# Copyright (c) 2013 VMware, Inc. All rights reserved.
#
#    Licensed under the Apache License, Version 2.0 (the "License"); you may
#    not use this file except in compliance with the License. You may obtain
#    a copy of the License at
#
#         http://www.apache.org/licenses/LICENSE-2.0
#
#    Unless required by applicable law or agreed to in writing, software
#    distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
#    WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
#    License for the specific language governing permissions and limitations
#    under the License.
#

import uuid

import compile
from oslo_log import log as logging

LOG = logging.getLogger(__name__)


# A unifier designed for the bi_unify_atoms routine
# which is used by a backward-chaining style datalog implementation.
# Main goal: minimize memory allocation by manipulating only unifiers
#   to keep variable namespaces separate.

class BiUnifier(object):
    """A unifier designed for bi_unify_atoms.

    Recursive datastructure. When adding a binding variable u to
    variable v, keeps a reference to the unifier for v.
    A variable's identity is its name plus its unification context.
    This enables a variable with the same name but from two
    different atoms to be treated as different variables.
    """
    class Value(object):
        def __init__(self, value, unifier):
            # actual value
            self.value = value
            # unifier context
            self.unifier = unifier

        def __str__(self):
            return "<{},{}>".format(
                str(self.value), repr(self.unifier))

        def recur_str(self):
            if self.unifier is None:
                recur = str(self.unifier)
            else:
                recur = self.unifier.recur_str()
            return "<{},{}>".format(
                str(self.value), recur)

        def __eq__(self, other):
            return self.value == other.value and self.unifer == other.unifier

        def __repr__(self):
            return "Value(value={}, unifier={})".format(
                repr(self.value), repr(self.unifier))

    class Undo(object):
        def __init__(self, var, unifier):
            self.var = var
            self.unifier = unifier

        def __str__(self):
            return "<var: {}, unifier: {}>".format(
                str(self.var), str(self.unifier))

        def __eq__(self, other):
            return self.var == other.var and self.unifier == other.unifier

    def __init__(self, dictionary=None):
        # each value is a Value
        self.contents = {}
        if dictionary is not None:
            for var, value in dictionary.items():
                self.add(var, value, None)

    def add(self, var, value, unifier):
        value = self.Value(value, unifier)
        # LOG.debug("Adding %s -> %s to unifier %s", var, value, self)
        self.contents[var] = value
        return self.Undo(var, self)

    def delete(self, var):
        if var in self.contents:
            del self.contents[var]

    def value(self, term):
        if term in self.contents:
            return self.contents[term]
        else:
            return None

    def apply(self, term, caller=None):
        return self.apply_full(term, caller=caller)[0]

    def apply_full(self, term, caller=None):
        """Recursively apply unifiers to TERM.

        Return (i) the final value and (ii) the final unifier.
        If the final value is a variable, instantiate
        with a new variable if not in KEEP_VARS
        """
        # LOG.debug("apply_full(%s, %s)", term, self)
        val = self.value(term)
        if val is None:
            # If result is a variable and this variable is not one of those
            #   in the top-most calling context, then create a new variable
            #   name based on this Binding.
            # This process avoids improper variable capture.
            #   Outputting the same variable with the same binding twice will
            #   generate the same output, but outputting the same variable with
            #   different bindings will generate different outputs.
            # Note that this variable name mangling
            #   is not done for the top-most variables,
            #   which makes output a bit easier to read.
            # Unfortunately, the process is non-deterministic from one run
            #   to the next, which makes testing difficult.
            if (caller is not None and term.is_variable() and
                    not (term in caller.variables and caller.binding is self)):
                return (compile.Variable(term.name + str(id(self))), self)
            else:
                return (term, self)
        elif val.unifier is None or not val.value.is_variable():
            return (val.value, val.unifier)
        else:
            return val.unifier.apply_full(val.value)

    def is_one_to_one(self):
        image = set()  # set of all things mapped TO
        for x in self.contents:
            val = self.apply(x)
            if val in image:
                return False
            image.add(val)
        return True

    def __str__(self):
        s = repr(self)
        s += "={"
        s += ",".join(["{}:{}".format(str(var), str(val))
                       for var, val in self.contents.items()])
        s += "}"
        return s

