add redirection of __Cat__ to allow overrides for more advanced behaviour

[nmigen.git] / nmigen / hdl / ast.py

from abc import ABCMeta, abstractmethod
import warnings
import functools
from collections import OrderedDict
from collections.abc import Iterable, MutableMapping, MutableSet, MutableSequence
from enum import Enum
from itertools import chain

from .. import tracer
from .._utils import *
from .._unused import *


__all__ = [
    "Shape", "signed", "unsigned",
    "Value", "Const", "C", "AnyConst", "AnySeq", "Operator", "Mux", "Part", "Slice", "Cat", "Repl",
    "Array", "ArrayProxy",
    "_InternalSwitch", "_InternalAssign", "_InternalRepl", "_InternalCat",
    "Signal", "ClockSignal", "ResetSignal",
    "UserValue", "ValueCastable",
    "Sample", "Past", "Stable", "Rose", "Fell", "Initial",
    "Statement", "Switch",
    "Property", "Assign", "Assert", "Assume", "Cover",
    "ValueKey", "ValueDict", "ValueSet", "SignalKey", "SignalDict", "SignalSet",
]


class DUID:
    """Deterministic Unique IDentifier."""
    __next_uid = 0
    def __init__(self):
        self.duid = DUID.__next_uid
        DUID.__next_uid += 1


class Shape:
    """Bit width and signedness of a value.

    A ``Shape`` can be constructed using:
      * explicit bit width and signedness;
      * aliases :func:`signed` and :func:`unsigned`;
      * casting from a variety of objects.

    A ``Shape`` can be cast from:
      * an integer, where the integer specifies the bit width;
      * a range, where the result is wide enough to represent any element of the range, and is
        signed if any element of the range is signed;
      * an :class:`Enum` with all integer members or :class:`IntEnum`, where the result is wide
        enough to represent any member of the enumeration, and is signed if any member of
        the enumeration is signed.

    Parameters
    ----------
    width : int
        The number of bits in the representation, including the sign bit (if any).
    signed : bool
        If ``False``, the value is unsigned. If ``True``, the value is signed two's complement.
    """
    def __init__(self, width=1, signed=False):
        if not isinstance(width, int) or width < 0:
            raise TypeError("Width must be a non-negative integer, not {!r}"
                            .format(width))
        self.width = width
        self.signed = signed

    def __iter__(self):
        return iter((self.width, self.signed))

    @staticmethod
    def cast(obj, *, src_loc_at=0):
        if isinstance(obj, Shape):
            return obj
        if isinstance(obj, int):
            return Shape(obj)
        if isinstance(obj, tuple):
            width, signed = obj
            warnings.warn("instead of `{tuple}`, use `{constructor}({width})`"
                          .format(constructor="signed" if signed else "unsigned", width=width,
                                  tuple=obj),
                          DeprecationWarning, stacklevel=2 + src_loc_at)
            return Shape(width, signed)
        if isinstance(obj, range):
            if len(obj) == 0:
                return Shape(0, obj.start < 0)
            signed = obj.start < 0 or (obj.stop - obj.step) < 0
            width  = max(bits_for(obj.start, signed),
                         bits_for(obj.stop - obj.step, signed))
            return Shape(width, signed)
        if isinstance(obj, type) and issubclass(obj, Enum):
            min_value = min(member.value for member in obj)
            max_value = max(member.value for member in obj)
            if not isinstance(min_value, int) or not isinstance(max_value, int):
                raise TypeError("Only enumerations with integer values can be used "
                                "as value shapes")
            signed = min_value < 0 or max_value < 0
            width  = max(bits_for(min_value, signed), bits_for(max_value, signed))
            return Shape(width, signed)
        raise TypeError("Object {!r} cannot be used as value shape".format(obj))

    def __repr__(self):
        if self.signed:
            return "signed({})".format(self.width)
        else:
            return "unsigned({})".format(self.width)

    def __eq__(self, other):
        if isinstance(other, tuple) and len(other) == 2:
            width, signed = other
            if isinstance(width, int) and isinstance(signed, bool):
                return self.width == width and self.signed == signed
            else:
                raise TypeError("Shapes may be compared with other Shapes and (int, bool) tuples, "
                        "not {!r}"
                        .format(other))
        if not isinstance(other, Shape):
            raise TypeError("Shapes may be compared with other Shapes and (int, bool) tuples, "
                    "not {!r}"
                    .format(other))
        return self.width == other.width and self.signed == other.signed


def unsigned(width):
    """Shorthand for ``Shape(width, signed=False)``."""
    return Shape(width, signed=False)


def signed(width):
    """Shorthand for ``Shape(width, signed=True)``."""
    return Shape(width, signed=True)


class Value(metaclass=ABCMeta):
    @staticmethod
    def cast(obj):
        """Converts ``obj`` to an nMigen value.

        Booleans and integers are wrapped into a :class:`Const`. Enumerations whose members are
        all integers are converted to a :class:`Const` with a shape that fits every member.
        """
        if isinstance(obj, Value):
            return obj
        if isinstance(obj, int):
            return Const(obj)
        if isinstance(obj, Enum):
            return Const(obj.value, Shape.cast(type(obj)))
        if isinstance(obj, ValueCastable):
            return obj.as_value()
        raise TypeError("Object {!r} cannot be converted to an nMigen value".format(obj))

    def __init__(self, *, src_loc_at=0):
        super().__init__()
        self.src_loc = tracer.get_src_loc(1 + src_loc_at)

    def __Repl__(self, count, *, src_loc_at=0):
        return _InternalRepl(self, count, src_loc_at=src_loc_at)

    def __Cat__(self, *args, src_loc_at=0):
        args = [self] + list(args)
        return _InternalCat(*args, src_loc_at=src_loc_at)

    def __Mux__(self, val1, val0):
        return _InternalMux(self, val1, val0)

    def __Switch__(self, cases, *, src_loc=None, src_loc_at=0, case_src_locs={}):
        return _InternalSwitch(self, cases, src_loc=src_loc,
                               src_loc_at=src_loc_at,
                               case_src_locs=case_src_locs)

    def __Assign__(self, rhs, *, src_loc_at=0):
        return _InternalAssign(self, rhs, src_loc_at=src_loc_at)

    def __bool__(self):
        raise TypeError("Attempted to convert nMigen value to Python boolean")

    def __invert__(self):
        return Operator("~", [self])
    def __neg__(self):
        return Operator("-", [self])

    def __add__(self, other):
        return Operator("+", [self, other])
    def __radd__(self, other):
        return Operator("+", [other, self])
    def __sub__(self, other):
        return Operator("-", [self, other])
    def __rsub__(self, other):
        return Operator("-", [other, self])

    def __mul__(self, other):
        return Operator("*", [self, other])
    def __rmul__(self, other):
        return Operator("*", [other, self])

    def __check_divisor(self):
        width, signed = self.shape()
        if signed:
            # Python's division semantics and Verilog's division semantics differ for negative
            # divisors (Python uses div/mod, Verilog uses quo/rem); for now, avoid the issue
            # completely by prohibiting such division operations.
            raise NotImplementedError("Division by a signed value is not supported")
    def __mod__(self, other):
        other = Value.cast(other)
        other.__check_divisor()
        return Operator("%", [self, other])
    def __rmod__(self, other):
        self.__check_divisor()
        return Operator("%", [other, self])
    def __floordiv__(self, other):
        other = Value.cast(other)
        other.__check_divisor()
        return Operator("//", [self, other])
    def __rfloordiv__(self, other):
        self.__check_divisor()
        return Operator("//", [other, self])

