<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def all_partitions(mechanism, purview, node_labels=None):
 """Return all possible partitions of a mechanism and purview. Partitions can consist of any number of parts. Args: mechanism (tuple[int]):
 A mechanism. purview (tuple[int]):
 A purview. Yields: KPartition: A partition of this mechanism and purview into ``k`` parts. """

    for mechanism_partition in partitions(mechanism):
        mechanism_partition.append([])
        n_mechanism_parts = len(mechanism_partition)
        max_purview_partition = min(len(purview), n_mechanism_parts)
        for n_purview_parts in range(1, max_purview_partition + 1):
            n_empty = n_mechanism_parts - n_purview_parts
            for purview_partition in k_partitions(purview, n_purview_parts):
                purview_partition = [tuple(_list)
                                     for _list in purview_partition]
                # Extend with empty tuples so purview partition has same size
                # as mechanism purview
                purview_partition.extend([()] * n_empty)

                # Unique permutations to avoid duplicates empties
                for purview_permutation in set(
                        permutations(purview_partition)):

                    parts = [
                        Part(tuple(m), tuple(p))
                        for m, p in zip(mechanism_partition,
                                        purview_permutation)
                    ]

                    # Must partition the mechanism, unless the purview is fully
                    # cut away from the mechanism.
                    if parts[0].mechanism == mechanism and parts[0].purview:
                        continue

                    yield KPartition(*parts, node_labels=node_labels)