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content/blog/fold-not-only-reduces.md
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content/blog/fold-not-only-reduces.md
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---
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title: "Fold Not Only Reduces"
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date: 2022-11-09T15:15:10-05:00
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draft: false
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tags: []
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math: false
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---
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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`.
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This misconception is aided by one of the most common fold examples: summing a list.
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Scala Example:
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```scala
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List(1, 2, 3, 4, 5).foldLeft(0)((c, n) => c + n)
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// Returns 15
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```
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Haskell Example:
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```haskell
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foldl (+) 0 [1,2,3,4,5]
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-- Returns 15
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```
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However, let us look more closely at the type signature of `foldLeft` on a list of type `X`.
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Haskell:
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```
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(B -> X -> B) -> B -> [X] -> B
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```
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Scala:
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```
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(id: B)(op: (B, X) => B): B
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```
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There are a few things we can note here:
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- The return type is not influenced by the list type `X` at all.
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- The return type must match the type of the id of the fold.
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- 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`)
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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.
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Scala Example:
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```scala
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List(5, 7, 1, 8, 9, 3).foldLeft(List.empty[Int])((c, n) => if n > 5 then c :+ n else c)
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// Returns List(7, 8, 9)
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```
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Haskell Example:
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```haskell
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l5 c n if n > 5 then c ++ [n] else c
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foldl l5 [] [5, 7, 1, 8, 9, 3]
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-- Returns [7,8,9]
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```
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