In this homework you will implement currying using OO techniques and operator overloading in Python. Currying is the technique of transforming a function that takes multiple arguments in such a way that it can be called as a chain of functions. This is better explained using an example.

Say we have a function add that adds a bunch of numbers. Rather than writing add(3, 5, 4, 1) we want to use currying to create an adder function that can be extended using a chain of calls. We would then have adder(3)(5)(4)(1)(). Let us assume we have the currying function that can create this adder given the add2 function (the binary version of add) and a start value. Let us call it curry. Then we have adder = curry(add2, 0).

In the general case, curry(add2, ival) returns us an adder function that can do two things:

1. Create another adder function like itself by adding a specified value to its current value (e.g. adder(aval)),
2. Return us its current value, via adder(). A few examples follow:

   add2 = lambda x, y : x + y  
   adder = curry(add2, 5) # creates a 5 adder
   print adder() # prints 5
   adder = adder(3) # creates an 8 adder 
   print adder() # prints 8
   print adder(2)() # prints 10
   print adder(1)() # prints 9
   print

Now assume that the curry function takes an optional parameter called kind. If its value is “Eager” (which is the default), then the resulting curried function behaves such that when a new value is added via (val) the new result is computed right away, eagerly. If the parameter value is “Lazy”, then the resulting curried function behaves such that when a new value is added via (val) it is just 'remembered' and the entire result is computed lazily, when the () operation is performed for the first time. Here is an example:

    adder0 = curry(add2, 0) # Eager
    adder18 = adder0(3)(4,5)(6)
    print adder18() # prints 18
    print adder18(2)() # prints 20
    print

    lazyAdder0 = curry(add2, 0, 'Lazy')
    lazyAdder18 = lazyAdder0(3)(4,5)(6)
    print lazyAdder18() # prints 18
    print lazyAdder18(2)() # prints 20

The two code segments above would behave exactly the same, because the laziness of the evaluation does not change the result. However, consider the following alternative:

    def sleepingAdd(x, y):
        import time
        for i in xrange(0, y):
            print ".",
            time.sleep(1);
        return x + y;
    
    sadder0 = curry(sleepingAdd, 0)
    print "Hey",
    sadder10 = sadder0(3)(4,2)(1) # sleeps 10 secs (prints 10 dots) 
    print "Yo"
    print sadder10() # prints 10
    print "Hey",
    sadder10() # returns 10
    print "Yo"
    print
    
    lazySadder0 = curry(sleepingAdd, 0, 'Lazy')
    print "Hey",
    lazySadder10 =  lazySadder0(3)(4,2)(1) 
    print "Yo"
    print lazySadder10() # sleeps 10 secs (prints 10 dots), prints 10
    print "Hey",
    lazySadder10() # returns 10
    print "Yo"

This time, we replaced the add2 function that was curried with the sleepingAdd function. The latter is a function with a side effect, as it prints dots to the output. A consequence of this is that, the two outputs corresponding to the above two code segments would be different. Here is what the output looks like:

Hey . . . . . . . . . . Yo
10
Hey Yo

Hey Yo
. . . . . . . . . . 10
Hey Yo

There are two deliverables:

D1) Write a report explaining what you understand from eager and lazy evaluation. Describe why the above example gives two different outputs.

D2) Implement the curry function. Some hints follow:

1. The curry function will return an object. This object would be an instance of a class you write. In fact, you have to write two classes: one for the eager version and one for the lazy version.
2. The class you write will overload the () operator. Depending on the number of arguments, it will behave differently. If there are no arguments, then the result of the computation is returned. If there are one or more arguments, then a new object that incorporates additional values are returned.
3. In summary, you would be using objects to emulate functions, via overloading the () operator.

Note: This homework requires learning about the following things in Python:

• Defining functions and lambdas (only used in the example code above)
• Handling variable number of arguments in functions
• Defining classes, instantiating and using objects
• Operator overloading

Put your code and report under a directory named lastname_name_hw2 and make an archive from that directory. Your report should be named lastname_name_hw2.pdf (or .txt). For example, the following Unix commands could be used:

    mkdir lastname_name_hw2
    cd lastname_name
        ...
        (edit and test your files in this directory)
        ...
    cd ..
    tar -cvzf lastname_name_hw2.tar.gz lastname_name_hw2

Then e-mail this newly generated file (named lastname_name_hw2.tar.gz) to your TA Doğukan Çağatay (dogukan.cagatay@bilkent.edu.tr).

Collaboration on the homework is not allowed. Reports in formats other than .txt and .pdf are not accepted.