CS 61A Lab 10

Iterators, Generators, Streams, and Tail-Calls

Iterators

Remember the for loop? (We really hope so.) The object that the for loop iterates over is required to be an iterable!

for elem in iterable:
    # do something

for loops only work with iterables, and that means that the object you want to use a for loop on must implement the iterable interface. In particular, a for loop makes use of two methods: __iter__ and __next__. In other words, an object that implements the iterable interface must implement an __iter__ method that returns an object that implements the __next__ method.

This object that implements the __next__ method is called an iterator. While the iterator interface also requires that the object implement the __next__ and __iter__ methods, it does not require the __iter__ method to return a new object.

Here is an example of a class definition for an object that implements the iterator interface:

class AnIterator(object):
    def __init__(self):
        self.current = 0

    def __next__(self):
        if self.current > 5:
            raise StopIteration
        self.current += 1
        return self.current

    def __iter__(self):
        return self

Let's go ahead and try out our new toy.

>>> for i in AnIterator():
...     print(i)
...
1
2
3
4
5

This is somewhat equivalent to running:

t = AnIterator()
t = t.__iter__()
try:
    while True:
        print(t.__next__())
except StopIteration as e:
    pass

Q1

Try running each of the given iterators in a for loop. Why does each work or not work?

class IteratorA(object):
    def __init__(self):
        self.start = 5

    def __next__(self):
        if self.start == 100:
            raise StopIteration
        self.start += 5
        return self.start

    def __iter__(self):
        return self
class IteratorB(object):
    def __init__(self):
        self.start = 5

    def __iter__(self):
        return self
class IteratorC(object):
    def __init__(self):
        self.start = 5

    def __next__(self):
        if self.start == 10:
            raise StopIteration
        self.start += 1
        return self.start
class IteratorD(object):
    def __init__(self):
        self.start = 1

    def __next__(self):
        self.start += 1
        return self.start

    def __iter__(self):
        return self

Watch out on this one. The amount of output might scare you.

For one of the above iterators that works, try this:

>>> i = IteratorA()
>>> for item in i:
...     print(item)

Then again:

>>> for item in i:
...     print(item)

With that in mind, try writing an iterator that "restarts" every time it is run through a for loop.

>>> i = IteratorRestart(2, 7)
>>> for item in i:
...     print(item)
# should print 2 to 7
>>> for item in i:
...     print(item)
# should still print 2 to 7

Q2

Write an iterator that takes a string as input:

>>> s = Str("hello")
>>> for char in s:
...     print(char)
...
h
e
l
l
o

Generators

A generator is a special type of iterator that can be written using a yield statement:

def <generator_function>():
    <somevariable> = <something>
    while <predicate>:
        yield <something>
        <increment variable>

A generator function can also be run through a for loop:

def generator():
    i = 0
    while i < 6:
        yield i
        i += 1

for i in generator():
    print(i)

To better figure out what is happening, try this:

def generator():
    print("Starting here")
    i = 0
    while i < 6:
        print("Before yield")
        yield i
        print("After yield")
        i += 1

>>> g = generator()
>>> g
___ # what is this thing?
>>> g.__iter__()
___
>>> g.__next__()
___
>>> g.__next__()
____

Trace through the code and make sure you know where and why each statement is printed.

You might have noticed from the Iterators section that the Iterator defined without a __next__ method failed to run in the for loop. However, this is not always the case.

class IterGen(object):
    def __init__(self):
        self.start = 5

    def __iter__(self):
        while self.start < 10:
            self.start += 1
            yield self.start

for i in IterGen():
    print(i)

Think for a moment about why that works.

Think more.

Longer.

Okay, I'll tell you.

The for loop only expects the object returned by __iter__ to have a __next__ method, and the __iter__ method is a generator function in this case. Therefore, when __iter__ is called, it returns a generator object, which you can call __next__ on.

Q3

Write a generator that counts down to 0.

Write it in both ways: using a generator function on its own, and within the __iter__ method of a class.

def countdown(n):
    """
    >>> for number in countdown(5):
    ...     print(number)
    ...
    5
    4
    3
    2
    1
    0
    """
class Countdown(object):

Q4

Like in the iterator section, write a generator that outputs each character of a string.

def char_gen(str):
    """
    >>> for char in char_gen("hello"):
    ...     print(char)
    ...
    h
    e
    l
    l
    o
    """

Q5

Write a generator that outputs the hailstone sequence from homework 1.

def hailstone(n):
    """
    >>> for num in hailstone(10):
    ...     print(num)
    ...
    10
    5
    16
    8
    4
    2
    1
    """

And now you know how for loops work! Or more importantly, you have become a better computer scientist.

