Built-in Mathematica Symbol

Fold

Fold[f, x, list]
gives the last element of FoldList[f, x, list].

The head need not be List:

Use Throw to exit a Fold:

Fold to the right:

Create a nested polynomial (Horner form):

HornerForm directly produces this output:

Form a continued fraction:

Form a number from digits:

Form an alternating sum:

Form a binary tree:

Form a left-branching binary tree:

Form a function composition:

Apply an indexed sequence of functions:

Successively partition a list:

Folding with an empty list does not apply the function at all:

Fold returns the last element of FoldList:

Functions that ignore their second argument give the same result as in Nest:

An explicit form of the primitive recursive function r[z, r[s, r[s, r[s, p[2]]]]] [more info]:

Generate all subsets of a set:

Find all possible sums of any of the elements of a list of numbers:

The fourth Swinnerton-Dyer polynomial [more info]: