In Haskell, `
foldl
` and `
foldr
` are higher-order functions that allow you to reduce a list to a single value by applying a binary operation to the elements of the list. The key difference between `foldl` and `foldr` lies in their evaluation order and associativity.
1. `foldl` (Left Fold) : * `foldl` is a left-associative fold that starts from the leftmost element of the list and accumulates the result by repeatedly applying the binary operation.
* It evaluates the list elements in a left-to-right fashion, one at a time, and updates the accumulator on each step.
* The type signature of `
foldl
` is: `
foldl :: (b -> a -> b) -> b -> [a] -> b
`.
2. `foldr` (Right Fold) : * `foldr` is a right-associative fold that starts from the rightmost element of the list and accumulates the result by repeatedly applying the binary operation.
* It evaluates the list elements in a right-to-left fashion, one at a time, and updates the accumulator on each step.
* The type signature of `
foldr
` is: `
foldr :: (a -> b -> b) -> b -> [a] -> b
`.
Key Differences :* Evaluation Order: `foldl` evaluates the list from left to right, while `foldr` evaluates the list from right to left.
* Associativity: `foldl` is left-associative, meaning it groups elements from the left side first, while `foldr` is right-associative, grouping elements from the right side first.
* Laziness: `foldr` has better support for lazy evaluation, allowing it to work with infinite lists or potentially large data structures more efficiently. `foldl` is not suitable for processing infinite lists due to strict left evaluation.
* Performance: In general, `foldr` is more efficient for lazy evaluation and right-associative operations, while `foldl` is more efficient for strict left-associative operations. However, the performance characteristics can vary depending on the specific operation and data structure.
Choosing between `
foldl
` and `
foldr
` depends on the specific use case, desired evaluation order, associativity requirements, and potential performance considerations.