Streams

A stream is our third example of a lazy sequence. A stream is a lazily evaluated RList. In other words, the stream's elements (except for the first element) are only evaluated when the values are needed.

Take a look at the following code:

class Stream:
    class empty:
        def __repr__(self):
            return 'Stream.empty'
    empty = empty()

    def __init__(self, first, compute_rest=lambda: Stream.empty):
        assert callable(compute_rest), 'compute_rest must be callable.'
        self.first = first
        self._compute_rest = compute_rest

    @property
    def rest(self):
        if self._compute_rest is not None:
            self._rest = self._compute_rest()
            self._compute_rest = None
        return self._rest

    def __repr__(self):
        return 'Stream({0}, <...>)'.format(repr(self.first))

We represent Streams using Python objects, similar to the way we defined RLists. We nest streams inside one another, and compute one element of the sequence at a time.

Note that instead of specifying all of the elements in __init__, we provide a function, compute_rest, that encapsulates the algorithm used to calculate the remaining elements of the stream. Remember that the code in the function body is not evaluated until it is called, which lets us implement the desired evaluation behavior.

This implementation of streams also uses memoization. The first time a program asks a Stream for its rest field, the Stream code computes the required value using compute_rest, saves the resulting value, and then returns it. After that, every time the rest field is referenced, the stored value is simply returned and it is not computed again.

Here is an example:

def make_integer_stream(first=1):
    def compute_rest():
        return make_integer_stream(first+1)
    return Stream(first, compute_rest)

Notice what is happening here. We start out with a stream whose first element is 1, and whose compute_rest function creates another stream. So when we do compute the rest, we get another stream whose first element is one greater than the previous element, and whose compute_rest creates another stream. Hence, we effectively get an infinite stream of integers, computed one at a time. This is almost like an infinite recursion, but one which can be viewed one step at a time, and so does not crash.

Q1

Write a procedure make_fib_stream() that creates an infinite stream of Fibonacci Numbers. Make the first two elements of the stream 0 and 1.

Hint: Consider using a helper procedure that can take two arguments, then think about how to start calling that procedure.

def make_fib_stream():

Q2

Write a procedure sub_streams that takes in two streams s1, s2, and returns a new stream that is the result of subtracting elements from s1 by elements from s2. For instance, if s1 was (1, 2, 3, ...) and s2 was (2, 4, 6, ...), then the output would be the stream (-1, -2, -3, ...). You can assume that both Streams are infinite.

def sub_streams(s1, s2):

Q3

Define a procedure that inputs an infinite Stream, s, and a target value and returns True if the stream converges to the target within a certain number of values. For this example we will say the stream converges if the difference between two consecutive values and the difference between the value and the target drop below max_diff for 10 consecutive values. (Hint: create the stream of differences between consecutive elements using sub_streams)

def converges_to(s, target, max_diff=0.00001, num_values=100):

Higher Order Functions on Streams

Naturally, as the theme has always been in this class, we can abstract our stream procedures to be higher order. Take a look at filter_stream:

def filter_stream(filter_func, stream):
    def make_filtered_rest():
        return filter_stream(filter_func, stream.rest)
    if stream is Stream.empty:
        return stream
    elif filter_func(stream.first):
        return Stream(stream.first, make_filtered_rest)
    else:
        return filter_stream(filter_funct, stream.rest)

You can see how this function might be useful. Notice how the Stream we create has as its compute_rest function a procedure that promises to filter out the rest of the Stream when asked. So at any one point, the entire stream has not been filtered. Instead, only the part of the stream that has been referenced has been filtered, but the rest will be filtered when asked. We can model other higher order Stream procedures after this one, and we can combine our higher order Stream procedures to do incredible things!

Q4

In a similar model to filter_stream, let's recreate the procedure map_stream from lecture, that given a stream stream and a one-argument function func, returns a new stream that is the result of applying func on every element in stream.

def stream_map(func, stream):

Q5

What does the following Stream output? Try writing out the first few values of the stream to see the pattern.

def my_stream():
    def compute_rest():
        return add_streams(map_stream(double, 
                                      my_stream()), 
                                      my_stream())
    return Stream(1, compute_rest)

Tail Calls

Recall from lecture that Scheme supports tail-call optimization. The example we used was factorial (shown in both Python and Scheme):

def fact(n):
    if n == 0:
        return 1
    return n * fact(n - 1)

(define (fact n)
    (if (= n 0)
        1
        (* n (fact (- n 1)))))

Notice that in this version of factorial, the return expressions both use recursive calls, and then use the values for more "work." In other words, the current frame needs to sit around, waiting for the recursive call to return with a value. Then the current frame can use that value to calculate the final answer.

