A Fold for Every Occasion We can actually come up with a generic notion of folding which can apply to a whole bunch of different types. That is, we can systematically define a fold function for lists, trees and more. This generic notion of fold corresponds to the catamorphisms @pelotom mentioned in his comment. Recursive … Read more
Now that you’ve edited to ask an almost completely different question, I’ll give a different answer. Rather than point to a tutorial on maps and folds, I’ll just give one. In Scala, you first need to know how to create an anonymous function. It goes like so, from most general to more specific: (var1: Type1, … Read more
The Pythonic way of summing an array is using sum. For other purposes, you can sometimes use some combination of reduce (from the functools module) and the operator module, e.g.: def product(xs): return reduce(operator.mul, xs, 1) Be aware that reduce is actually a foldl, in Haskell terms. There is no special syntax to perform folds, … Read more
Welcome to the world of lazy evaluation. When you think about it in terms of strict evaluation, foldl looks “good” and foldr looks “bad” because foldl is tail recursive, but foldr would have to build a tower in the stack so it can process the last item first. However, lazy evaluation turns the tables. Take, … Read more
Some explanations are in order! What is the id function for? What is the role of? Why should we need it here? id is the identity function, id x = x, and is used as the equivalent of zero when building up a chain of functions with function composition, (.). You can find it defined … Read more
How folds differ seems to be a frequent source of confusion, so here’s a more general overview: Consider folding a list of n values [x1, x2, x3, x4 … xn ] with some function f and seed z. foldl is: Left associative: f ( … (f (f (f (f z x1) x2) x3) x4) …) … Read more
reduce vs foldLeft A big big difference, not mentioned in any other stackoverflow answer relating to this topic clearly, is that reduce should be given a commutative monoid, i.e. an operation that is both commutative and associative. This means the operation can be parallelized. This distinction is very important for Big Data / MPP / … Read more