    def recur_str(self):
        s = repr(self)
        s += "={"
        s += ",".join(["{}:{}".format(var, val.recur_str())
                       for var, val in self.contents.items()])
        s += "}"
        return s

    def __eq__(self, other):
        return self.contents == other.contents


def binding_str(binding):
    """Handles string conversion of either dictionary or Unifier."""
    if isinstance(binding, dict):
        s = ",".join(["{}: {}".format(str(var), str(val))
                     for var, val in binding.items()])
        return '{' + s + '}'
    else:
        return str(binding)


def undo_all(changes):
    """Undo all the changes in CHANGES."""
    # LOG.debug("undo_all(%s)",
    #     "[" + ",".join([str(x) for x in changes]) + "]")
    if changes is None:
        return
    for change in changes:
        if change.unifier is not None:
            change.unifier.delete(change.var)


def same_schema(atom1, atom2, theoryname=None):
    """Return True if ATOM1 and ATOM2 have the same schema.

    THEORYNAME is the default theory name.
    """
    if not atom1.table.same(atom2.table, theoryname):
        return False
    if len(atom1.arguments) != len(atom2.arguments):
        return False
    return True


def bi_unify_atoms(atom1, unifier1, atom2, unifier2, theoryname=None):
    """Unify atoms.

    If possible, modify BiUnifier UNIFIER1 and BiUnifier UNIFIER2 so that
    ATOM1.plug(UNIFIER1) == ATOM2.plug(UNIFIER2).
    Returns None if not possible; otherwise, returns
    a list of changes to unifiers that can be undone
    with undo-all. May alter unifiers besides UNIFIER1 and UNIFIER2.
    THEORYNAME is the default theory name.
    """
    # logging.debug("Unifying %s under %s and %s under %s",
    #      atom1, unifier1, atom2, unifier2)
    if not same_schema(atom1, atom2, theoryname):
        return None
    return bi_unify_lists(atom1.arguments, unifier1,
                          atom2.arguments, unifier2)


def bi_unify_lists(iter1, unifier1, iter2, unifier2):
    """Unify lists.

    If possible, modify BiUnifier UNIFIER1 and BiUnifier UNIFIER2 such that
    iter1.plug(UNIFIER1) == iter2.plug(UNIFIER2), assuming PLUG is defined
    over lists.  Returns None if not possible; otherwise, returns
    a list of changes to unifiers that can be undone
    with undo-all. May alter unifiers besides UNIFIER1 and UNIFIER2.
    """
    if len(iter1) != len(iter2):
        return None
    changes = []
    for i in xrange(0, len(iter1)):
        assert isinstance(iter1[i], compile.Term)
        assert isinstance(iter2[i], compile.Term)
        # grab values for args
        val1, binding1 = unifier1.apply_full(iter1[i])
        val2, binding2 = unifier2.apply_full(iter2[i])
        # logging.debug("val(%s)=%s at %s, val(%s)=%s at %s",
        #     atom1.arguments[i], val1, binding1,
        #     atom2.arguments[i], val2, binding2)
        # assign variable (if necessary) or fail
        if val1.is_variable() and val2.is_variable():
            # logging.debug("1 and 2 are variables")
            if bi_var_equal(val1, binding1, val2, binding2):
                continue
            else:
                changes.append(binding1.add(val1, val2, binding2))
        elif val1.is_variable() and not val2.is_variable():
            # logging.debug("Left arg is a variable")
            changes.append(binding1.add(val1, val2, binding2))
        elif not val1.is_variable() and val2.is_variable():
            # logging.debug("Right arg is a variable")
            changes.append(binding2.add(val2, val1, binding1))
        elif val1 == val2:
            continue
        else:
            # logging.debug("Unify failure: undoing")
            undo_all(changes)
            return None
    return changes

# def plug(atom, binding, withtable=False):
#     """ Returns a tuple representing the arguments to ATOM after having
#         applied BINDING to the variables in ATOM. """
#     if withtable is True:
#         result = [atom.table]
#     else:
#         result = []
#     for i in xrange(0, len(atom.arguments)):
#         if (atom.arguments[i].is_variable() and
#             atom.arguments[i].name in binding):
#             result.append(binding[atom.arguments[i].name])
#         else:
#             result.append(atom.arguments[i].name)
#     return tuple(result)


def match_tuple_atom(tupl, atom):
    """Get bindings.