As an example, consider a call to fact(5) (Shown with Scheme below). We make a new frame for the call, and in carrying out the body of the function, we hit the recursive case, where we want to multiply 5 by the return value of the call to fact(4). Then we want to return this product as the answer to fact(5). However, before calculating this product, we must wait for the call to fact(4). The current frame stays while it waits. This is true for every successive recursive call, so by calling fact(5), at one point we will have the frame of fact(5) as well as the frames of fact(4), fact(3), fact(2), and fact(1), all waiting for fact(0).

(fact 5)
(* 5 (fact 4))
(* 5 (* 4 (fact 3)))
(* 5 (* 4 (* 3 (fact 2))))
(* 5 (* 4 (* 3 (* 2 (fact 1)))))
(* 5 (* 4 (* 3 (* 2 (* 1 (fact 0))))))
(* 5 (* 4 (* 3 (* 2 (* 1 1)))))
(* 5 (* 4 (* 3 (* 2 1))))
(* 5 (* 4 (* 3 2)))
(* 5 (* 4 6))
(* 5 24)
120

Keeping all these frames around wastes a lot of space, so our goal is to come up with an implementation of factorial that uses a constant amount of space. We notice that in Python we can do this with a while loop:

def fact_while(n):
    total = 1
    while n > 0:
        total = total * n
        n = n - 1
    return total

However, Scheme doesn't have for and while constructs. No problem! Everything that can be written with while and for loops and also be written recursively. Instead of a variable, we introduce a new parameter to keep track of the total.

def fact(n):
    def fact_optimized(n, total):
        if n == 0:
            return total
        return fact_optimized(n - 1, total * n)
    return fact_optimized(n, 1)

(define (fact n)
    (define (fact-optimized n total)
        (if (= n 0)
            total
            (fact-optimized (- n 1) (* total n))))
    (fact-optimized n 1))

Why is this better?

Because Scheme supports tail-call optimization (note that Python does not), it knows when it no longer needs to keep around frames because there is no further calculation to do. Looking at the last line in fact_optimized, we notice that it returns the same thing that the recursive call does, no more work required. Scheme realizes that there is no reason to keep around a frame that has no work left to do, so it just has the return of the recursive call return directly to whatever called the current frame.

Therefore the last line in fact_optimized is a tail-call.

Q1

To sum it up (with vocabulary!), here is the quote from lecture: "A procedure call that has not yet returned is active. Some procedure calls are tail calls. A Scheme interpreter should support an unbounded number of active tail calls."

A tail call is a call expression in a tail context:

Call expressions in "tail contexts" are tail calls, because there is no reason to keep the current frame "active."

For the following procedures, decide whether each is tail-call optimized. Do not run the procedures (they may not work)!

Check the recursive calls in tail positions (there might be multiple). Is it in a tail context? In other words, does the last recursive call need to return to the caller because there is still more work to be done with it?

List what each of the tail-calls are to help decide if they are optimized.

(define (question-a x)
    (if (= x 0)
        0
        (+ x (question-a (- x 1)))))
(define (question-b x y)
    (if (= x 0)
        y
        (question-b (- x 1) (+ y x))))
(define (question-c x y)
    (if (= x y)
        #t
        (if (< x y)
            #f
            (or (question-c (- x 1) (- y 2)) #f))))
(define (question-d x y)
    (cond ((= x y) #t)
            ((< x y) #f)
            (else (or #f (question-d (- x 1) (- y 2))))))
(define (question-e x y)
    (if (> x y)
        (question-e (- y 1) x)
        (question-e (+ x 10) y)))
(define (question-f n)
    (if (question-f n)
        (question-f (- n 1))
        (question-f (+ n 10))))

Q2

Write a function last, which takes in a Scheme list and returns the last element of the list. Make sure it is tail recursive!

(define (last s)

Q3

Write the tail recursive version of a function that returns the nth fibonacci number. It might be beneficial to try writing a normal recursive solution and/or a iterative Python version first.

(define (fib n)

Q4

Write a tail-recursive function reverse that takes in a Scheme list a returns a reversed copy. Hint: use a helper function!

(define (reverse-iter lst)

Q5

Write a tail-recursive function that inserts number n into a sorted list of numbers, s. Hint: Use the built-in scheme function append.

(define (insert n s)