    def __check_shamt(self):
        width, signed = self.shape()
        if signed:
            # Neither Python nor HDLs implement shifts by negative values; prohibit any shifts
            # by a signed value to make sure the shift amount can always be interpreted as
            # an unsigned value.
            raise TypeError("Shift amount must be unsigned")
    def __lshift__(self, other):
        other = Value.cast(other)
        other.__check_shamt()
        return Operator("<<", [self, other])
    def __rlshift__(self, other):
        self.__check_shamt()
        return Operator("<<", [other, self])
    def __rshift__(self, other):
        other = Value.cast(other)
        other.__check_shamt()
        return Operator(">>", [self, other])
    def __rrshift__(self, other):
        self.__check_shamt()
        return Operator(">>", [other, self])

    def __and__(self, other):
        return Operator("&", [self, other])
    def __rand__(self, other):
        return Operator("&", [other, self])
    def __xor__(self, other):
        return Operator("^", [self, other])
    def __rxor__(self, other):
        return Operator("^", [other, self])
    def __or__(self, other):
        return Operator("|", [self, other])
    def __ror__(self, other):
        return Operator("|", [other, self])

    def __eq__(self, other):
        return Operator("==", [self, other])
    def __ne__(self, other):
        return Operator("!=", [self, other])
    def __lt__(self, other):
        return Operator("<", [self, other])
    def __le__(self, other):
        return Operator("<=", [self, other])
    def __gt__(self, other):
        return Operator(">", [self, other])
    def __ge__(self, other):
        return Operator(">=", [self, other])

    def __abs__(self):
        width, signed = self.shape()
        if signed:
            return Mux(self >= 0, self, -self)
        else:
            return self

    def __len__(self):
        return self.shape().width

    def __getitem__(self, key):
        n = len(self)
        if isinstance(key, int):
            if key not in range(-n, n):
                raise IndexError(f"Index {key} is out of bounds for a {n}-bit value")
            if key < 0:
                key += n
            return Slice(self, key, key + 1)
        elif isinstance(key, slice):
            start, stop, step = key.indices(n)
            if step != 1:
                return Cat(self[i] for i in range(start, stop, step))
            return Slice(self, start, stop)
        else:
            raise TypeError("Cannot index value with {}".format(repr(key)))

    def as_unsigned(self):
        """Conversion to unsigned.

        Returns
        -------
        Value, out
            This ``Value`` reinterpreted as a unsigned integer.
        """
        return Operator("u", [self])

    def as_signed(self):
        """Conversion to signed.

        Returns
        -------
        Value, out
            This ``Value`` reinterpreted as a signed integer.
        """
        return Operator("s", [self])

    def bool(self):
        """Conversion to boolean.

        Returns
        -------
        Value, out
            ``1`` if any bits are set, ``0`` otherwise.
        """
        return Operator("b", [self])

    def any(self):
        """Check if any bits are ``1``.

        Returns
        -------
        Value, out
            ``1`` if any bits are set, ``0`` otherwise.
        """
        return Operator("r|", [self])

    def all(self):
        """Check if all bits are ``1``.

        Returns
        -------
        Value, out
            ``1`` if all bits are set, ``0`` otherwise.
        """
        return Operator("r&", [self])

    def xor(self):
        """Compute pairwise exclusive-or of every bit.

        Returns
        -------
        Value, out
            ``1`` if an odd number of bits are set, ``0`` if an even number of bits are set.
        """
        return Operator("r^", [self])

    def implies(premise, conclusion):
        """Implication.

        Returns
        -------
        Value, out
            ``0`` if ``premise`` is true and ``conclusion`` is not, ``1`` otherwise.
        """
        return ~premise | conclusion

    def bit_select(self, offset, width):
        """Part-select with bit granularity.

        Selects a constant width but variable offset part of a ``Value``, such that successive
        parts overlap by all but 1 bit.

        Parameters
        ----------
        offset : Value, int
            Index of first selected bit.
        width : int
            Number of selected bits.

        Returns
        -------
        Part, out
            Selected part of the ``Value``
        """
        offset = Value.cast(offset)
        if type(offset) is Const and isinstance(width, int):
            return self[offset.value:offset.value + width]
        return Part(self, offset, width, stride=1, src_loc_at=1)

    def word_select(self, offset, width):
        """Part-select with word granularity.

        Selects a constant width but variable offset part of a ``Value``, such that successive
        parts do not overlap.

        Parameters
        ----------
        offset : Value, int
            Index of first selected word.
        width : int
            Number of selected bits.

        Returns
        -------
        Part, out
            Selected part of the ``Value``
        """
        offset = Value.cast(offset)
        if type(offset) is Const and isinstance(width, int):
            return self[offset.value * width:(offset.value + 1) * width]
        return Part(self, offset, width, stride=width, src_loc_at=1)

    def matches(self, *patterns):
        """Pattern matching.

        Matches against a set of patterns, which may be integers or bit strings, recognizing
        the same grammar as ``Case()``.

        Parameters
        ----------
        patterns : int or str
            Patterns to match against.

        Returns
        -------
        Value, out
            ``1`` if any pattern matches the value, ``0`` otherwise.
        """
        matches = []
        for pattern in patterns:
            if not isinstance(pattern, (int, str, Enum)):
                raise SyntaxError("Match pattern must be an integer, a string, or an enumeration, "
                                  "not {!r}"
                                  .format(pattern))
            if isinstance(pattern, str) and any(bit not in "01- \t" for bit in pattern):
                raise SyntaxError("Match pattern '{}' must consist of 0, 1, and - (don't care) "
                                  "bits, and may include whitespace"
                                  .format(pattern))
            if (isinstance(pattern, str) and
                    len("".join(pattern.split())) != len(self)):
                raise SyntaxError("Match pattern '{}' must have the same width as match value "
                                  "(which is {})"
                                  .format(pattern, len(self)))
            if isinstance(pattern, int) and bits_for(pattern) > len(self):
                warnings.warn("Match pattern '{:b}' is wider than match value "
                              "(which has width {}); comparison will never be true"
                              .format(pattern, len(self)),
                              SyntaxWarning, stacklevel=3)
                continue
            if isinstance(pattern, str):
                pattern = "".join(pattern.split()) # remove whitespace
                mask    = int(pattern.replace("0", "1").replace("-", "0"), 2)
                pattern = int(pattern.replace("-", "0"), 2)
                matches.append((self & mask) == pattern)
            elif isinstance(pattern, int):
                matches.append(self == pattern)
            elif isinstance(pattern, Enum):
                matches.append(self == pattern.value)
            else:
                assert False
        if not matches:
            return Const(0)
        elif len(matches) == 1:
            return matches[0]
        else:
            return Cat(*matches).any()

    def shift_left(self, amount):
        """Shift left by constant amount.

        Parameters
        ----------
        amount : int
            Amount to shift by.

