![]() ![]() While this does the job fine for short lists, it can become problematic if your list has a few million values in it. You might have noticed that for a list of 4 terms, we expanded our function call to a single chain of 5 additions. Congratulations on your first useful recursive function in Erlang! Length of a Tail Recursion To see how len/1 would behave when ran, let's try it on a given list, say : Given each value in a list counts as a length of 1, the function can be rewritten the following way:Īnd now you've got your own recursive function to calculate the length of a list. This means we only need to count the first one and the function can call itself on the second element. Note that the second element is a list itself. This means we can use the pattern to match against lists of one or more elements, as a list of length one will be defined as ] and a list of length two will be defined as ]]. It was mentioned earlier that lists are defined recursively as ]]]. Well of course it's useless, because it's not yet recursive, which brings us to the hardest part: extending our function so it calls itself for lists longer than 1 or 0. We can write this down:Īwesome! We can calculate the length of lists, given the length is either 0 or 1! Very useful indeed. This sounds like enough to get going with our definition. Then the next simplest list has a length of 1: = 1. So let's make a mental note that = 0 when dealing with lengths. With most recursive functions, I find the base case easier to write first: what's the simplest input we can have to find a length from? Surely an empty list is the simplest one, with a length of 0. So we know from the beginning that we will need: We'll implement a function to count how many elements a list contains. Let's try to make it slightly more practical. At that point we no longer tell our function to call itself and it stops its execution right there. In our case, the stopping condition is when n is equal to 0. We looped! A definition of recursion could be made short by saying "a function that calls itself." However, we need to have a stopping condition (the real term is base case), because we'd otherwise loop infinitely. So that's quick and easy for some mathematical definitions which are recursive in nature. With the help of pattern matching, we can shorten the definition a bit: We'll rename n! to fac(N) to restrict our syntax a bit and then we get the following:Īnd this factorial function is now done! It's pretty similar to the mathematical definition, really. What we've got here is a function name ( n!), guards (the ifs) and a the function body ( 1 and n((n-1)!)). ![]() Take a look at the parts of the notation: n!, 1 and n((n-1)!) and then the ifs. How can such a function be translated from mathematical notation to Erlang? The conversion is simple enough. For any value above 0, we return n multiplied by the factorial of n-1, which unfolds until it reaches 1: ![]() What this tells us is that if the value of n we have is 0, we return the result 1. Such a function can be expressed the following way in mathematical notation: The factorial of 4 would be 4! = 4 x 3 x 2 x 1 = 24. To give some examples, the factorial of 3 is 3! = 3 x 2 x 1 = 6. x n, or alternatively n x ( n-1) x ( n-2) x. The factorial of a number n is the product of the sequence 1 x 2 x 3 x. A basic mathematical function such as the factorial of a value is a good example of a function that can be expressed recursively. If you don't, you can give them more attention! Recursion can also be explained with the help of mathematical concepts and functions. I suppose you remember how invariable variables were explained in the intro chapter. Instead, functional programmers rely on a silly concept named recursion. The answer to this is "what is a loop?" Truth is, functional programming languages usually do not offer looping constructs like for and while. Some readers accustomed with imperative and object-oriented programming languages might be wondering why loops weren't shown already. However, you might prefer reading it with syntax highlighting, which requires Javascript! Recursion Hello recursion! Hey there, it appears your Javascript is disabled. ![]()
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