expr, lambda expr: expr**2)
    [((x**2, 1), 2), ((3, y**2), z)]

    >>> path = "/*/*/Symbol"
    >>> expr = t + sin(x + 1) + cos(x + y + E)

    >>> epath(path, expr)
    [x, x, y]
    >>> epath(path, expr, lambda expr: 2*expr)
    t + sin(2*x + 1) + cos(2*x + 2*y + E)

    """
    _epath = EPath(path)

    if expr is None:
        return _epath
    if func is None:
        return _epath.select(expr)
    else:
        return _epath.apply(expr, func, args, kwargs)