"""Driver of graph construction, optimization, and linking.

"""
__docformat__ = "restructuredtext en"

import copy
import copy_reg
import cPickle
import itertools
import time
import warnings

import numpy

import theano
from theano import gof
from theano.gof.python25 import partial
import theano.compile.mode
from theano.compile.io import (
    In, SymbolicInput, SymbolicInputKit, SymbolicOutput)
from theano.compile.ops import deep_copy_op, view_op
from theano.gof.graph import is_same_graph
from theano.gof.op import ops_with_inner_function

import logging
_logger = logging.getLogger('theano.compile.function_module')


class UnusedInputError(Exception):
    """
    A symbolic input passed to function is not needed
    """
    pass


def alias_root(v):
    """Return the variable to which v is aliased by view_maps and destroy_maps"""
    if v.owner is None:
        return v
    vmap = getattr(v.owner.op, 'view_map', {})
    dmap = getattr(v.owner.op, 'destroy_map', {})
    outpos = v.owner.outputs.index(v)
    v_views = vmap.get(outpos, []) + dmap.get(outpos, [])
    if len(v_views) > 1:
        raise NotImplementedError(
            str(v) + " is a view/destroyed version of more then one inputs. "
            "Currently, we only support the case where an output is a view or "
            "a destroyed version of one input.")
    elif v_views:
        return alias_root(v.owner.inputs[v_views[0]])
    else:
        return v


def view_tree_set(v, treeset):
    """Add to `treeset` all variables that are views of v, given that v is not a view"""
    treeset.add(v)
    for cl, v_input_pos_to_cl in v.clients:
        if cl == 'output':
            continue
        vmap = getattr(cl.op, 'view_map', {})
        dmap = getattr(cl.op, 'destroy_map', {})
        for opos, iposlist in vmap.items() + dmap.items():
            if v_input_pos_to_cl in iposlist:
                if cl.outputs[opos] not in treeset:
                    view_tree_set(cl.outputs[opos], treeset)


def infer_reuse_pattern(fgraph, outputs_to_disown):
    """
    Given an fgraph and a list of variables, returns the list or set of all variables which may
    share the same underlying data storage as any of the specified variables. Used internally
    by function, FunctionMaker.

    This list (or set) is also refered to as no_recycling sometimes, especially by linker code.
    """
    rval = set()
    for o in outputs_to_disown:
        view_tree_set(alias_root(o), rval)
    # remove from rval all of the inputs, constants, values.
    rval = set(r for r in rval if r.owner is not None)

    return rval


def fgraph_updated_vars(fgraph, expanded_inputs):
    """
    Reconstruct the full "updates" dictionary, mapping from FunctionGraph input
    variables to the fgraph outputs that will replace their values.

    :rtype: dict variable -> variable
    """
    updated_vars = {}
    potential_values = list(fgraph.outputs)  # copy the list
    if len(expanded_inputs) != len(fgraph.inputs):
        raise ValueError('expanded_inputs must match len(fgraph.inputs)')
    for e_input, ivar in reversed(zip(expanded_inputs, fgraph.inputs)):
        if e_input.update is not None:
            updated_vars[ivar] = potential_values.pop()
    return updated_vars


class Supervisor:
    """
    Listener for FunctionGraph events which makes sure that no operation overwrites the
    contents of protected Variables. The outputs of the FunctionGraph are protected by default.
    """

    def __init__(self, protected):
        self.protected = list(protected)

    def validate(self, fgraph):
        if not hasattr(fgraph, 'destroyers'):
            return True
        for r in self.protected + list(fgraph.outputs):
            if fgraph.destroyers(r):
                raise gof.InconsistencyError(
                    "Trying to destroy a protected Variable.", r)


def std_fgraph(input_specs, output_specs, accept_inplace=False):
    """
    Makes an FunctionGraph corresponding to the input specs and the output
    specs.  Any SymbolicInput in the input_specs, if its update field
    is not None, will add an output to the FunctionGraph corresponding to that
    update. The return value is the FunctionGraph as well as a list of
    SymbolicOutput instances corresponding to the updates.

    If accept_inplace is False, the graph will be checked for inplace
    operations and an exception will be raised if it has any. If
    accept_inplace is True, a DestroyHandler will be added to the FunctionGraph
    if there are any inplace operations.

    The returned FunctionGraph is a clone of the graph between the provided
    inputs and outputs.
    """
    orig_inputs = [spec.variable for spec in input_specs]
    updates = [spec.update for spec in input_specs if spec.update]
    orig_outputs = [spec.variable for spec in output_specs] + updates

    fgraph = gof.fg.FunctionGraph(orig_inputs, orig_outputs)

    for node in fgraph.apply_nodes:
        if getattr(node.op, 'destroy_map', None):
            if not accept_inplace:
                raise TypeError("Graph must not contain inplace operations",
                                node, node.op)
            else:
                fgraph.attach_feature(gof.DestroyHandler())
                break

    # We need to protect all immutable inputs from inplace operations.
    fgraph.attach_feature(
        Supervisor(input
                   for spec, input in zip(input_specs, fgraph.inputs)
                   if not (spec.mutable or
                           (hasattr(fgraph, 'destroyers') and
                            fgraph.destroyers(input)))))

    # If named nodes are replaced, keep the name
    for feature in std_fgraph.features:
        fgraph.attach_feature(feature())
    return fgraph, map(SymbolicOutput, updates)


std_fgraph.features = [gof.toolbox.PreserveNames]


class AliasedMemoryError(Exception):
    """Memory is aliased that should not be"""
    pass


###
### Function
###


DUPLICATE = ['DUPLICATE'] # unique id object used as a placeholder for duplicate entries
class Function(object):
    """
    Type of the functions returned by theano.function or theano.FunctionMaker.create.


    `Function` is the callable object that does computation.  It has the storage of inputs and
    outputs, performs the packing and unpacking of inputs and return values.  It implements the
    square-bracket indexing so that you can look up the value of a symbolic node.

    Functions are copyable via {{{fn.copy()}}} and {{{copy.copy(fn)}}}.
    When a function is copied, this instance is duplicated.  Contrast with self.maker
    (instance of `FunctionMaker`) that is shared between copies.
    The meaning of copying a function is that the containers and their current values will all be duplicated.
    This requires that mutable inputs be copied, whereas immutable inputs may be shared between copies.



    A Function instance is hashable, on the basis of its memory address (its id).

    A Function instance is only equal to itself.

    A Function instance may be serialized using the `pickle` or `cPickle` modules.
    This will save all default inputs, the graph, and *** to the pickle file (WRITEME).

    A Function instance have a ``trust_input`` field that default to
    False. When True, we don't do extra check of the input to give
    better error message. In some case, python code will still return
    the good results if you pass a python or numpy scalar instead of a
    numpy tensor.  C code should raise an error if you pass an object
    of the wrong type.

    """

    pickle_aliased_memory_strategy = 'warn'
    """How to deal with pickling finding aliased storage.

    Meaningful settings are: 'ignore', 'warn', 'raise'

    If the value is 'warn', then a message will be printed to stderr if aliased storage is
    dectected during pickle.dump.

    If the value is 'raise', then an AliasedMemoryError will be raised if aliased storage is
    detected during pickle.dump.

    """

    input_storage = None
    """list of Container instances"""

    output_storage = None
    """list of Container instances"""

    indices = None
    """list of (SymbolicInput|SymbolicInputKit, indices, [SymbolicInput,...]), one tuple for
    each input

    The first tuple element is the SymbolicInput object for the corresponding function input.

    The second and third tuple elements are used only by Kits, which are deprecated.
    """

    defaults = None
    """ list of 3-tuples, one 3-tuple for each input.

    Tuple element 0: Bool:  Is this input required at each function call?
    Tuple element 1: Bool:  Should this inputs value be reverted after each call?
    Tuple element 2: Any:  The value associated with this input.
    """

    unpack_single = None
    """Bool: for outputs lists of length 1, should the 0'th element be returned directly?"""

    return_none = None
    """Bool: whether the function should return None or not"""

    maker = None
    """FunctionMaker instance"""

    fn = None
    """a function that evaluates the graph.  Typically a linker's make_thunk method created this
    function."""

    finder = None
    """Dictionary mapping several kinds of things to containers.

    We set an entry in finder for:

    - the index of the input

    - the variable instance the input is based on

    - the name of the input

    All entries map to the container or to DUPLICATE if an ambiguity is detected
    """

    inv_finder = None
    """Dict. Reverse lookup of `finder`.

    It maps container -> SymbolicInput
    """

    def __init__(self, fn, input_storage, output_storage, indices, outputs,
                 defaults, unpack_single, return_none, maker):
        """
        Initialize attributes. create finder, inv_finder.
        """

        self.fn = fn
        self.input_storage = input_storage
        self.output_storage = output_storage
        self.indices = indices
        self.outputs = outputs
        self.defaults = defaults
        self.unpack_single = unpack_single
        self.return_none = return_none
        self.maker = maker
        self.profile = None  # reassigned in FunctionMaker.create
        self.trust_input = False  # If True, we don't check the input parameter
        self.name = None
        self.nodes_with_inner_function = []

        # We will be popping stuff off this `containers` object.  It is a copy.
        containers = list(self.input_storage)
        finder = {}
        inv_finder = {}

        def distribute(indices, cs, value):
            input.distribute(value, indices, cs)
            for c in cs:
                c.provided += 1
        #def assign(c, v):
            #c.data = v

        # Store the list of names of named inputs.
        named_inputs = []
        # Count the number of un-named inputs.
        n_unnamed_inputs = 0

        #setters = []
        # Initialize the storage
        # this loop works by modifying the elements (as variable c) of self.input_storage inplace.
        for i, ((input, indices, sinputs), (required, refeed, value)) in enumerate(zip(self.indices, defaults)):
            if indices is None: # this is true iff input is not a SymbolicInputKit
                c = containers[0]  #containers is being used as a stack. Here we pop off the next one.
                c.strict = getattr(input, 'strict', False)
                c.allow_downcast = getattr(input, 'allow_downcast', None)

                if value is not None:
                    # Always initialize the storage.
                    if isinstance(value, gof.Container):
                        # There is no point in obtaining the current value
                        # stored in the container, since the container is
                        # shared.
                        # For safety, we make sure 'refeed' is False, since
                        # there is no need to refeed the defaullt value.
                        assert not refeed
                    else:
                        c.value = value
                c.required = required
                c.implicit = input.implicit
                c.provided = 0 # this is a count of how many times the input has been provided (reinitialized to 0 on __call__)
                finder[i] = c
                finder[input.variable] = c
                if input.name not in finder:
                    finder[input.name] = c
                else:
                    finder[input.name] = DUPLICATE
                if input.name is None:
                    n_unnamed_inputs += 1
                else:
                    named_inputs.append(input.name)
                #backport
                #finder[input.name] = c if input.name not in finder else DUPLICATE
                # inv_finder maps the container to the input (useful for one error message)
                inv_finder[c] = input
                #setters.append(partial(assign, c))
                containers[:1] = []
            else:
                # TODO The following code may need to do something to handle
                # implicit inputs.

                # The input is a SymbolicInputKit, so we take as many containers as the Kit provides inputs
                cs = containers[:len(indices)]
                # distribute does the initialization of the containers
                input.distribute(value, indices, cs)
                f = partial(distribute, indices, cs)
                # Like before, we set a finder entry for the kit. Note that
                # we are not mapping to a container but to a function which
                # can reinitialize all the containers
                finder[i] = f
                finder[input] = f
                if input.name not in finder:
                    finder[input.name] = f
                else:
                    finder[input.name] = DUPLICATE
                #backport
                #finder[input.name] = f if input.name not in finder else DUPLICATE
                #setters.append(f)
                # For each input in the kit and its corresponding container, we put an entry in finder.
                # This allows the user to micro-manage elements of the kit if need be.
                # All containers inherit the required field and have their own "provided" counter
                for c, sin in zip(cs, sinputs):
                    finder[sin.variable] = c
                    finder[sin.name] = c
                    if sin.name not in finder:
                        finder[sin.name] = c
                    else:
                        finder[sin.name] = DUPLICATE
                    #backport
                    #finder[sin.name] = c if sin.name not in finder else DUPLICATE
                    inv_finder[c] = input
                    c.required = required
                    c.provided = 0
                containers[:len(indices)] = []

        self.finder = finder
        self.inv_finder = inv_finder

        # this class is important in overriding the square-bracket notation:
        #     fn.value[x]
        # self reference is available via the closure on the class
        class ValueAttribute(object):
            def __getitem__(self, item):
                try:
                    s = finder[item]
                except KeyError:
                    raise TypeError("Unknown input or state: %s" % str(item))
                if s is DUPLICATE:
                    raise TypeError("Ambiguous name: %s - please check the names "\
                        "of the inputs of your function for duplicates." % str(item))
                if isinstance(s, gof.Container):
                    return s.value
                else:
                    raise NotImplementedError
            def __setitem__(self, item, value):
                try:
                    s = finder[item]
                except KeyError:
                    # Print informative error message.
                    msg = get_info_on_inputs(named_inputs, n_unnamed_inputs)
                    raise TypeError("Unknown input or state: %s. %s" %
                                    (str(item), msg))
                if s is DUPLICATE:
                    raise TypeError("Ambiguous name: %s - please check the names "\
                        "of the inputs of your function for duplicates." % str(item))
                if isinstance(s, gof.Container):
                    s.value = value
                    s.provided += 1
                else:
                    s(value)
            def __contains__(self, item):
                return finder.__contains__(item)

        # this class is important in overriding the square-bracket notation:
        #     fn.container[x]
        # self reference is available via the closure on the class
        class ContainerAttribute(object):
            def __getitem__(self, item):
                return finder[item]
            def __contains__(self, item):
                return finder.__contains__(item)
            # You cannot set the container

        self._value = ValueAttribute()
        self._container = ContainerAttribute()