    Returns a binding dictionary that when applied to ATOM's arguments
    gives exactly TUPLE, or returns None if no such binding exists.
    """
    if len(tupl) != len(atom.arguments):
        return None
    binding = {}
    for i in xrange(0, len(tupl)):
        arg = atom.arguments[i]
        if arg.is_variable():
            if arg.name in binding:
                oldval = binding[arg.name]
                if oldval != tupl[i]:
                    return None
            else:
                binding[arg.name] = tuple[i]
    return binding


def match_atoms(atom1, unifier, atom2):
    """Modify UNIFIER so that ATOM1.plug(UNIFIER) == ATOM2.

    ATOM2 is assumed to be ground.
    UNIFIER is assumed to be a BiUnifier.
    Return the changes to UNIFIER or None if matching is impossible.

    Matching is a special case of instance-checking since ATOM2
    in this case must be ground, whereas there is no such limitation
    for instance-checking.  This makes the code significantly simpler
    and faster.
    """
    if not same_schema(atom1, atom2):
        return None
    changes = []
    for i in xrange(0, len(atom1.arguments)):
        val, binding = unifier.apply_full(atom1.arguments[i])
        # LOG.debug("val(%s)=%s at %s; comparing to object %s",
        #     atom1.arguments[i], val, binding, atom2.arguments[i])
        if val.is_variable():
            changes.append(binding.add(val, atom2.arguments[i], None))
        else:
            if val.name != atom2.arguments[i].name:
                undo_all(changes)
                return None
    return changes


def bi_var_equal(var1, unifier1, var2, unifier2):
    """Check var equality.

    Returns True iff variable VAR1 in unifier UNIFIER1 is the same
    variable as VAR2 in UNIFIER2.
    """
    return (var1 == var2 and unifier1 is unifier2)


def same(formula1, formula2):
    """Check formulas are the same.

    Determine if FORMULA1 and FORMULA2 are the same up to a variable
    renaming. Treats FORMULA1 and FORMULA2 as having different
    variable namespaces. Returns None or the pair of unifiers.
    """
    if isinstance(formula1, compile.Literal):
        if isinstance(formula2, compile.Rule):
            return None
        elif formula1.is_negated() != formula2.is_negated():
            return None
        else:
            u1 = BiUnifier()
            u2 = BiUnifier()
            if same_atoms(formula1, u1, formula2, u2, set()) is not None:
                return (u1, u2)
            return None
    elif isinstance(formula1, compile.Rule):
        if isinstance(formula2, compile.Literal):
            return None
        else:
            if len(formula1.body) != len(formula2.body):
                return None
            u1 = BiUnifier()
            u2 = BiUnifier()
            bound2 = set()
            result = same_atoms(formula1.head, u1, formula2.head, u2, bound2)
            if result is None:
                return None
            for i in xrange(0, len(formula1.body)):
                result = same_atoms(
                    formula1.body[i], u1, formula2.body[i], u2, bound2)
                if result is None:
                    return None
            return (u1, u2)
    else:
        return None


def same_atoms(atom1, unifier1, atom2, unifier2, bound2):
    """Check whether atoms are identical.

