{{Short description|Family of higher-order functions}}
In [[functional programming]], a '''fold''' (also termed '''reduce''', '''accumulate''', '''aggregate''', '''compress''', or '''inject''') refers tois a family of [[higher-order function]]s that [[analysis|analyzeanalyzes]] a [[Recursive data type|recursive]] data structure and through use of a given combining operation, recombinerecombines the results of [[recursion|recursively]] processing its constituent parts, building up a return value. Fold also termed as '''reduce''', '''accumulate''', '''aggregate''', '''compress''', or '''inject'''. Typically, a fold is presented with a combining [[Subroutine|function]], a top [[Node (computer science)|node]] of a [[data structure]], and possibly some default values to be used under certain conditions. The fold then proceeds to combine elements of the data structure's [[hierarchy]], using the function in a systematic way.
Folds are in a sense dual to [[Unfold (higher-order function)|unfolds]], which take a ''seed'' value and apply a function [[corecursion|corecursively]] to decide how to progressively construct a corecursive data structure, whereas a fold recursively breaks that structure down, replacing it with the results of applying a combining function at each node on its [[Terminal and nonterminal symbols|terminal]] values and the recursive results ([[catamorphism]], versus [[anamorphism]] of unfolds).