        # Compute self.n_returned_outputs.
        # This is used only when fn.need_update_inputs is False
        # because we're using one of the VM objects and it is
        # putting updates back into the input containers all by itself.
        assert len(self.maker.expanded_inputs) == len(self.input_storage)
        self.n_returned_outputs = len(self.output_storage)
        for input in self.maker.expanded_inputs:
            if input.update is not None:
                self.n_returned_outputs -= 1

        for node in self.maker.fgraph.apply_nodes:
            if node.op in ops_with_inner_function.keys():
                self.nodes_with_inner_function.append(node.op)

    def __contains__(self, item):
        return self.value.__contains__(item)

    def __getitem__(self, item):
        return self.value[item]

    def __setitem__(self, item, value):
        self.value[item] = value

    def __copy__(self):
        defaults = [default for _1, _2, default in self.defaults]
        cpy = self.maker.create(defaults, trustme=True)
        for (input, _1, _2), here, there in zip(self.indices,
                                                self.input_storage,
                                                cpy.input_storage):
            if input.mutable and here is not None:
                there.data = copy.copy(here.data)
            else:
                there.data = here.data
        return cpy

    def __call__(self, *args, **kwargs):
        profile = self.profile
        t0 = time.time()

        # Reinitialize each container's 'provided' counter
        if self.trust_input:
            i = 0
            for arg in args:
                s = self.input_storage[i]
                s.storage[0] = arg
                i += 1
        else:
            for c in self.input_storage:
                c.provided = 0

            if len(args) + len(kwargs) > len(self.input_storage):
                raise TypeError("Too many parameter passed to theano function")

            # Set positional arguments
            i = 0
            for arg in args:
                #TODO: provide a Param option for skipping the filter if we
                #      really want speed.
                s = self.input_storage[i]
                # see this emails for a discuation about None as input
                # https://groups.google.com/group/theano-dev/browse_thread/thread/920a5e904e8a8525/4f1b311a28fc27e5
                if arg is None:
                    s.storage[0] = arg
                else:
                    try:
                        s.storage[0] = s.type.filter(arg, strict=s.strict,
                                allow_downcast=s.allow_downcast)

                    except Exception, e:
                        function_name = "theano function"
                        if self.name:
                            function_name += ' with name "' + self.name + '" '
                        #end if
                        e.args = tuple(["Bad input argument to " + function_name +
                                        " at index %d(0-based)" % i] +
                                       list(e.args))
                        raise
                    #end except
                #end if
                s.provided += 1
                i += 1

        # Set keyword arguments
        if kwargs:  # for speed, skip the iteritems for empty kwargs
            for k, arg in kwargs.iteritems():
                self[k] = arg

        if not self.trust_input and (
            not hasattr(self, '_check_for_aliased_inputs') or
            self._check_for_aliased_inputs):
            ## Collect aliased inputs among the storage space
            args_share_memory = []
            for i in xrange(len(self.input_storage)):
                i_var = self.maker.inputs[i].variable
                i_val = self.input_storage[i].storage[0]
                if hasattr(i_var.type, 'may_share_memory'):
                    is_aliased = False
                    for j in xrange(len(args_share_memory)):

                        group_j = itertools.izip(
                            [self.maker.inputs[k].variable for k
                             in args_share_memory[j]],
                            [self.input_storage[k].storage[0] for k
                             in args_share_memory[j]])
                        if numpy.any([(var.type is i_var.type and
                                        var.type.may_share_memory(val,i_val))
                                       for (var,val) in group_j]):

                            is_aliased = True
                            args_share_memory[j].append(i)
                            break

                    if not is_aliased:
                        args_share_memory.append([i])

                # Check for groups of more than one argument that share memory
                for group in args_share_memory:
                    if len(group) > 1:
                        # see if any of these arguments are mutable
                        mutable = numpy.any([(self.maker.inputs[idx].mutable or
                                             self.maker.inputs[idx].borrow)
                                             for idx in group])
                        # copy all but the first
                        for idx in group[1:]:
                            self.input_storage[i].storage[0] = copy.copy(
                                self.input_storage[i].storage[0])

        # Check if inputs are missing, or if inputs were set more than once, or
        # if we tried to provide inputs that are supposed to be implicit.
        if not self.trust_input:
            for c in self.input_storage:
                if c.required and not c.provided:
                    raise TypeError("Missing required input: %s" %
                                    getattr(self.inv_finder[c], 'variable',
                                            self.inv_finder[c]))
                if c.provided > 1:
                    raise TypeError("Multiple values for input: %s" %
                                    getattr(self.inv_finder[c], 'variable',
                                            self.inv_finder[c]))
                if c.implicit and c.provided > 0:
                    raise TypeError(
                        'Tried to provide value for implicit input: %s'
                        % getattr(self.inv_finder[c], 'variable',
                                  self.inv_finder[c]))

        # Do the actual work
        t0_fn = time.time()
        try:
            outputs = self.fn()
        except Exception:
            if hasattr(self.fn, 'position_of_error'):
                # this is a new vm-provided function or c linker
                # they need this because the exception manipulation
                # done by raise_with_op is not implemented in C.
                if hasattr(self.fn, 'thunks'):
                    # For the CVM
                    gof.link.raise_with_op(
                        self.fn.nodes[self.fn.position_of_error],
                        self.fn.thunks[self.fn.position_of_error])
                else:
                    # For the c linker We don't have access from
                    # python to all the temps values So for now, we
                    # just don't print the extra shapes/strides info
                    gof.vm.raise_with_op(
                        self.fn.nodes[self.fn.position_of_error])
            else:
                # old-style linkers raise their own exceptions
                raise

        dt_fn = time.time() - t0_fn
        self.maker.mode.fn_time += dt_fn
        if profile:
            profile.vm_call_time += dt_fn

        # Retrieve the values that were computed
        if outputs is None:
            outputs = [x.data for x in self.output_storage]
        assert len(outputs) == len(self.output_storage)

        # Remove internal references to required inputs.
        # These cannot be re-used anyway.
        for c in self.input_storage:
            if c.required:
                c.storage[0] = None

        # if we are allowing garbage collection, remove the input and
        # output reference from the internal storage cells
        if getattr(self.fn, 'allow_gc', False):
            assert len(self.output_storage) == len(self.maker.fgraph.outputs)
            for o_container, o_variable in zip(self.output_storage,
                                               self.maker.fgraph.outputs):
                if o_variable.owner is not None:
                    # this node is the variable of computation
                    # WARNING: This circumvents the 'readonly' attribute in x
                    o_container.storage[0] = None

        if getattr(self.fn, 'need_update_inputs', True):
            # Update the inputs that have an update function
            for input, storage in reversed(zip(self.maker.expanded_inputs,
                                               self.input_storage)):
                if input.update is not None:
                    storage.data = outputs.pop()
        else:
            outputs = outputs[:self.n_returned_outputs]

