--- date: 2022-11-09 15:15:10-05:00 draft: false math: false medium_enabled: true medium_post_id: b419f7d25313 tags: - Functional Programming - Scala - Haskell title: Fold Not Only Reduces --- One misconception when first learning about fold is that it takes a list of elements of a certain type (`List[T]`) and "reduces" it to a single item of type `T`. This misconception is aided by one of the most common fold examples: summing a list. Scala Example: ```scala List(1, 2, 3, 4, 5).foldLeft(0)((c, n) => c + n) // Returns 15 ``` Haskell Example: ```haskell foldl (+) 0 [1,2,3,4,5] -- Returns 15 ``` However, let us look more closely at the type signature of `foldLeft` on a list of type `X`. Haskell: ``` (B -> X -> B) -> B -> [X] -> B ``` Scala: ``` (id: B)(op: (B, X) => B): B ``` There are a few things we can note here: - The return type is not influenced by the list type `X` at all. - The return type must match the type of the id of the fold. - The operation takes two arguments, with the first type matching the id/start (`B`) and the second type matching the type within the list (`X`) To show an example of how we don't need to "reduce", let's return the elements of a list that's greater than 5. Scala Example: ```scala List(5, 7, 1, 8, 9, 3).foldLeft(List.empty[Int])((c, n) => if n > 5 then c :+ n else c) // Returns List(7, 8, 9) ``` Haskell Example: ```haskell l5 c n if n > 5 then c ++ [n] else c foldl l5 [] [5, 7, 1, 8, 9, 3] -- Returns [7,8,9] ```