    Modifies UNIFIER1 and UNIFIER2 to demonstrate
    that ATOM1 and ATOM2 are identical up to a variable renaming.
    Returns None if not possible or the list of changes if it is.
    BOUND2 is the set of variables already bound in UNIFIER2
    """
    def die():
        undo_all(changes)
        return None
    LOG.debug("same_atoms(%s, %s)", atom1, atom2)
    if not same_schema(atom1, atom2):
        return None
    changes = []
    # LOG.debug("same_atoms entering loop")
    for i in xrange(0, len(atom1.arguments)):
        val1, binding1 = unifier1.apply_full(atom1.arguments[i])
        val2, binding2 = unifier2.apply_full(atom2.arguments[i])
        # LOG.debug("val1: %s at %s; val2: %s at %s",
        #     val1, binding1, val2, binding2)
        if val1.is_variable() and val2.is_variable():
            if bi_var_equal(val1, binding1, val2, binding2):
                continue
            # if we already bound either of these variables, not SAME
            if not bi_var_equal(val1, binding1, atom1.arguments[i], unifier1):
                # LOG.debug("same_atoms: arg1 already bound")
                return die()
            if not bi_var_equal(val2, binding2, atom2.arguments[i], unifier2):
                # LOG.debug("same_atoms: arg2 already bound")
                return die()
            if val2 in bound2:
                # LOG.debug("same_atoms: binding is not 1-1")
                return die()
            changes.append(binding1.add(val1, val2, binding2))
            bound2.add(val2)
        elif val1.is_variable():
            # LOG.debug("val1 is a variable")
            return die()
        elif val2.is_variable():
            # LOG.debug("val2 is a variable")
            return die()
        elif val1 != val2:
            # one is a variable and one is not or unmatching object constants
            # LOG.debug("val1 != val2")
            return die()
    return changes


def instance(formula1, formula2):
    """Determine if FORMULA1 is an instance of FORMULA2.

    If there is some binding that when applied to FORMULA1 results
    in FORMULA2. Returns None or a unifier.
    """
    LOG.debug("instance(%s, %s)", formula1, formula2)
    if isinstance(formula1, compile.Literal):
        if isinstance(formula2, compile.Rule):
            return None
        elif formula1.is_negated() != formula2.is_negated():
            return None
        else:
            u = BiUnifier()
            if instance_atoms(formula1, formula2, u) is not None:
                return u
            return None
    elif isinstance(formula1, compile.Rule):
        if isinstance(formula2, compile.Literal):
            return None
        else:
            if len(formula1.body) != len(formula2.body):
                return None
            u = BiUnifier()
            result = instance_atoms(formula1.head, formula2.head, u)
            if result is None:
                return None
            for i in xrange(0, len(formula1.body)):
                result = same_atoms(
                    formula1.body[i], formula2.body[i], u)
                if result is None:
                    return None
            return u
    else:
        return None


def instance_atoms(atom1, atom2, unifier2):
    """Check atoms equality by adding bindings.

    Adds bindings to UNIFIER2 to make ATOM1 equal to ATOM2
    after applying UNIFIER2 to ATOM2 only.   Returns None if
    no such bindings make equality hold.
    """
    def die():
        undo_all(changes)
        return None
    LOG.debug("instance_atoms(%s, %s)", atom1, atom2)
    if not same_schema(atom1, atom2):
        return None
    unifier1 = BiUnifier()
    changes = []
    for i in xrange(0, len(atom1.arguments)):
        val1, binding1 = unifier1.apply_full(atom1.arguments[i])
        val2, binding2 = unifier2.apply_full(atom2.arguments[i])
        # LOG.debug("val1: %s at %s; val2: %s at %s",
        #     val1, binding1, val2, binding2)
        if val1.is_variable() and val2.is_variable():
            if bi_var_equal(val1, binding1, val2, binding2):
                continue
            # if we already bound either of these variables, not INSTANCE
            if not bi_var_equal(val1, binding1, atom1.arguments[i], unifier1):
                # LOG.debug("instance_atoms: arg1 already bound")
                return die()
            if not bi_var_equal(val2, binding2, atom2.arguments[i], unifier2):
                # LOG.debug("instance_atoms: arg2 already bound")
                return die()
            # add binding to UNIFIER2
            changes.append(binding2.add(val2, val1, binding1))
        elif val1.is_variable():
            return die()
        elif val2.is_variable():
            changes.append(binding2.add(val2, val1, binding1))
            # LOG.debug("var2 is a variable")
        elif val1 != val2:
            # unmatching object constants
            # LOG.debug("val1 != val2")
            return die()
    return changes


def skolemize(formulas):
    """Instantiate all variables consistently with UUIDs in the formulas."""
    # create binding then plug it in.
    variables = set()
    for formula in formulas:
        variables |= formula.variables()

    binding = {}
    for var in variables:
        binding[var] = compile.Term.create_from_python(str(uuid.uuid4()))

    return [formula.plug(binding) for formula in formulas]