        # Put default values back in the storage
        for i, (required, refeed, value) in enumerate(self.defaults):
            if refeed:
                if isinstance(value, gof.Container):
                    value = value.storage[0]
                self[i] = value
        #
        # NOTE: This logic needs to be replicated in
        #       scan.
        #       grep for 'PROFILE_CODE'
        #

        dt_call = time.time() - t0
        self.maker.mode.call_time += dt_call
        if profile:
            profile.fct_callcount += 1
            profile.fct_call_time += dt_call
            if hasattr(self.fn, 'update_profile'):
                self.fn.update_profile(profile)

        if self.return_none:
            return None
        elif self.unpack_single and len(outputs) == 1:
            return outputs[0]
        else:
            return outputs

    value = property(
        lambda self: self._value,
        None,  # this property itself is not settable
        doc="dictionary-like access to the values associated with Variables")
    container = property(
        lambda self: self._container,
        None,  # this property itself is not settable
        doc="""dictionary-like access to the containers associated with Variables""")


    def free(self):
        """
        When allow_gc = False, clear the Variables in storage_map
        """
        # 1.no allow_gc return False 2.has allow_gc, if allow_gc is False, return True
        if not getattr(self.fn, 'allow_gc', True):
            for key in self.fn.storage_map.keys():
                if not isinstance(key, theano.gof.Constant):
                    self.fn.storage_map[key][0] = None
            
            for node in self.nodes_with_inner_function:
                ops_with_inner_function[node.op].free()


# pickling/deepcopy support for Function

def _pickle_Function(f):
    #copy of the input storage list
    ins = list(f.input_storage)
    input_storage = []

    for (input, indices, inputs), (required, refeed, default) in zip(f.indices, f.defaults):
        if isinstance(input, SymbolicInputKit):
            li = len(indices)
            if not default:
                input_storage.append(ins[:li])
            else:
                input_storage.append(default)
            ins[:li] = []
        else:
            input_storage.append(ins[0])
            del ins[0]

    inputs_data = [x.data for x in f.input_storage]

    # HACK to detect aliased storage.
    # This is here because aliased relationships are not [currently] preserved across the pickle operation
    if not (f.pickle_aliased_memory_strategy == 'ignore'):
        all_data = input_storage + inputs_data # addition here means list append
        for i, d_i in enumerate(all_data):
            for j, d_j in enumerate(all_data):
                if (i < j) and isinstance(d_i, numpy.ndarray) and isinstance(d_j, numpy.ndarray):
                    if numpy.may_share_memory(d_i, d_j):
                        if f.pickle_aliased_memory_strategy == 'warn':
                            _logger.warning(('aliased relationship between'
                                    ' Function arguments %s, %s'
                                    ' will not be preserved by un-pickling'
                                    ' operation') %(str(d_i), str(d_j)))
                        else:
                            raise AliasedMemoryError(d_i, d_j)
    rval = (_constructor_Function, (f.maker, input_storage, inputs_data))
    return rval

def _constructor_Function(maker, input_storage, inputs_data):
    if not theano.config.unpickle_function:
        return None
    f = maker.create(input_storage, trustme = True)
    assert len(f.input_storage) == len(inputs_data)
    for container, x in zip(f.input_storage, inputs_data):
        assert (container.data is x) or \
            (isinstance(x, numpy.ndarray) and (container.data == x).all()) or \
            (container.data == x)
    return f

copy_reg.pickle(Function, _pickle_Function)



###
### SanityCheckFunction
###

class SanityCheckFunction(Function):
    """Deprecated. It is not used and not tested anywhere in Theano!

    Also, we should remove the check_equal and related function in
    this file, and use Type.values_equals() instead.

    """

    def __init__(self, others, check_equal, *args, **kwargs):
        super(SanityCheckFunction, self).__init__(*args, **kwargs)
        self.others = others
        self.check_equal = check_equal
        # DEPRECATED?  Is this just for DualLinker?
        warnings.warn("SanityCheckFunction is deprecated")

    def __setitem__(self, item, value):
        super(SanityCheckFunction, self).__setitem__(item, value)
        for fn in self.others:
            fn[item] = value

    def __call__(self, *args, **kwargs):

        for fn in self.others:
            for stor1, stor2 in zip(self.input_storage, fn.input_storage):
                stor2.value = copy.copy(stor1.value)

        variables = super(SanityCheckFunction, self).__call__(*args, **kwargs)

        all_outputs = [copy.copy(c.value) for c in self.output_storage] # we keep a copy to make sure it's not overwritten
        for fn in self.others:
            fn(*args, **kwargs)

            for i, (c1, c2, input) in enumerate(zip(self.input_storage, fn.input_storage, self.maker.inputs)):
                if not input.mutable:
                    if not self.check_equal(c1.value, c2.value):
                        name = c2.name
                        if name:
                            the_name = name
                        else:
                            the_name = ""
                        raise ValueError("Input #%i%s using %s and %s differs."
                                         % (i,
                                            #backport
                                            #" (%s)" % name if name else "",
                                            " (%s)" % the_name,
                                            self.maker.mode,
                                            fn.maker.mode),
                                         c1.value, c2.value)

            # This checks all output storage (this includes state variables that we updated)
            # This is ok because the variables of a call stick around in their storage
            for i, (r1, c2) in enumerate(zip(all_outputs, fn.output_storage)):
                r2 = c2.value
                if not self.check_equal(r1, r2):
                    name = c2.name
                    if name:
                        the_name = name
                    else:
                        the_name = ""
                    raise ValueError("Variable #%i%s using %s and %s differs."
                                     % (i,
                                        #backport
                                        #" (%s)" % name if name else "",
                                        " (%s)" % the_name,
                                        self.maker.mode,
                                        fn.maker.mode),
                                     r1, r2)
        return variables


###
### FunctionMaker
###

def insert_deepcopy(fgraph, wrapped_inputs, wrapped_outputs):
    """
    Insert deepcopy in the fgraph to break aliasing of outputs
    """
    # This loop was inserted to remove aliasing between outputs when they all
    # evaluete to the same value. Originally it was OK for outputs to be aliased,
    # but some of the outputs can be shared variables, and is not good for shared
    # variables to be aliased. It might be possible to optimize this by making sure
    # there is no aliasing only between shared variables.

    # If some outputs are constant, we add deep copy to respect the memory contract

    # We don't insert deep copy when the output.borrow is True for all conserned outputs.

    assert len(wrapped_inputs) == len(fgraph.inputs)
    assert len(wrapped_outputs) == len(fgraph.outputs)
    reason = "insert_deepcopy"
    updated_fgraph_inputs = [fgraph_i for i, fgraph_i in zip(wrapped_inputs, fgraph.inputs) if getattr(i, 'update', False)]