        Returns
        -------
        Value, out
            If the amount is positive, the input shifted left. Otherwise, the input shifted right.
        """
        if not isinstance(amount, int):
            raise TypeError("Shift amount must be an integer, not {!r}".format(amount))
        if amount < 0:
            return self.shift_right(-amount)
        if self.shape().signed:
            return Cat(Const(0, amount), self).as_signed()
        else:
            return Cat(Const(0, amount), self) # unsigned

    def shift_right(self, amount):
        """Shift right by constant amount.

        Parameters
        ----------
        amount : int
            Amount to shift by.

        Returns
        -------
        Value, out
            If the amount is positive, the input shifted right. Otherwise, the input shifted left.
        """
        if not isinstance(amount, int):
            raise TypeError("Shift amount must be an integer, not {!r}".format(amount))
        if amount < 0:
            return self.shift_left(-amount)
        if self.shape().signed:
            return self[amount:].as_signed()
        else:
            return self[amount:] # unsigned

    def rotate_left(self, amount):
        """Rotate left by constant amount.

        Parameters
        ----------
        amount : int
            Amount to rotate by.

        Returns
        -------
        Value, out
            If the amount is positive, the input rotated left. Otherwise, the input rotated right.
        """
        if not isinstance(amount, int):
            raise TypeError("Rotate amount must be an integer, not {!r}".format(amount))
        amount %= len(self)
        return Cat(self[-amount:], self[:-amount]) # meow :3

    def rotate_right(self, amount):
        """Rotate right by constant amount.

        Parameters
        ----------
        amount : int
            Amount to rotate by.

        Returns
        -------
        Value, out
            If the amount is positive, the input rotated right. Otherwise, the input rotated right.
        """
        if not isinstance(amount, int):
            raise TypeError("Rotate amount must be an integer, not {!r}".format(amount))
        amount %= len(self)
        return Cat(self[amount:], self[:amount])

    def eq(self, value):
        """Assignment.

        Parameters
        ----------
        value : Value, in
            Value to be assigned.

        Returns
        -------
        Assign
            Assignment statement that can be used in combinatorial or synchronous context.
        """
        return Assign(self, value, src_loc_at=1)

    @abstractmethod
    def shape(self):
        """Bit width and signedness of a value.

        Returns
        -------
        Shape
            See :class:`Shape`.

        Examples
        --------
        >>> Signal(8).shape()
        Shape(width=8, signed=False)
        >>> Const(0xaa).shape()
        Shape(width=8, signed=False)
        """
        pass # :nocov:

    def _lhs_signals(self):
        raise TypeError("Value {!r} cannot be used in assignments".format(self))

    @abstractmethod
    def _rhs_signals(self):
        pass # :nocov:

    def _as_const(self):
        raise TypeError("Value {!r} cannot be evaluated as constant".format(self))

    __hash__ = None


@final
class Const(Value):
    """A constant, literal integer value.

    Parameters
    ----------
    value : int
    shape : int or tuple or None
        Either an integer ``width`` or a tuple ``(width, signed)`` specifying the number of bits
        in this constant and whether it is signed (can represent negative values).
        ``shape`` defaults to the minimum possible width and signedness of ``value``.

    Attributes
    ----------
    width : int
    signed : bool
    """
    src_loc = None

    @staticmethod
    def normalize(value, shape):
        width, signed = shape
        mask = (1 << width) - 1
        value &= mask
        if signed and value >> (width - 1):
            value |= ~mask
        return value

    def __init__(self, value, shape=None, *, src_loc_at=0):
        # We deliberately do not call Value.__init__ here.
        self.value = int(value)
        if shape is None:
            shape = Shape(bits_for(self.value), signed=self.value < 0)
        elif isinstance(shape, int):
            shape = Shape(shape, signed=self.value < 0)
        else:
            shape = Shape.cast(shape, src_loc_at=1 + src_loc_at)
        self.width, self.signed = shape
        self.value = self.normalize(self.value, shape)

    def shape(self):
        return Shape(self.width, self.signed)

    def _rhs_signals(self):
        return SignalSet()

    def _as_const(self):
        return self.value

    def __repr__(self):
        return "(const {}'{}d{})".format(self.width, "s" if self.signed else "", self.value)


C = Const  # shorthand


class AnyValue(Value, DUID):
    def __init__(self, shape, *, src_loc_at=0):
        super().__init__(src_loc_at=src_loc_at)
        self.width, self.signed = Shape.cast(shape, src_loc_at=1 + src_loc_at)
        if not isinstance(self.width, int) or self.width < 0:
            raise TypeError("Width must be a non-negative integer, not {!r}"
                            .format(self.width))

    def shape(self):
        return Shape(self.width, self.signed)

    def _rhs_signals(self):
        return SignalSet()


@final
class AnyConst(AnyValue):
    def __repr__(self):
        return "(anyconst {}'{})".format(self.width, "s" if self.signed else "")


@final
class AnySeq(AnyValue):
    def __repr__(self):
        return "(anyseq {}'{})".format(self.width, "s" if self.signed else "")


@final
class Operator(Value):
    def __init__(self, operator, operands, *, src_loc_at=0):
        super().__init__(src_loc_at=1 + src_loc_at)
        self.operator = operator
        self.operands = [Value.cast(op) for op in operands]

    def shape(self):
        def _bitwise_binary_shape(a_shape, b_shape):
            a_bits, a_sign = a_shape
            b_bits, b_sign = b_shape
            if not a_sign and not b_sign:
                # both operands unsigned
                return Shape(max(a_bits, b_bits), False)
            elif a_sign and b_sign:
                # both operands signed
                return Shape(max(a_bits, b_bits), True)
            elif not a_sign and b_sign:
                # first operand unsigned (add sign bit), second operand signed
                return Shape(max(a_bits + 1, b_bits), True)
            else:
                # first signed, second operand unsigned (add sign bit)
                return Shape(max(a_bits, b_bits + 1), True)

        op_shapes = list(map(lambda x: x.shape(), self.operands))
        if len(op_shapes) == 1:
            (a_width, a_signed), = op_shapes
            if self.operator in ("+", "~"):
                return Shape(a_width, a_signed)
            if self.operator == "-":
                return Shape(a_width + 1, True)
            if self.operator in ("b", "r|", "r&", "r^"):
                return Shape(1, False)
            if self.operator == "u":
                return Shape(a_width, False)
            if self.operator == "s":
                return Shape(a_width, True)
        elif len(op_shapes) == 2:
            (a_width, a_signed), (b_width, b_signed) = op_shapes
            if self.operator in ("+", "-"):
                width, signed = _bitwise_binary_shape(*op_shapes)
                return Shape(width + 1, signed)
            if self.operator == "*":
                return Shape(a_width + b_width, a_signed or b_signed)
            if self.operator in ("//", "%"):
                assert not b_signed
                return Shape(a_width, a_signed)
            if self.operator in ("<", "<=", "==", "!=", ">", ">="):
                return Shape(1, False)
            if self.operator in ("&", "^", "|"):
                return _bitwise_binary_shape(*op_shapes)
            if self.operator == "<<":
                assert not b_signed
                return Shape(a_width + 2 ** b_width - 1, a_signed)
            if self.operator == ">>":
                assert not b_signed
                return Shape(a_width, a_signed)
        elif len(op_shapes) == 3:
            if self.operator == "m":
                s_shape, a_shape, b_shape = op_shapes
                return _bitwise_binary_shape(a_shape, b_shape)
        raise NotImplementedError("Operator {}/{} not implemented"
                                  .format(self.operator, len(op_shapes))) # :nocov:

    def _rhs_signals(self):
        return union(op._rhs_signals() for op in self.operands)

    def __repr__(self):
        return "({} {})".format(self.operator, " ".join(map(repr, self.operands)))


def Mux(sel, val1, val0):
    if isinstance(sel, bool): # one instance where Mux is passed an actual bool
        sel = Value.cast(sel)
    return sel.__Mux__(val1, val0)


def _InternalMux(sel, val1, val0):
    """Choose between two values.

