The first element of this new list is twice the head of the argument, and we obtain the rest of the result by recursively calling doubleList on the tail of the argument. The term tail recursion refers to a form of recursion in which the final operation of a function is a call to the function itself. An exception will be thrown in the case of an empty ByteString. O(1) Extract the elements after the head of a ByteString, which must be non-empty. In the recursive case, doubleList builds up a new list by using (:). The problem with the stack overflow was the result of keeping a long list of computations to do after "this next step." When the tail gets to an empty list, the base case will be invoked and recursion will stop. So this whole thing crashes and burns: Stack space overflow: current size 8388608 bytes. Haskell has many recursive ... (xs) and says that to concatenate the two lists, concatenate the tail of the first list with the second list, and then tack the head x on the front. It is a special case of unionBy, which allows the programmer to supply their own equality test. Accumulating parameters is merely a means to turn an almost tail recursive implementation into a tail recursive implementation. fact2 x = tailFact x 1 where tailFact 0 a = a tailFact n a = tailFact (n-1) (n * a) The fact2 function wraps a call to tailFact a function that’s tail recursive. List-based recursion . More serious performance concerns arise occasionally from Haskell's laziness but we'll talk about it later. If you must write the recursion manually then it's still pretty simple. The union function returns the list union of the two lists. The tail recursive version eliminated the need to store all these computational intermediaries. This is common practice to make functions tail recursive (List.fold_left vs. List.fold_right). myRec :: [a] -> b myRec [] = e myRec (h:t) = f h (myRec t) Note that e and f above are unbound. We should be using the tail recursive fold_left. Haskell have built in type for list recursion, and we can inject some high-order function into the foldl and foldr to get the ideal list we want. The result is as close to the above definition as it gets: Your base case is the empty list. For example, >>> "dog" `union` "cow" "dogcw" Duplicates, and elements of the first list, are removed from the the second list, but if the first list contains duplicates, so will the result. In the non-empty case, you apply the function recursively to the tail, and (optionally) combine that with the head. This is called tail recursion optimization, where the recursive call at the very end of a function is simply turned into a goto to the beginning of the function. Tail Recursion. Now, in a strict language, this would be tail-recursive, and there would be no problem. The key idea of doubly recursive is to use a returned accumulator as another recursion’s accumulator. Notice the difference between foldl and foldr's order of function combination so their high order function injected is slightly different. the recursive part: for a longer list, compare the head of the list and the maximum of the tail (this is where recursion happens); the maximum of the list is the bigger of the two; So let’s write this up in Haskell. However, as Haskell is lazy, my googling has led me to understand that (s+x) and (l+1) will be passed down the recursion as thunks. We should be using the tail recursive fold_left. I want to write the flattening function that takes a nested list and return a flatten one in haskell, however different depths of list are different types and thus you cannot simply write a general function to deal it. Tail recursion is an important programming concept because it allows us to program recursively, but also because xkcd says it is. Thrown in the case of an empty ByteString Extract the elements after the head of a ByteString, which be... 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