Hey. Hope you have been enjoying the series so far.
Today is the Day 5 of the #100DaysOfCodeChallenge. Received a problem previously asked by Jane Street (refer the hyperlink for the company details) with a medium tag to it. This question is a true puzzle and can be solved in a minute if your functional programming understanding is strong.

You may get confused with the question, just like the way I did. I will try my best in putting the solution in the simplest way possible. You can always reach out to me if you need help.

The Question On Day #5:

cons(a, b) constructs a pair, and car(pair) and cdr(pair) returns the first and last element of that pair. For example, car(cons(3, 4)) returns 3, and cdr(cons(3, 4)) returns 4.

Given this implementation of cons:

def cons(a, b):
    def pair(f):
        return f(a, b)
    return pair

Implement car and cdr.

Explanation

The question is a bit confusing but let us try to understand it clearly.

• cons is a function which takes two inputs (consider integers). It returns a value which is an function defined inside itself, i.e. pair.
• pair is a function which takes a function f as input and returns the return value of its input function, i.e. the return value of the function f is returned by pair.
• Now f is a function which will return a value.
• f is the key to all our solution.

Algorithm

• The end value obtained on calling the function cons is a function pointer pointing to the pair function.
• The required implementation goes as follows:

Python Code

Output
3
4

Explanation

When car(cons(3,4)) is called,

1. cons(3,4) is invoked in the first place.
2. cons returns the function pair function.
3. The parameter passed to the car function is the pair function.
4. car function returns the value returned by calling the pair function.
5. pair function takes a function as input, so we pass the left function to it.
6. pair function returns the value obtained by passing a, b to a a function f. So, our left is the function f, which takes a, b as input and returns a as output to the pair function.
7. Now the same a is returned by pair function to the car function, which will again return the same value of a.
8. Now a is returned at the end and printed.
9. Same goes with the function cdr.

The Python visualiser is very much needed to understand this logic more clearly, please refer it here.

I hope you were able to understand this problem.
Feel free to reach out for any query clearance.

Thanks and cheers:)