fold: Successively apply a function to the elements of a sequence
In zatonovo/lambda.tools: Tools for Modeling Data with Functional Programming

Description Arguments Value Usage Details Author(s) References See Also Examples

Apply a function to each element of a sequence and the accumulated value of the previous function applications

`x`	Any indexable data structure
`fn`	A binary operator
`acc`	Accumulator

An object containing the accumulated result.

fold(x, fn, acc, ...) %::% . : Function : . : ... : .

fold(x, fn, acc, ...)

The fold operation is a generalization of the summation and product operators in mathematics. The idea is that the elements of a sequence can have a function applied to them and then can be aggregated in some arbitrary way. In terms of the summation operator, the general structure is sum f(x_i). This means that the function f is applied to each element of x and then added to some intermediate accumulator. This is equivalent to a function f' : A x B -> B where the single function is responsible for both applying f and also aggregating the accumulated value.

A 2D fold is similar to a 2D map in the sense that the function operates on the columns of x. This indicates that fn takes a vector and not a scalar as the first argument. If fn is vectorized, then the behavior of fold will be equivalent to a 2D map over the rows!

Brian Lee Yung Rowe

Haskell Wiki, http://www.haskell.org/haskellwiki/Fold

Brian Lee Yung Rowe, Modeling Data With Functional Programming In R.

map foldrange foldblock

x <- 1:10

# This is equivalent to the summation operator
sum(x) == fold(x, function(a,b) a+b, 0)
sum(x^2) == fold(x, function(a,b) a^2 + b, 0)

# This is equivalent to the product operator
prod(x) == fold(x, function(a,b) a*b, 1)

# Note the equivalence with map
x <- matrix(1:24, ncol=4)
map(t(x), function(a) sum(a)) == fold(x, function(a,b) a + b, 0)