    Parameters
    ----------
    sel : Value, in
        Selector.
    val1 : Value, in
    val0 : Value, in
        Input values.

    Returns
    -------
    Value, out
        Output ``Value``. If ``sel`` is asserted, the Mux returns ``val1``, else ``val0``.
    """
    sel = Value.cast(sel)
    if len(sel) != 1:
        sel = sel.bool()
    return Operator("m", [sel, val1, val0])


@final
class Slice(Value):
    def __init__(self, value, start, stop, *, src_loc_at=0):
        if not isinstance(start, int):
            raise TypeError("Slice start must be an integer, not {!r}".format(start))
        if not isinstance(stop, int):
            raise TypeError("Slice stop must be an integer, not {!r}".format(stop))

        n = len(value)
        if start not in range(-(n+1), n+1):
            raise IndexError("Cannot start slice {} bits into {}-bit value".format(start, n))
        if start < 0:
            start += n
        if stop not in range(-(n+1), n+1):
            raise IndexError("Cannot stop slice {} bits into {}-bit value".format(stop, n))
        if stop < 0:
            stop += n
        if start > stop:
            raise IndexError("Slice start {} must be less than slice stop {}".format(start, stop))

        super().__init__(src_loc_at=src_loc_at)
        self.value = Value.cast(value)
        self.start = int(start)
        self.stop  = int(stop)

    def shape(self):
        return Shape(self.stop - self.start)

    def _lhs_signals(self):
        return self.value._lhs_signals()

    def _rhs_signals(self):
        return self.value._rhs_signals()

    def __repr__(self):
        return "(slice {} {}:{})".format(repr(self.value), self.start, self.stop)


@final
class Part(Value):
    def __init__(self, value, offset, width, stride=1, *, src_loc_at=0):
        if not isinstance(width, int) or width < 0:
            raise TypeError("Part width must be a non-negative integer, not {!r}".format(width))
        if not isinstance(stride, int) or stride <= 0:
            raise TypeError("Part stride must be a positive integer, not {!r}".format(stride))

        super().__init__(src_loc_at=src_loc_at)
        self.value  = value
        self.offset = Value.cast(offset)
        self.width  = width
        self.stride = stride

    def shape(self):
        return Shape(self.width)

    def _lhs_signals(self):
        return self.value._lhs_signals()

    def _rhs_signals(self):
        return self.value._rhs_signals() | self.offset._rhs_signals()

    def __repr__(self):
        return "(part {} {} {} {})".format(repr(self.value), repr(self.offset),
                                           self.width, self.stride)


@final
def Cat(*args, src_loc_at=0):
    """Concatenate values.

    Behaviour is required to be identical to _InternalCat.
    The first argument "defines" the way that all others are
    handled.  If the first argument is derived from UserValue,
    it is not downcast to a type Value because doing so would
    lose the opportunity for "redirection" (Value.__Cat__ would
    always be called).
    """
    # flatten the args and convert to tuple (not a generator)
    args = tuple(flatten(args))
    # check if there are no arguments (zero-length Signal).
    if len(args) == 0:
        return _InternalCat(*args, src_loc_at=src_loc_at)
    # determine if the first is a UserValue.
    if isinstance(args[0], UserValue):
        first = args[0] # take UserValue directly, do not downcast
    else:
        first = Value.cast(args[0]) # ok to downcast to Value
    # all other arguments are safe to downcast to Value
    rest = [Value.cast(v) for v in flatten(args[1:])]
    # assume first item defines the "handling" for all others
    return first.__Cat__(*rest, src_loc_at=src_loc_at)


class _InternalCat(Value):
    """Concatenate values.

    Form a compound ``Value`` from several smaller ones by concatenation.
    The first argument occupies the lower bits of the result.
    The return value can be used on either side of an assignment, that
    is, the concatenated value can be used as an argument on the RHS or
    as a target on the LHS. If it is used on the LHS, it must solely
    consist of ``Signal`` s, slices of ``Signal`` s, and other concatenations
    meeting these properties. The bit length of the return value is the sum of
    the bit lengths of the arguments::

        len(Cat(args)) == sum(len(arg) for arg in args)

    Parameters
    ----------
    *args : Values or iterables of Values, inout
        ``Value`` s to be concatenated.

    Returns
    -------
    Value, inout
        Resulting ``Value`` obtained by concatentation.
    """
    def __init__(self, *args, src_loc_at=0):
        super().__init__(src_loc_at=src_loc_at)
        self.parts = [Value.cast(v) for v in flatten(args)]

    def shape(self):
        return Shape(sum(len(part) for part in self.parts))

    def _lhs_signals(self):
        return union((part._lhs_signals() for part in self.parts), start=SignalSet())

    def _rhs_signals(self):
        return union((part._rhs_signals() for part in self.parts), start=SignalSet())

    def _as_const(self):
        value = 0
        for part in reversed(self.parts):
            value <<= len(part)
            value |= part._as_const()
        return value

    def __repr__(self):
        return "(cat {})".format(" ".join(map(repr, self.parts)))


@final
def Repl(value, count, *, src_loc_at=0):
    return value.__Repl__(count, src_loc_at=src_loc_at)


class _InternalRepl(Value):
    """Replicate a value

    An input value is replicated (repeated) several times
    to be used on the RHS of assignments::

        len(Repl(s, n)) == len(s) * n

    Parameters
    ----------
    value : Value, in
        Input value to be replicated.
    count : int
        Number of replications.

    Returns
    -------
    Repl, out
        Replicated value.
    """
    def __init__(self, value, count, *, src_loc_at=0):
        if not isinstance(count, int) or count < 0:
            raise TypeError("Replication count must be a non-negative integer, not {!r}"
                            .format(count))

        super().__init__(src_loc_at=src_loc_at)
        self.value = Value.cast(value)
        self.count = count

    def shape(self):
        return Shape(len(self.value) * self.count)

    def _rhs_signals(self):
        return self.value._rhs_signals()

    def __repr__(self):
        return "(repl {!r} {})".format(self.value, self.count)


# @final
class Signal(Value, DUID):
    """A varying integer value.

    Parameters
    ----------
    shape : ``Shape``-castable object or None
        Specification for the number of bits in this ``Signal`` and its signedness (whether it
        can represent negative values). See ``Shape.cast`` for details.
        If not specified, ``shape`` defaults to 1-bit and non-signed.
    name : str
        Name hint for this signal. If ``None`` (default) the name is inferred from the variable
        name this ``Signal`` is assigned to.
    reset : int or integral Enum
        Reset (synchronous) or default (combinatorial) value.
        When this ``Signal`` is assigned to in synchronous context and the corresponding clock
        domain is reset, the ``Signal`` assumes the given value. When this ``Signal`` is unassigned
        in combinatorial context (due to conditional assignments not being taken), the ``Signal``
        assumes its ``reset`` value. Defaults to 0.
    reset_less : bool
        If ``True``, do not generate reset logic for this ``Signal`` in synchronous statements.
        The ``reset`` value is only used as a combinatorial default or as the initial value.
        Defaults to ``False``.
    attrs : dict
        Dictionary of synthesis attributes.
    decoder : function or Enum
        A function converting integer signal values to human-readable strings (e.g. FSM state
        names). If an ``Enum`` subclass is passed, it is concisely decoded using format string
        ``"{0.name:}/{0.value:}"``, or a number if the signal value is not a member of
        the enumeration.

