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One often wants to choose the [[identity element]] of the operation ''f'' as the initial value ''z''. When no initial value seems appropriate, for example, when one wants to fold the function which computes the maximum of its two parameters over a non-empty list to get the maximum element of the list, there are variants of <code>foldr</code> and <code>foldl</code> which use the last and first element of the list respectively as the initial value. In Haskell and several other languages, these are called <code>foldr1</code> and <code>foldl1</code>, the 1 making reference to the automatic provision of an initial element, and the fact that the lists they are applied to must have at least one element.
These folds use type-symmetrical binary operation: the types of both its arguments, and its result, must be the same. [[Richard Bird (computer scientist)|Richard Bird]] in his 2010 book proposes<ref name="foldrn">Richard Bird, "Pearls of Functional Algorithm Design", Cambridge University Press 2010, {{ISBN|978-0-521-51338-8}}, p. 42</ref> "a general fold function on non-empty lists" <code>foldrn</code> which transforms its last element, by applying an additional argument function to it, into a value of the result type before starting the folding itself, and is thus able to use type-asymmetrical binary operation like the regular <code>foldr</code> to produce a result of type different from the list's elements type.
===Implementation===
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