    # We can't use fgraph.inputs as this don't include Constant Value.
    all_graph_inputs = gof.graph.inputs(fgraph.outputs)

    for i in xrange(len(fgraph.outputs)):
        views_of_output_i = set()
        view_tree_set(alias_root(fgraph.outputs[i]), views_of_output_i)
        copied = False
        # do not allow outputs to be aliased
        for j in xrange(i + 1, len(fgraph.outputs)):
            # We could don't put deep copy if both outputs have borrow==True
            # and not(wrapped_outputs[i].borrow and wrapped_outputs[j].borrow):
            if fgraph.outputs[j] in views_of_output_i:
                if wrapped_outputs[i].borrow and wrapped_outputs[j].borrow:
                    fgraph.change_input('output', i, view_op(fgraph.outputs[i]),
                                     reason=reason)
                else:
                    fgraph.change_input('output', i, deep_copy_op(fgraph.outputs[i]),
                                     reason=reason)
                copied = True
                break

        if not copied:
            for input_j in all_graph_inputs:
                # do not allow outputs to be aliased to an inputs (j), unless
                # a) that j'th input has been 'destroyed' by e.g. in-place computations
                # b) that j'th input is a shared variable that is also being updated
                if (hasattr(fgraph, 'get_destroyers_of') and
                    fgraph.get_destroyers_of(input_j)):
                    continue
                if input_j in updated_fgraph_inputs:
                    continue
                if input_j in views_of_output_i:
                    # We don't put deep_copy_op if the input and the output have borrow==True
                    if input_j in fgraph.inputs:
                        j = fgraph.inputs.index(input_j)
                        if wrapped_outputs[i].borrow and wrapped_inputs[j].borrow:
                            fgraph.change_input('output', i, view_op(fgraph.outputs[i]),
                                             reason="insert_deepcopy")
                            break
                        else:
                            fgraph.change_input('output', i, deep_copy_op(fgraph.outputs[i]),
                                             reason="insert_deepcopy")
                            break
                    elif wrapped_outputs[i].borrow:
                        fgraph.change_input('output', i, view_op(fgraph.outputs[i]),
                                         reason="insert_deepcopy")
                        break
                    else:
                        fgraph.change_input('output', i, deep_copy_op(fgraph.outputs[i]),
                                         reason="insert_deepcopy")
                        break

NODEFAULT = ['NODEFAULT']


class FunctionMaker(object):
    """`FunctionMaker` is the class to `create` `Function` instances.

    This class has the fgraph, the optimizer, and the linker.  When copying a `Function`, there is
    no need to duplicate the `FunctionMaker` instance.  Deepcopy still copies both, which can
    variable in re-compilation.

    """

    @staticmethod
    def wrap_in(input):
        if isinstance(input, (SymbolicInput, SymbolicInputKit)):
            return input
        elif isinstance(input, gof.Variable):
            # r -> SymbolicInput(variable=r)
            return SymbolicInput(input)
        elif isinstance(input, (list, tuple)):
            # (r, u) -> SymbolicInput(variable=r, update=u)
            if len(input) == 2:
                return SymbolicInput(input[0], update=input[1])
            else:
                raise TypeError("Expected two elements in the list or tuple.", input)
        else:
            raise TypeError("Unknown input type: %s (%s), expected Variable instance", type(input), input)

    @staticmethod
    def expand_in(sinput, rinputs):
        # For SymbolicInputKits, this extracts a list of SymbolicInput instances
        # and corresponding indices such that these SymbolicInputs are representative
        # of some of the Variable instances in inputs.
        # For SymbolicInput, this returns None as the list of indices and a list with
        # just the SymbolicInput.
        if isinstance(sinput, SymbolicInputKit):
            return sinput.complete(rinputs)
        elif isinstance(sinput, SymbolicInput):
            return [None, [sinput]]

    def env_getter(self):
        warnings.warn("FunctionMaker.env is deprecated, it has been renamed 'fgraph'",
                stacklevel=2)
        return self.fgraph

    def env_setter(self, value):
        warnings.warn("FunctionMaker.env is deprecated, it has been renamed 'fgraph'",
                stacklevel=2)
        self.fgraph = value

    def env_deleter(self):
        warnings.warn("FunctionMaker.env is deprecated, it has been renamed 'fgraph'",
                stacklevel=2)
        del self.fgraph

    env = property(env_getter, env_setter, env_deleter)

    @staticmethod
    def wrap_out(output):
        if isinstance(output, SymbolicOutput):
            return output
        elif isinstance(output, gof.Variable):
            return SymbolicOutput(output)
        else:
            raise TypeError("Unknown output type: %s (%s)", type(output), output)
        
    def optimize_graph_with_cache(self, optimizer, inputs, outputs):
        # This function is not finished
        from theano.gof.compilelock import get_lock, release_lock
        import os.path

        graph_db_file = os.path.join(theano.config.compiledir, 'optimized_graphs.pkl')

        # the inputs, outputs, and size of the graph to be optimized
        inputs_new = [inp.variable for inp in inputs]
        outputs_new = [out.variable for out in outputs]
        size_new = len(self.fgraph.apply_nodes)
        need_optimize = False
        get_lock()
        key = None
        #Beginning of cache optimizations.
        #Could be refactored in different functions.
        def load_graph_db():
            if os.path.isfile(graph_db_file):
                print 'graph_db already exists'
            else:
                # create graph_db
                f = open(graph_db_file, 'wb')
                print 'create new graph_db in %s' % graph_db_file
                #file needs to be open and closed for every pickle
                f.close()
            # load the graph_db dictionary
            try:
                f = open(graph_db_file, 'rb')
                #Temporary hack to allow theano.scan_module.tests.test_scan.T_Scan
                #to finish. Should be changed in definitive version.
                tmp = theano.config.unpickle_function
                theano.config.unpickle_function = False
                graph_db = cPickle.load(f)
                
                #hack end
                f.close()
                print 'graph_db loaded and it is not empty'
            except EOFError, e:
                # the file has nothing in it
                print e
                print 'graph_db loaded and it is empty'
                graph_db = {}
            finally:
                theano.config.unpickle_function = tmp
                
            return graph_db

        def find_same_graph_in_db(graph_db):
            # If found_graph_in_db is None, then need to optimize.
            # Otherwise, return the graph found.
            found_graph_in_db = None
            # The sole purpose of this loop is to set 'need_optimize' by
            # going through graph_db, looking for graph that has the same
            # computation performed. 
            for graph_old, graph_optimized in graph_db.iteritems():
                inputs_old = graph_old.inputs
                outputs_old = graph_old.outputs
                size_old = len(graph_old.apply_nodes)
                # Some heuristics to check is the same graphs have
                # already been optimized before.
                if len(inputs_new) != len(inputs_old):
                    # If the inputs are of different size,
                    # two graphs are for sure different
                    print 'need to optimize, because input size is different'
                    continue
                elif len(outputs_new) != len(outputs_old):
                    # If the inputs are of different size,
                    # two graphs are for sure different
                    print 'need to optimize, because output size is different'
                    continue
                elif not all(input_new.type == input_old.type for
                             input_new, input_old in zip(inputs_new, inputs_old)):
                    print 'need to optimize, because inputs are of different types'
                    continue
                elif not all(output_new.type == output_old.type for
                             output_new, output_old in zip(outputs_new, outputs_old)):
                    print 'need to optimize, because outputs are of different types'
                    continue
                elif not size_old == size_new:
                    print 'need to optimize, because numbers of nodes in graph are different'
                    continue
                else:
                    flags = []
                    for output_new, output_old, i in zip(
                            outputs_new, outputs_old, range(len(outputs_new))):
                        print 'loop through outputs node for both graphs'
                        graph_old.variables = set(gof.graph.variables(
                            graph_old.inputs, graph_old.outputs))