    Attributes
    ----------
    width : int
    signed : bool
    name : str
    reset : int
    reset_less : bool
    attrs : dict
    decoder : function
    """

    def __init__(self, shape=None, *, name=None, reset=0, reset_less=False,
                 attrs=None, decoder=None, src_loc_at=0):
        super().__init__(src_loc_at=src_loc_at)

        if name is not None and not isinstance(name, str):
            raise TypeError("Name must be a string, not {!r}".format(name))
        self.name = name or tracer.get_var_name(depth=2 + src_loc_at, default="$signal")

        if shape is None:
            shape = unsigned(1)
        self.width, self.signed = Shape.cast(shape, src_loc_at=1 + src_loc_at)

        if isinstance(reset, Enum):
            reset = reset.value
        if not isinstance(reset, int):
            raise TypeError("Reset value has to be an int or an integral Enum")

        reset_width = bits_for(reset, self.signed)
        if reset != 0 and reset_width > self.width:
            warnings.warn("Reset value {!r} requires {} bits to represent, but the signal "
                          "only has {} bits"
                          .format(reset, reset_width, self.width),
                          SyntaxWarning, stacklevel=2 + src_loc_at)

        self.reset = reset
        self.reset_less = bool(reset_less)

        self.attrs = OrderedDict(() if attrs is None else attrs)

        if decoder is None and isinstance(shape, type) and issubclass(shape, Enum):
            decoder = shape
        if isinstance(decoder, type) and issubclass(decoder, Enum):
            def enum_decoder(value):
                try:
                    return "{0.name:}/{0.value:}".format(decoder(value))
                except ValueError:
                    return str(value)
            self.decoder = enum_decoder
            self._enum_class = decoder
        else:
            self.decoder = decoder
            self._enum_class = None

    # Not a @classmethod because nmigen.compat requires it.
    @staticmethod
    def like(other, *, name=None, name_suffix=None, src_loc_at=0, **kwargs):
        """Create Signal based on another.

        Parameters
        ----------
        other : Value
            Object to base this Signal on.
        """
        if name is not None:
            new_name = str(name)
        elif name_suffix is not None:
            new_name = other.name + str(name_suffix)
        else:
            new_name = tracer.get_var_name(depth=2 + src_loc_at, default="$like")
        kw = dict(shape=Value.cast(other).shape(), name=new_name)
        if isinstance(other, Signal):
            kw.update(reset=other.reset, reset_less=other.reset_less,
                      attrs=other.attrs, decoder=other.decoder)
        kw.update(kwargs)
        return Signal(**kw, src_loc_at=1 + src_loc_at)

    def shape(self):
        return Shape(self.width, self.signed)

    def _lhs_signals(self):
        return SignalSet((self,))

    def _rhs_signals(self):
        return SignalSet((self,))

    def __repr__(self):
        return "(sig {})".format(self.name)


@final
class ClockSignal(Value):
    """Clock signal for a clock domain.

    Any ``ClockSignal`` is equivalent to ``cd.clk`` for a clock domain with the corresponding name.
    All of these signals ultimately refer to the same signal, but they can be manipulated
    independently of the clock domain, even before the clock domain is created.

    Parameters
    ----------
    domain : str
        Clock domain to obtain a clock signal for. Defaults to ``"sync"``.
    """
    def __init__(self, domain="sync", *, src_loc_at=0):
        super().__init__(src_loc_at=src_loc_at)
        if not isinstance(domain, str):
            raise TypeError("Clock domain name must be a string, not {!r}".format(domain))
        if domain == "comb":
            raise ValueError("Domain '{}' does not have a clock".format(domain))
        self.domain = domain

    def shape(self):
        return Shape(1)

    def _lhs_signals(self):
        return SignalSet((self,))

    def _rhs_signals(self):
        raise NotImplementedError("ClockSignal must be lowered to a concrete signal") # :nocov:

    def __repr__(self):
        return "(clk {})".format(self.domain)


@final
class ResetSignal(Value):
    """Reset signal for a clock domain.

    Any ``ResetSignal`` is equivalent to ``cd.rst`` for a clock domain with the corresponding name.
    All of these signals ultimately refer to the same signal, but they can be manipulated
    independently of the clock domain, even before the clock domain is created.

    Parameters
    ----------
    domain : str
        Clock domain to obtain a reset signal for. Defaults to ``"sync"``.
    allow_reset_less : bool
        If the clock domain is reset-less, act as a constant ``0`` instead of reporting an error.
    """
    def __init__(self, domain="sync", allow_reset_less=False, *, src_loc_at=0):
        super().__init__(src_loc_at=src_loc_at)
        if not isinstance(domain, str):
            raise TypeError("Clock domain name must be a string, not {!r}".format(domain))
        if domain == "comb":
            raise ValueError("Domain '{}' does not have a reset".format(domain))
        self.domain = domain
        self.allow_reset_less = allow_reset_less

    def shape(self):
        return Shape(1)

    def _lhs_signals(self):
        return SignalSet((self,))

    def _rhs_signals(self):
        raise NotImplementedError("ResetSignal must be lowered to a concrete signal") # :nocov:

    def __repr__(self):
        return "(rst {})".format(self.domain)


class Array(MutableSequence):
    """Addressable multiplexer.

    An array is similar to a ``list`` that can also be indexed by ``Value``s; indexing by an integer or a slice works the same as for Python lists, but indexing by a ``Value`` results
    in a proxy.

    The array proxy can be used as an ordinary ``Value``, i.e. participate in calculations and
    assignments, provided that all elements of the array are values. The array proxy also supports
    attribute access and further indexing, each returning another array proxy; this means that
    the results of indexing into arrays, arrays of records, and arrays of arrays can all
    be used as first-class values.

    It is an error to change an array or any of its elements after an array proxy was created.
    Changing the array directly will raise an exception. However, it is not possible to detect
    the elements being modified; if an element's attribute or element is modified after the proxy
    for it has been created, the proxy will refer to stale data.

