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Folds can be regarded as consistently replacing the structural components of a data structure with functions and values. Lists, for example, are built up in many functional languages from two primitives: any list is either an empty list, commonly called nil ([]), or is constructed by prefixing an element in front of another list, creating what is called a cons node ( Cons(X1,Cons(X2,Cons ...
Various languages differ on this. Some raise an exception. Some stop after the length of the shortest list and ignore extra items on the other lists. Some continue on to the length of the longest list, and for the lists that have already ended, pass some placeholder value to the function indicating no value.
Here, the list [0..] represents , x^2>3 represents the predicate, and 2*x represents the output expression.. List comprehensions give results in a defined order (unlike the members of sets); and list comprehensions may generate the members of a list in order, rather than produce the entirety of the list thus allowing, for example, the previous Haskell definition of the members of an infinite list.
For example, a ranged loop like for x = 1 to 10 can be implemented as iteration through a generator, as in Python's for x in range(1, 10). Further, break can be implemented as sending finish to the generator and then using continue in the loop.
The types of objects that can be iterated across (my_list in the example) are based on classes that inherit from the library class ITERABLE. The iteration form of the Eiffel loop can also be used as a boolean expression when the keyword loop is replaced by either all (effecting universal quantification) or some (effecting existential ...
[2] [3] [4] The reduction of sets of elements is an integral part of programming models such as Map Reduce, where a reduction operator is applied to all elements before they are reduced. Other parallel algorithms use reduction operators as primary operations to solve more complex problems. Many reduction operators can be used for broadcasting ...
The method was frequently used for testing 'first time' conditions, as in this suitably commented IBM/360 assembler example. It uses instruction overlay to reduce the instruction path length by (N×1)−1 where N is the number of records on the file (−1 being the overhead to perform the overlay).
The loop counter is used to decide when the loop should terminate and for the program flow to continue to the next instruction after the loop. A common identifier naming convention is for the loop counter to use the variable names i , j , and k (and so on if needed), where i would be the most outer loop, j the next inner loop, etc.