Fibonacci in ML

Fibonacci sequence is a mathematical sequence of numbers where each number is the sum of the two preceding ones. In programming, Fibonacci sequence is a popular problem-solving task for beginners. Here's how you can implement Fibonacci sequence in ML.

Code

fun fib_seq n =
    let
        fun fib_helper x y count =
            if count = n then y
            else fib_helper (y, x + y) (count + 1)
    in
        if n = 0 then 0
        else fib_helper (0, 1) 1
    end

Explanation

The Fibonacci sequence starts with 0, 1 and then the next number is the sum of the two preceding ones. For example, the third number is 0 + 1 = 1, the fourth number is 1 + 1 = 2 and so on.

In this ML code, we define a function fib_seq that takes an integer n as an input and returns the nth Fibonacci number.

The function works by calling a helper function fib_helper which takes in two integers x and y and a counter count. The count keeps track of how many numbers have been generated so far, starting from 1.

If count equals n, the function returns the Fibonacci number generated so far, which is y. If not, it calls itself with y and x + y as the new values of x and y respectively, and count+1 as the new value of count.

In the fib_seq function, if n is 0, it returns 0 as the Fibonacci number. Otherwise, it calls fib_helper with (0,1) as the initial values of x and y respectively, and 1 as the initial value of count.

Usage

To use this code, you can load it into the SML REPL or compiler and call it like this:

- fib_seq 0;
val it = 0 : int

- fib_seq 10;
val it = 55 : int

- fib_seq 20;
val it = 6765 : int

Conclusion

Fibonacci series is a common task in programming interviews and implementing it in different programming languages can be a good exercise for beginners to practice their problem-solving and programming skills. Implementing Fibonacci sequence in ML demonstrates the use of functional programming concepts like recursion, pattern matching, and immutable variables, typical of languages in the ML family.