from operator import add, mul, sub

square = lambda x: x * x

identity = lambda x: x

triple = lambda x: 3 * x

increment = lambda x: x + 1

def accumulate(combiner, base, n, term):
    while n > 0:
        base = combiner(base, term(n))
        n = n - 1
    return base

def compose1(f, g):
    """Return a function h, such that h(x) = f(g(x))."""
    def h(x):
        return f(g(x))
    return h


def make_repeater(f, n):
    """Return the function that computes the nth application of f.

    >>> add_three = make_repeater(increment, 3)
    >>> add_three(5)
    8
    >>> make_repeater(triple, 5)(1) # 3 * 3 * 3 * 3 * 3 * 1
    243
    >>> make_repeater(square, 2)(5) # square(square(5))
    625
    >>> make_repeater(square, 4)(5) # square(square(square(square(5))))
    152587890625
    >>> make_repeater(square, 0)(5) # Yes, it makes sense to apply the function zero times!
    5
    """
    return accumulate(compose1, lambda x : x, n, lambda  x : f)


def take_turn(num_rolls, opponent_score, dice=six_sided):
    """Simulate a turn rolling NUM_ROLLS dice, which may be 0 (Free Bacon).
    Return the points scored for the turn by the current player.

    num_rolls:       The number of dice rolls that will be made.
    opponent_score:  The total score of the opponent.
    dice:            A function that simulates a single dice roll outcome.
    """
    # Leave these assert statements here; they help check for errors.
    assert type(num_rolls) == int, 'num_rolls must be an integer.'
    assert num_rolls >= 0, 'Cannot roll a negative number of dice in take_turn.'
    assert num_rolls <= 10, 'Cannot roll more than 10 dice.'
    assert opponent_score < 100, 'The game should be over.'
    # BEGIN PROBLEM 3
    if num_rolls > 0:
        return roll_dice(num_rolls)
    else:
        return free_bacon(opponent_score)
    # END PROBLEM 3