                        #using clone allowed to avoid a lot of errors
                        #deep copy seemed to had.
                        f2 = graph_old.clone(check_integrity=False)
                        t1 = output_new
                        t2 = f2.outputs[i]

                        #Used to remove "already used by another graph error
                        def removeAllFgraph(remove):
                            if hasattr(remove, 'fgraph'):
                                del remove.fgraph
                            if hasattr(remove, 'owner'):
                                if remove.owner is None:
                                    pass
                                else:
                                    if hasattr(remove.owner, 'fgraph'):
                                        del remove.owner.fgraph
                                    if hasattr(remove.owner, 'inputs'):
                                        remove.owner.inputs = [removeAllFgraph(
                                            i) for i in remove.owner.inputs]
                                        for o in remove.owner.outputs:
                                            if hasattr(o, 'fgraph'):
                                                del o.fgraph
                            return remove

                        t2 = removeAllFgraph(t2)

                        givens = dict(zip(gof.graph.inputs([t1]),
                                        gof.graph.inputs([t2])))

                        temp = dict(zip(gof.graph.inputs([t1]),
                                    gof.graph.inputs([t2])))

                        #hack to remove inconstent entry in givens
                        #seems to work that but source of inconsistency
                        #could be worth investigating.
                        for key, value in temp.iteritems():
                            if key.type != value.type:
                                del givens[key]

                        flag = is_same_graph(t1, t2, givens=givens)

                        flags.append(flag)

                    is_same = all(flags)
                    if is_same:
                        # found the match
                        print 'found a match, no need to optimize'
                        found_graph_in_db = graph_optimized
                        break
            return found_graph_in_db
                   
        graph_db = load_graph_db()
        print 'loaded graph_db from %s, size=%d' % (graph_db_file, len(graph_db))
        found_graph = find_same_graph_in_db(graph_db)
        if found_graph:
            self.fgraph = found_graph
            optimizer_profile = None
        else:
            # this is a brand new graph, optimize it, save it to graph_db
            print 'graph not found in graph_db, optimizing the graph'
            self.fgraph.variables = set(gof.graph.variables(
                self.fgraph.inputs, self.fgraph.outputs))
            #check_integrity parameters was added to ignore 
            #"excess cached variables" errors. Works that way
            #but once again the error couldbe worth
            #investigating.
            before_opt = self.fgraph.clone(check_integrity=False)
            optimizer_profile = optimizer(self.fgraph)
            graph_db.update({before_opt:self.fgraph})
            f = open(graph_db_file, 'wb')
            cPickle.dump(graph_db, f, -1)
            f.close()
            print 'new graph saved into graph_db'
        release_lock()
        return optimizer_profile
                
    def __init__(self, inputs, outputs,
            mode=None, accept_inplace=False, function_builder=Function,
            profile=None, on_unused_input=None, fgraph=None):
        """
        :type inputs: a list of SymbolicInput instances

        :type outputs: a list of SymbolicOutput instances
                    outputs may also be a single Variable (not a list), in which
                    case the functions produced by FunctionMaker will return
                    their output value directly

        :param mode: a Mode instance telling FunctionMaker how to optimize and link.  None
            means to use the `config.mode`.

        :param accept_inplace: True iff it is acceptable to have inplace operations
            in the graph from the inputs to the outputs

        :param on_unused_input: What to do if a variable in the 'inputs' list
            is not used in the graph. Possible values are:
                - 'raise': raise an error
                - 'warn': log a warning
                - 'ignore': do not do anything
                - None: Use the value in the Theano flags on_unused_input
        """
        mode = theano.compile.mode.get_mode(mode)

        # figure out which profile object to use (if any)
        # to help with forward-porting ProfileMode,
        # we allow ProfileMode to provide a ProfileStats object
        # using this somewhat awkward mechanism.
        mode_profile = getattr(mode, 'profile', None)
        if (profile is not None and
            profile is not False and
            mode_profile is not None):
            raise TypeError(
                    'profile passed via both "mode" and "profile" arguments')
        self.profile = profile = profile or mode_profile
        if profile or theano.config.cxx:
            # This is very important:
            # 1) We preload the cache here to don't have its timming
            #    included in optimization that compile function.
            # 2) If other repo that import Theano have Theano ops defined,
            #    we need to refresh the cache here. Otherwise, their is import
            #    order problems.
            #    When device=gpu, we compile during Theano import. This trigger
            #    the loading of the cache. But unpickling the cache ask that the
            #    other repos Ops are completly loaded, which isn't always the
            #    case!
            #    If a module isn't completly loaded and their unpickling fail,
            #    it mean it is safe for this function compilation to skip them,
            #    but not for futur compilation. So reloading the cache at each
            #    compilation fix this problem.
            # 3) This help propagate knowledge of newly compiled module to
            #    concurrent process.
            theano.gof.cc.get_module_cache().refresh()
        # Handle the case where inputs and/or outputs is a single Variable (not in a list)
        self.orig_outputs = outputs
        unpack_single = False
        return_none = False
        if outputs is None:
            return_none = True
            outputs = []
        if not isinstance(outputs, (list, tuple)):
            unpack_single = True
            outputs = [outputs]
        if not isinstance(inputs, (list, tuple)):
            inputs = [inputs]

        # Wrap them in In or Out instances if needed.
        inputs, outputs = map(self.wrap_in, inputs), map(self.wrap_out, outputs)
        _inputs = gof.graph.inputs([o.variable for o in outputs] + [i.update
            for i in inputs if getattr(i, 'update', False)])

        # Check if some input variables are unused
        self._check_unused_inputs(inputs, outputs, on_unused_input)

        # Make a list of (SymbolicInput|SymblicInputKits, indices, [SymbolicInput,...]), one 
        # tuple for each input. (See Function.indices for more details)
        indices = [[input] + self.expand_in(input, _inputs) for input in inputs]

        if fgraph is None:
            need_opt = True
            # make the fgraph (copies the graph, creates NEW INPUT AND OUTPUT VARIABLES)
            fgraph, additional_outputs = std_fgraph(inputs, outputs, accept_inplace)
            fgraph.profile = profile
        else:
            # fgraph is already an optimized one
            need_opt = False
            _, additional_outputs = std_fgraph(inputs, outputs, accept_inplace)
            pass
        
        self.fgraph = fgraph

        # Fetch the optimizer and linker
        optimizer, linker = mode.optimizer, copy.copy(mode.linker)
        if need_opt:
            compute_test_value_orig = theano.config.compute_test_value
            add_stack_trace_on_call_orig = gof.Op.add_stack_trace_on_call
            try:
                # optimize the fgraph
                theano.config.compute_test_value = theano.config.compute_test_value_opt
                gof.Op.add_stack_trace_on_call = False
                start_optimizer = time.time()

                # now optimize the graph
                if theano.config.cache_optimizations:
                    optimizer_profile = self.optimize_graph_with_cache(
                        optimizer, inputs, outputs)
                else:    
                    optimizer_profile = optimizer(fgraph)
                    
                end_optimizer = time.time()
                opt_time = end_optimizer - start_optimizer
                if profile:
                    profile.optimizer_time += opt_time
                    if theano.config.profile_optimizer:
                        profile.optimizer_profile = (optimizer, optimizer_profile)
                _logger.debug('Optimizing took %f seconds', opt_time)