    Examples
    --------

    Simple array::

        gpios = Array(Signal() for _ in range(10))
        with m.If(bus.we):
            m.d.sync += gpios[bus.addr].eq(bus.w_data)
        with m.Else():
            m.d.sync += bus.r_data.eq(gpios[bus.addr])

    Multidimensional array::

        mult = Array(Array(x * y for y in range(10)) for x in range(10))
        a = Signal.range(10)
        b = Signal.range(10)
        r = Signal(8)
        m.d.comb += r.eq(mult[a][b])

    Array of records::

        layout = [
            ("r_data", 16),
            ("r_en",   1),
        ]
        buses  = Array(Record(layout) for busno in range(4))
        master = Record(layout)
        m.d.comb += [
            buses[sel].r_en.eq(master.r_en),
            master.r_data.eq(buses[sel].r_data),
        ]
    """
    def __init__(self, iterable=()):
        self._inner    = list(iterable)
        self._proxy_at = None
        self._mutable  = True

    def __getitem__(self, index):
        if isinstance(index, Value):
            if self._mutable:
                self._proxy_at = tracer.get_src_loc()
                self._mutable  = False
            return ArrayProxy(self, index)
        else:
            return self._inner[index]

    def __len__(self):
        return len(self._inner)

    def _check_mutability(self):
        if not self._mutable:
            raise ValueError("Array can no longer be mutated after it was indexed with a value "
                             "at {}:{}".format(*self._proxy_at))

    def __setitem__(self, index, value):
        self._check_mutability()
        self._inner[index] = value

    def __delitem__(self, index):
        self._check_mutability()
        del self._inner[index]

    def insert(self, index, value):
        self._check_mutability()
        self._inner.insert(index, value)

    def __repr__(self):
        return "(array{} [{}])".format(" mutable" if self._mutable else "",
                                       ", ".join(map(repr, self._inner)))


@final
class ArrayProxy(Value):
    def __init__(self, elems, index, *, src_loc_at=0):
        super().__init__(src_loc_at=1 + src_loc_at)
        self.elems = elems
        self.index = Value.cast(index)

    def __getattr__(self, attr):
        return ArrayProxy([getattr(elem, attr) for elem in self.elems], self.index)

    def __getitem__(self, index):
        return ArrayProxy([        elem[index] for elem in self.elems], self.index)

    def _iter_as_values(self):
        return (Value.cast(elem) for elem in self.elems)

    def shape(self):
        unsigned_width = signed_width = 0
        has_unsigned = has_signed = False
        for elem_width, elem_signed in (elem.shape() for elem in self._iter_as_values()):
            if elem_signed:
                has_signed = True
                signed_width = max(signed_width, elem_width)
            else:
                has_unsigned = True
                unsigned_width = max(unsigned_width, elem_width)
        # The shape of the proxy must be such that it preserves the mathematical value of the array
        # elements. I.e., shape-wise, an array proxy must be identical to an equivalent mux tree.
        # To ensure this holds, if the array contains both signed and unsigned values, make sure
        # that every unsigned value is zero-extended by at least one bit.
        if has_signed and has_unsigned and unsigned_width >= signed_width:
            # Array contains both signed and unsigned values, and at least one of the unsigned
            # values won't be zero-extended otherwise.
            return signed(unsigned_width + 1)
        else:
            # Array contains values of the same signedness, or else all of the unsigned values
            # are zero-extended.
            return Shape(max(unsigned_width, signed_width), has_signed)

    def _lhs_signals(self):
        signals = union((elem._lhs_signals() for elem in self._iter_as_values()),
                        start=SignalSet())
        return signals

    def _rhs_signals(self):
        signals = union((elem._rhs_signals() for elem in self._iter_as_values()),
                        start=SignalSet())
        return self.index._rhs_signals() | signals

    def __repr__(self):
        return "(proxy (array [{}]) {!r})".format(", ".join(map(repr, self.elems)), self.index)


# TODO(nmigen-0.4): remove
class UserValue(Value):
    """Value with custom lowering.

    A ``UserValue`` is a value whose precise representation does not have to be immediately known,
    which is useful in certain metaprogramming scenarios. Instead of providing fixed semantics
    upfront, it is kept abstract for as long as possible, only being lowered to a concrete nMigen
    value when required.

    Note that the ``lower`` method will only be called once; this is necessary to ensure that
    nMigen's view of representation of all values stays internally consistent. If the class
    deriving from  ``UserValue`` is mutable, then it must ensure that after ``lower`` is called,
    it is not mutated in a way that changes its representation.

    The following is an incomplete list of actions that, when applied to an ``UserValue`` directly
    or indirectly, will cause it to be lowered, provided as an illustrative reference:
        * Querying the shape using ``.shape()`` or ``len()``;
        * Creating a similarly shaped signal using ``Signal.like``;
        * Indexing or iterating through individual bits;
        * Adding an assignment to the value to a ``Module`` using ``m.d.<domain> +=``.
    """
    @deprecated("instead of `UserValue`, use `ValueCastable`", stacklevel=3)
    def __init__(self, *, src_loc_at=0):
        super().__init__(src_loc_at=1 + src_loc_at)
        self.__lowered = None

    @abstractmethod
    def lower(self):
        """Conversion to a concrete representation."""
        pass # :nocov:

    def _lazy_lower(self):
        if self.__lowered is None:
            lowered = self.lower()
            if isinstance(lowered, UserValue):
                lowered = lowered._lazy_lower()
            self.__lowered = Value.cast(lowered)
        return self.__lowered

    def shape(self):
        return self._lazy_lower().shape()

    def _lhs_signals(self):
        return self._lazy_lower()._lhs_signals()

    def _rhs_signals(self):
        return self._lazy_lower()._rhs_signals()


class ValueCastable:
    """Base class for classes which can be cast to Values.

    A ``ValueCastable`` can be cast to ``Value``, meaning its precise representation does not have
    to be immediately known. This is useful in certain metaprogramming scenarios. Instead of
    providing fixed semantics upfront, it is kept abstract for as long as possible, only being
    cast to a concrete nMigen value when required.

    Note that it is necessary to ensure that nMigen's view of representation of all values stays
    internally consistent. The class deriving from ``ValueCastable`` must decorate the ``as_value``
    method with the ``lowermethod`` decorator, which ensures that all calls to ``as_value`` return
    the same ``Value`` representation. If the class deriving from ``ValueCastable`` is mutable,
    it is up to the user to ensure that it is not mutated in a way that changes its representation
    after the first call to ``as_value``.
    """
    def __new__(cls, *args, **kwargs):
        self = super().__new__(cls)
        if not hasattr(self, "as_value"):
            raise TypeError(f"Class '{cls.__name__}' deriving from `ValueCastable` must override "
                            "the `as_value` method")

        if not hasattr(self.as_value, "_ValueCastable__memoized"):
            raise TypeError(f"Class '{cls.__name__}' deriving from `ValueCastable` must decorate "
                            "the `as_value` method with the `ValueCastable.lowermethod` decorator")
        return self

    @staticmethod
    def lowermethod(func):
        """Decorator to memoize lowering methods.

        Ensures the decorated method is called only once, with subsequent method calls returning the
        object returned by the first first method call.

        This decorator is required to decorate the ``as_value`` method of ``ValueCastable`` subclasses.
        This is to ensure that nMigen's view of representation of all values stays internally
        consistent.
        """
        @functools.wraps(func)
        def wrapper_memoized(self, *args, **kwargs):
            if not hasattr(self, "_ValueCastable__lowered_to"):
                self.__lowered_to = func(self, *args, **kwargs)
            return self.__lowered_to
        wrapper_memoized.__memoized = True
        return wrapper_memoized


@final
class Sample(Value):
    """Value from the past.

    A ``Sample`` of an expression is equal to the value of the expression ``clocks`` clock edges
    of the ``domain`` clock back. If that moment is before the beginning of time, it is equal
    to the value of the expression calculated as if each signal had its reset value.
    """
    def __init__(self, expr, clocks, domain, *, src_loc_at=0):
        super().__init__(src_loc_at=1 + src_loc_at)
        self.value  = Value.cast(expr)
        self.clocks = int(clocks)
        self.domain = domain
        if not isinstance(self.value, (Const, Signal, ClockSignal, ResetSignal, Initial)):
            raise TypeError("Sampled value must be a signal or a constant, not {!r}"
                            .format(self.value))
        if self.clocks < 0:
            raise ValueError("Cannot sample a value {} cycles in the future"
                             .format(-self.clocks))
        if not (self.domain is None or isinstance(self.domain, str)):
            raise TypeError("Domain name must be a string or None, not {!r}"
                            .format(self.domain))

    def shape(self):
        return self.value.shape()

    def _rhs_signals(self):
        return SignalSet((self,))

    def __repr__(self):
        return "(sample {!r} @ {}[{}])".format(
            self.value, "<default>" if self.domain is None else self.domain, self.clocks)


def Past(expr, clocks=1, domain=None):
    return Sample(expr, clocks, domain)


def Stable(expr, clocks=0, domain=None):
    return Sample(expr, clocks + 1, domain) == Sample(expr, clocks, domain)


def Rose(expr, clocks=0, domain=None):
    return ~Sample(expr, clocks + 1, domain) & Sample(expr, clocks, domain)


def Fell(expr, clocks=0, domain=None):
    return Sample(expr, clocks + 1, domain) & ~Sample(expr, clocks, domain)


@final
class Initial(Value):
    """Start indicator, for model checking.

    An ``Initial`` signal is ``1`` at the first cycle of model checking, and ``0`` at any other.
    """
    def __init__(self, *, src_loc_at=0):
        super().__init__(src_loc_at=src_loc_at)

    def shape(self):
        return Shape(1)

    def _rhs_signals(self):
        return SignalSet((self,))

    def __repr__(self):
        return "(initial)"


class _StatementList(list):
    def __repr__(self):
        return "({})".format(" ".join(map(repr, self)))


class Statement:
    def __init__(self, *, src_loc_at=0):
        self.src_loc = tracer.get_src_loc(1 + src_loc_at)

    @staticmethod
    def cast(obj):
        if isinstance(obj, Iterable):
            return _StatementList(list(chain.from_iterable(map(Statement.cast, obj))))
        else:
            if isinstance(obj, Statement):
                return _StatementList([obj])
            else:
                raise TypeError("Object {!r} is not an nMigen statement".format(obj))


@final
def Assign(lhs, rhs, *, src_loc_at=0):
    return lhs.__Assign__(rhs, src_loc_at=src_loc_at)


class _InternalAssign(Statement):
    def __init__(self, lhs, rhs, *, src_loc_at=0):
        super().__init__(src_loc_at=src_loc_at)
        self.lhs = Value.cast(lhs)
        self.rhs = Value.cast(rhs)

    def _lhs_signals(self):
        return self.lhs._lhs_signals()

    def _rhs_signals(self):
        return self.lhs._rhs_signals() | self.rhs._rhs_signals()

    def __repr__(self):
        return "(eq {!r} {!r})".format(self.lhs, self.rhs)


class UnusedProperty(UnusedMustUse):
    pass


class Property(Statement, MustUse):
    _MustUse__warning = UnusedProperty

    def __init__(self, test, *, _check=None, _en=None, src_loc_at=0):
        super().__init__(src_loc_at=src_loc_at)
        self.test   = Value.cast(test)
        self._check = _check
        self._en    = _en
        if self._check is None:
            self._check = Signal(reset_less=True, name="${}$check".format(self._kind))
            self._check.src_loc = self.src_loc
        if _en is None:
            self._en = Signal(reset_less=True, name="${}$en".format(self._kind))
            self._en.src_loc = self.src_loc

    def _lhs_signals(self):
        return SignalSet((self._en, self._check))

    def _rhs_signals(self):
        return self.test._rhs_signals()

    def __repr__(self):
        return "({} {!r})".format(self._kind, self.test)


@final
class Assert(Property):
    _kind = "assert"


@final
class Assume(Property):
    _kind = "assume"


@final
class Cover(Property):
    _kind = "cover"


# @final
def Switch(test, cases, *, src_loc=None, src_loc_at=0, case_src_locs={}):
    return test.__Switch__(cases, src_loc=src_loc, src_loc_at=src_loc_at,
                           case_src_locs=case_src_locs)


class _InternalSwitch(Statement):
    def __init__(self, test, cases, *, src_loc=None, src_loc_at=0, case_src_locs={}):
        if src_loc is None:
            super().__init__(src_loc_at=src_loc_at)
        else:
            # Switch is a bit special in terms of location tracking because it is usually created
            # long after the control has left the statement that directly caused its creation.
            self.src_loc = src_loc
        # Switch is also a bit special in that its parts also have location information. It can't
        # be automatically traced, so whatever constructs a Switch may optionally provide it.
        self.case_src_locs = {}

        self.test  = Value.cast(test)
        self.cases = OrderedDict()
        for orig_keys, stmts in cases.items():
            # Map: None -> (); key -> (key,); (key...) -> (key...)
            keys = orig_keys
            if keys is None:
                keys = ()
            if not isinstance(keys, tuple):
                keys = (keys,)
            # Map: 2 -> "0010"; "0010" -> "0010"
            new_keys = ()
            key_mask = (1 << len(self.test)) - 1
            for key in keys:
                if isinstance(key, str):
                    key = "".join(key.split()) # remove whitespace
                elif isinstance(key, int):
                    key = format(key & key_mask, "b").rjust(len(self.test), "0")
                elif isinstance(key, Enum):
                    key = format(key.value & key_mask, "b").rjust(len(self.test), "0")
                else:
                    raise TypeError("Object {!r} cannot be used as a switch key"
                                    .format(key))
                assert len(key) == len(self.test)
                new_keys = (*new_keys, key)
            if not isinstance(stmts, Iterable):
                stmts = [stmts]
            self.cases[new_keys] = Statement.cast(stmts)
            if orig_keys in case_src_locs:
                self.case_src_locs[new_keys] = case_src_locs[orig_keys]

    def _lhs_signals(self):
        signals = union((s._lhs_signals() for ss in self.cases.values() for s in ss),
                        start=SignalSet())
        return signals

    def _rhs_signals(self):
        signals = union((s._rhs_signals() for ss in self.cases.values() for s in ss),
                        start=SignalSet())
        return self.test._rhs_signals() | signals

    def __repr__(self):
        def case_repr(keys, stmts):
            stmts_repr = " ".join(map(repr, stmts))
            if keys == ():
                return "(default {})".format(stmts_repr)
            elif len(keys) == 1:
                return "(case {} {})".format(keys[0], stmts_repr)
            else:
                return "(case ({}) {})".format(" ".join(keys), stmts_repr)
        case_reprs = [case_repr(keys, stmts) for keys, stmts in self.cases.items()]
        return "(switch {!r} {})".format(self.test, " ".join(case_reprs))


class _MappedKeyCollection(metaclass=ABCMeta):
    @abstractmethod
    def _map_key(self, key):
        pass # :nocov:

    @abstractmethod
    def _unmap_key(self, key):
        pass # :nocov:


class _MappedKeyDict(MutableMapping, _MappedKeyCollection):
    def __init__(self, pairs=()):
        self._storage = OrderedDict()
        for key, value in pairs:
            self[key] = value

    def __getitem__(self, key):
        key = None if key is None else self._map_key(key)
        return self._storage[key]

    def __setitem__(self, key, value):
        key = None if key is None else self._map_key(key)
        self._storage[key] = value

    def __delitem__(self, key):
        key = None if key is None else self._map_key(key)
        del self._storage[key]

    def __iter__(self):
        for key in self._storage:
            if key is None:
                yield None
            else:
                yield self._unmap_key(key)

    def __eq__(self, other):
        if not isinstance(other, type(self)):
            return False
        if len(self) != len(other):
            return False
        for ak, bk in zip(sorted(self._storage), sorted(other._storage)):
            if ak != bk:
                return False
            if self._storage[ak] != other._storage[bk]:
                return False
        return True

    def __len__(self):
        return len(self._storage)

    def __repr__(self):
        pairs = ["({!r}, {!r})".format(k, v) for k, v in self.items()]
        return "{}.{}([{}])".format(type(self).__module__, type(self).__name__,
                                    ", ".join(pairs))


class _MappedKeySet(MutableSet, _MappedKeyCollection):
    def __init__(self, elements=()):
        self._storage = OrderedDict()
        for elem in elements:
            self.add(elem)

    def add(self, value):
        self._storage[self._map_key(value)] = None

    def update(self, values):
        for value in values:
            self.add(value)

    def discard(self, value):
        if value in self:
            del self._storage[self._map_key(value)]

    def __contains__(self, value):
        return self._map_key(value) in self._storage

    def __iter__(self):
        for key in [k for k in self._storage]:
            yield self._unmap_key(key)

    def __len__(self):
        return len(self._storage)

    def __repr__(self):
        return "{}.{}({})".format(type(self).__module__, type(self).__name__,
                                  ", ".join(repr(x) for x in self))


class ValueKey:
    def __init__(self, value):
        self.value = Value.cast(value)
        if isinstance(self.value, Const):
            self._hash = hash(self.value.value)
        elif isinstance(self.value, (Signal, AnyValue)):
            self._hash = hash(self.value.duid)
        elif isinstance(self.value, (ClockSignal, ResetSignal)):
            self._hash = hash(self.value.domain)
        elif isinstance(self.value, Operator):
            self._hash = hash((self.value.operator,
                               tuple(ValueKey(o) for o in self.value.operands)))
        elif isinstance(self.value, Slice):
            self._hash = hash((ValueKey(self.value.value), self.value.start, self.value.stop))
        elif isinstance(self.value, Part):
            self._hash = hash((ValueKey(self.value.value), ValueKey(self.value.offset),
                              self.value.width, self.value.stride))
        elif isinstance(self.value, _InternalCat):
            self._hash = hash(tuple(ValueKey(o) for o in self.value.parts))
        elif isinstance(self.value, ArrayProxy):
            self._hash = hash((ValueKey(self.value.index),
                              tuple(ValueKey(e) for e in self.value._iter_as_values())))
        elif isinstance(self.value, Sample):
            self._hash = hash((ValueKey(self.value.value), self.value.clocks, self.value.domain))
        elif isinstance(self.value, Initial):
            self._hash = 0
        else: # :nocov:
            raise TypeError("Object {!r} cannot be used as a key in value collections"
                            .format(self.value))

    def __hash__(self):
        return self._hash

    def __eq__(self, other):
        if type(other) is not ValueKey:
            return False
        if type(self.value) is not type(other.value):
            return False

        if isinstance(self.value, Const):
            return self.value.value == other.value.value
        elif isinstance(self.value, (Signal, AnyValue)):
            return self.value is other.value
        elif isinstance(self.value, (ClockSignal, ResetSignal)):
            return self.value.domain == other.value.domain
        elif isinstance(self.value, Operator):
            return (self.value.operator == other.value.operator and
                    len(self.value.operands) == len(other.value.operands) and
                    all(ValueKey(a) == ValueKey(b)
                        for a, b in zip(self.value.operands, other.value.operands)))
        elif isinstance(self.value, Slice):
            return (ValueKey(self.value.value) == ValueKey(other.value.value) and
                    self.value.start == other.value.start and
                    self.value.stop == other.value.stop)
        elif isinstance(self.value, Part):
            return (ValueKey(self.value.value) == ValueKey(other.value.value) and
                    ValueKey(self.value.offset) == ValueKey(other.value.offset) and
                    self.value.width == other.value.width and
                    self.value.stride == other.value.stride)
        elif isinstance(self.value, _InternalCat):
            return all(ValueKey(a) == ValueKey(b)
                        for a, b in zip(self.value.parts, other.value.parts))
        elif isinstance(self.value, ArrayProxy):
            return (ValueKey(self.value.index) == ValueKey(other.value.index) and
                    len(self.value.elems) == len(other.value.elems) and
                    all(ValueKey(a) == ValueKey(b)
                        for a, b in zip(self.value._iter_as_values(),
                                        other.value._iter_as_values())))
        elif isinstance(self.value, Sample):
            return (ValueKey(self.value.value) == ValueKey(other.value.value) and
                    self.value.clocks == other.value.clocks and
                    self.value.domain == self.value.domain)
        elif isinstance(self.value, Initial):
            return True
        else: # :nocov:
            raise TypeError("Object {!r} cannot be used as a key in value collections"
                            .format(self.value))

    def __lt__(self, other):
        if not isinstance(other, ValueKey):
            return False
        if type(self.value) != type(other.value):
            return False

        if isinstance(self.value, Const):
            return self.value < other.value
        elif isinstance(self.value, (Signal, AnyValue)):
            return self.value.duid < other.value.duid
        elif isinstance(self.value, Slice):
            return (ValueKey(self.value.value) < ValueKey(other.value.value) and
                    self.value.start < other.value.start and
                    self.value.end < other.value.end)
        else: # :nocov:
            raise TypeError("Object {!r} cannot be used as a key in value collections")

    def __repr__(self):
        return "<{}.ValueKey {!r}>".format(__name__, self.value)


class ValueDict(_MappedKeyDict):
    _map_key   = ValueKey
    _unmap_key = lambda self, key: key.value


class ValueSet(_MappedKeySet):
    _map_key   = ValueKey
    _unmap_key = lambda self, key: key.value


class SignalKey:
    def __init__(self, signal):
        self.signal = signal
        if isinstance(signal, Signal):
            self._intern = (0, signal.duid)
        elif type(signal) is ClockSignal:
            self._intern = (1, signal.domain)
        elif type(signal) is ResetSignal:
            self._intern = (2, signal.domain)
        else:
            raise TypeError("Object {!r} is not an nMigen signal".format(signal))

    def __hash__(self):
        return hash(self._intern)

    def __eq__(self, other):
        if type(other) is not SignalKey:
            return False
        return self._intern == other._intern

    def __lt__(self, other):
        if type(other) is not SignalKey:
            raise TypeError("Object {!r} cannot be compared to a SignalKey".format(signal))
        return self._intern < other._intern

    def __repr__(self):
        return "<{}.SignalKey {!r}>".format(__name__, self.signal)


class SignalDict(_MappedKeyDict):
    _map_key   = SignalKey
    _unmap_key = lambda self, key: key.signal


class SignalSet(_MappedKeySet):
    _map_key   = SignalKey
    _unmap_key = lambda self, key: key.signal