                #Add deep copy to respect the memory interface
                insert_deepcopy(fgraph, inputs, outputs + additional_outputs)
            finally:
                theano.config.compute_test_value = compute_test_value_orig
                gof.Op.add_stack_trace_on_call = add_stack_trace_on_call_orig
        
        # initialize the linker
        if not hasattr(linker, 'accept'):
            raise ValueError("'linker' parameter of FunctionMaker should be a Linker with an accept method " \
                             "or one of %s" % theano.compile.mode.predefined_linkers.keys())

        #the 'no_borrow' outputs are the ones for which that we can't return the internal storage pointer.
        assert len(fgraph.outputs) == len(outputs + additional_outputs)
        no_borrow = [output for output, spec in zip(fgraph.outputs, outputs + additional_outputs) if not spec.borrow]
        if no_borrow:
            self.linker = linker.accept(fgraph, no_recycling=infer_reuse_pattern(fgraph, no_borrow))
        else:
            self.linker = linker.accept(fgraph)

        if hasattr(linker, 'accept_var_updates'):
            # hacky thing so VMLinker knows about updates
            self.linker.accept_var_updates(
                    fgraph_updated_vars(fgraph, inputs))

        self.indices = indices
        self.inputs = inputs
        self.expanded_inputs = inputs
        self.outputs = outputs
        self.unpack_single = unpack_single
        self.return_none = return_none
        self.mode = mode
        self.accept_inplace = accept_inplace
        self.function_builder = function_builder
        self.on_unused_input = on_unused_input  # Used only for the pickling

        self.required = [(i.value is None) for i in self.inputs]
        self.refeed = [
                (i.value is not None and
                 not isinstance(i.value, gof.Container) and
                 i.update is None)
                for i in self.inputs
        ]

    def _check_unused_inputs(self, inputs, outputs, on_unused_input):
        if on_unused_input is None:
            on_unused_input = theano.config.on_unused_input

        if on_unused_input == 'ignore':
            return

        # There should be two categories of variables in inputs:
        #  - variables that have to be provided (used_inputs)
        #  - shared variables that will be updated
        used_inputs = gof.graph.ancestors(
                ([o.variable for o in outputs]
                 + [i.update for i in inputs if getattr(i, 'update', False)]),
                blockers=[i.variable for i in inputs])

        msg = ("theano.function was asked to create a function computing "
                "outputs given certain inputs, but the provided input "
                "variable at index %i is not part of the computational graph "
                "needed to compute the outputs: %s.\n%s")
        warn_msg = ("To make this warning into an error, you can pass the "
                "parameter on_unused_input='raise' to theano.function. "
                "To disable it completely, use on_unused_input='ignore'.")
        err_msg = ("To make this error into a warning, you can pass the "
                "parameter on_unused_input='warn' to theano.function. "
                "To disable it completely, use on_unused_input='ignore'.")

        for i in inputs:
            if ((i.variable not in used_inputs) and (i.update is None)):
                if on_unused_input == 'warn':
                    warnings.warn(msg % (inputs.index(i), i.variable, warn_msg), stacklevel=6)
                elif on_unused_input == 'raise':
                    raise UnusedInputError(msg % (inputs.index(i), i.variable, err_msg))
                else:
                    raise ValueError(("Invalid value for keyword "
                        "on_unused_input of theano.function: '%s'. "
                        "valid values are 'raise', 'warn', and 'ignore'."
                        % on_unused_input))

    def create(self, input_storage=None, trustme=False):
        """
        Create a function.

        input_storage -> a list matching the inputs list and providing default values
                    if the default for an input is None, then that input is a
                    required input. For an input with an update, the default
                    acts as initialization.
        trustme -> disables some exceptions, used internally
        """

        if input_storage is None:
            input_storage = [None] * len(self.inputs)
        input_storage_lists = []  # list of independent one-element lists, will be passed to the linker
        defaults = []

        # The following loop is to fill in the input_storage_lists and defaults lists.
        assert len(self.indices) == len(input_storage)
        for i, ((input, indices, subinputs), input_storage_i) in enumerate(zip(self.indices, input_storage)):

            # Replace any default value given as a variable by its container.
            # Note that this makes sense only in the context of shared variables,
            # but for now we avoid dealing directly with them to avoid dependency
            # on the shared variables work-in-progress repository.
            if isinstance(input_storage_i, gof.Variable):
                input_storage_i = input_storage_i.container

            if isinstance(input_storage_i, gof.Container):
                # If the default is a gof.Container, this means we want to
                # share the same storage. This is done by appending
                # input_storage_i.storage to input_storage_lists.
                if indices is not None:
                    raise TypeError("Cannot take a Container instance as default for a SymbolicInputKit.")
                input_storage_lists.append(input_storage_i.storage)

                storage = input_storage[i].storage[0]

            else:
                # Normal case: one new, independent storage unit
                input_storage_lists.append([input_storage_i])

                storage = input_storage_i

            required = self.required[i]
            refeed = self.refeed[i]
            #sanity check-- if an input is required it should not need to be refed
            assert not (required and refeed)

            #shared variables need neither be input by the user nor refed
            if input.shared:
                assert not required
                assert not refeed
                storage = None

            #if an input is required, it never need be refed
            if required:
                storage = None

            #make sure that we only store a value if we actually need it
            if storage is not None:
                assert refeed or not required

            defaults.append((required,
                refeed,
                storage))

        # Get a function instance
        start_linker = time.time()
        _fn, _i, _o = self.linker.make_thunk(input_storage=input_storage_lists)
        end_linker = time.time()

        linker_time = end_linker - start_linker
        _logger.debug('Linker took %f seconds', linker_time)
        if self.profile:
            self.profile.linker_time += linker_time
            _fn.time_thunks = self.profile.flag_time_thunks

        fn = self.function_builder(_fn, _i, _o, self.indices, self.outputs,
                defaults, self.unpack_single, self.return_none, self)
        fn.profile = self.profile
        return fn


def _pickle_FunctionMaker(self):
    kwargs = dict(
                inputs=self.inputs,
                outputs=self.orig_outputs,
                fgraph=self.fgraph,
                mode=self.mode,
                accept_inplace=self.accept_inplace,
                function_builder=self.function_builder,
                profile=self.profile,
                on_unused_input=self.on_unused_input,
                )
    return (_constructor_FunctionMaker, (kwargs,))


def _constructor_FunctionMaker(kwargs):
    if theano.config.unpickle_function:
        if theano.config.reoptimize_unpickled_function:
            del kwargs['fgraph']
        return FunctionMaker(**kwargs)
    else:
        return None

copy_reg.pickle(FunctionMaker, _pickle_FunctionMaker)


try:
    # Pickle of slice is implemented on python 2.6.  To enabled be
    # compatible with python 2.4, we implement pickling of slice
    # ourself.
    cPickle.dumps(slice(0, 10, 100))
except TypeError:
    # This slice pickle implementation seam backward and forward compatible.
    def _pickle_slice(s):
        return (slice, (s.start, s.stop, s.step))
    copy_reg.pickle(slice, _pickle_slice)


__checkers = []


def check_equal(x, y):
    for checker in __checkers:
        try:
            return checker(x, y)
        except Exception:
            continue
    return x == y
    #raise Exception('No checker for equality between %s and %s' % (x, y))


def register_checker(checker):
    __checkers.insert(0, checker)


def orig_function(inputs, outputs, mode=None, accept_inplace=False,
                  name=None, profile=None, on_unused_input=None):
    """
    Return a Function that will calculate the outputs from the inputs.

    :param inputs: list of `SymbolicInput` or `In` instances

    :param outputs: a SymbolicOutput or a list of `SymbolicOutput` or `Out`
        instances. The return value of the returned function will match the
        format of this argument (either the value itself or a list of one or more
        return values)

    :param mode: a descriptive string or a Mode instance. (Default of None
        means to use `config.mode` (See below for descriptive string list).

    :param name: an optional name for this fct. If used, the profile mode will
        print the time spent in this fct.

    Currently, the library provides the following mode strings:

     - FAST_RUN (default) (optimize without too much time)

     - FAST_COMPILE (minimal optimization)

     - ProfileMode(deprecated): allow to print a profile mode with mode.print_summary

     - DebugMode: verify many internal conditions that are normally assumed
       (slow)

    :param accept_inplace: True iff the graph can contain inplace operations
        prior to the optimization phase (default is False)

    :param profile: None or ProfileStats instance

    :param on_unused_input: What to do if a variable in the 'inputs' list is
        not used in the graph. Possible values are 'raise', 'warn', 'ignore'
        and None
    """

    # Every element of the input list will be upgraded to an `In` instance if
    # necessary, using the rules implemented by the `convert_function_input`
    # function.

    # Similarly, every element of the output list will be upgraded to an `Out`
    # instance if necessary:

    t1 = time.time()
    mode = theano.compile.mode.get_mode(mode)

    inputs = map(convert_function_input, inputs)
    if outputs is not None:
        if isinstance(outputs, (list, tuple)):
            outputs = map(FunctionMaker.wrap_out, outputs)
        else:
            outputs = FunctionMaker.wrap_out(outputs)

    defaults = [getattr(input, 'value', None) for input in inputs]

    if isinstance(mode, (list, tuple)):  # "mode comparison" semantics
        raise Exception("We do not support the passing of multiple modes")
    else:
        Maker = getattr(mode, 'function_maker', FunctionMaker)
        fn = Maker(inputs,
                   outputs,
                   mode,
                   accept_inplace=accept_inplace,
                   profile=profile,
                   on_unused_input=on_unused_input).create(
                       defaults)

    t2 = time.time()
    if profile:
        profile.compile_time += t2 - t1

    fn.name = name
    fn.maker.fgraph.name = name
    return fn


def convert_function_input(input):
    """
    Upgrade a input shortcut to an In instance.

    The rules for upgrading are as follows:

    - a `Variable` instance r will be upgraded like `In`(r)

    - a tuple (name, r) will be `In`(r, name=name)

    - a tuple (r, val) will be `In`(r, value=value, autoname=True)

    - a tuple ((r,up), val) will be
      `In`(r, value=value, update=up, autoname=True)

    - a tuple (name, r, val) will be `In`(r, name=name, value=value)

    - a tuple (name, (r,up), val) will be
      `In`(r, name=name, value=val, update=up, autoname=True)
    """
    if isinstance(input, (SymbolicInput, SymbolicInputKit)):
        return input
    elif isinstance(input, gof.Constant):
        raise TypeError('A Constant instance is not a legal function input',
                        input)
    elif isinstance(input, gof.Variable):
        return In(input)
    elif isinstance(input, (list, tuple)):
        orig = input
        if not input:
            raise TypeError("Nonsensical input specification: %s" % input)
        if isinstance(input[0], basestring):
            name = input[0]
            input = input[1:]
        else:
            name = None
        if isinstance(input[0], (list, tuple)):
            if len(input[0]) != 2 or len(input) != 2:
                raise TypeError("Invalid input syntax: %s (check "
                                "documentation or use an In instance)" % orig)
            (variable, update), value = input
        elif isinstance(input[0], gof.Variable):
            if len(input) == 1:
                variable, update, value = input[0], None, None
            elif len(input) == 2:
                (variable, value), update = input, None
            else:
                raise TypeError("Invalid input syntax: %s (check "
                                "documentation or use an In instance)" % orig)
        elif isinstance(input[0], (SymbolicInput, SymbolicInputKit)):
            if len(input) == 1:
                return input[0]
            elif len(input) == 2:
                input, value = input
                if name is not None:
                    input.name = name
                input.value = value
                return input
        else:
            raise TypeError("The input specification is not valid: %s" % input)

        if not isinstance(variable, gof.Variable):
            raise TypeError("Unknown input type: %s, expected Variable "
                            "instance" % type(variable), variable)
        if update is not None and not isinstance(update, gof.Variable):
            raise TypeError("Unknown update type: %s, expected Variable "
                            "instance" % type(update), update)
        if (value is not None and
            isinstance(value, (gof.Variable, SymbolicInput))):
            raise TypeError("The value for input %s should not be a Variable "
                            "or SymbolicInput instance (got: %s)" %
                            (variable, value))

        return In(variable, name=name, value=value, update=update)
    else:
        raise TypeError("Unknown input type: %s, expected Variable instance" %
                        type(input), input)


def get_info_on_inputs(named_inputs, n_unnamed_inputs):
    """Return a human-readable description of named and un-named inputs."""
    n_named_inputs = len(named_inputs)

    def get_plural(n):
        if n > 1:
            return 's'
        else:
            return ''

    if n_named_inputs == 0:
        if n_unnamed_inputs == 0:
            msg = 'The function is supposed to have no input.'
        else:
            if n_unnamed_inputs == 1:
                msg = ("The function has a single input variable which has no "
                        "name, and thus cannot be assigned through a keyword"
                        " argument (use 'name=...' in a Variable's "
                        "constructor to give it a name).")
            else:
                # Use plural.
                msg = ("The function has %s inputs, but none of them is named,"
                        " and thus they cannot be assigned through keyword "
                        "arguments (use 'name=...' in a Variable's "
                        "constructor to give it a name)." % n_unnamed_inputs)
    else:
        if n_unnamed_inputs == 0:
            msg = ("The function has %s named input%s (%s)." % (
                n_named_inputs, get_plural(n_named_inputs),
                ', '.join(named_inputs)))
        else:
            msg = ("The function has %s named input%s (%s), and %s unnamed "
                    "input%s which thus cannot be accessed through keyword "
                    "argument%s (use 'name=...' in a variable's constructor "
                    "to give it a name)." % (
                    n_named_inputs, get_plural(n_named_inputs),
                    ', '.join(named_inputs), n_unnamed_inputs,
                    get_plural(n_unnamed_inputs),
                    get_plural(n_unnamed_inputs)))
    return msg
