Catamorphism

Reduce is a function or method that is used to take the values in an array or a list and apply a function to successive members of the list to produce (or reduce them to), a single value.

Show how reduce (or foldl or foldr etc), work in your language.

Cf.

Fold

C#

<lang csharp>var nums = Enumerable.Range(1, 10);

int summation = nums.Aggregate((a, b) => a + b);

int product = nums.Aggregate((a, b) => a * b);

string concatenation = nums.Aggregate(String.Empty, (a, b) => a.ToString() + b.ToString());

Console.WriteLine("{0} {1} {2}", summation, product, concatenation); </lang>

JavaScript

<lang javascript>var nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10];

function add(a, b) {

   return a + b;

}

var summation = nums.reduce(add);

function mul(a, b) {

   return a * b;

}

var product = nums.reduce(mul, 1);

var concatenation = nums.reduce(add, "");

console.log(summation, product, concatenation); </lang>

Python

<lang python>>>> from operator import add >>> listoflists = [['the', 'cat'], ['sat', 'on'], ['the', 'mat']] >>> help(reduce) Help on built-in function reduce in module __builtin__:

reduce(...)

   reduce(function, sequence[, initial]) -> value
   
   Apply a function of two arguments cumulatively to the items of a sequence,
   from left to right, so as to reduce the sequence to a single value.
   For example, reduce(lambda x, y: x+y, [1, 2, 3, 4, 5]) calculates
   ((((1+2)+3)+4)+5).  If initial is present, it is placed before the items
   of the sequence in the calculation, and serves as a default when the
   sequence is empty.

>>> reduce(add, listoflists, []) ['the', 'cat', 'sat', 'on', 'the', 'mat'] >>> </lang>

Python

<lang python> from functools import reduce from operator import add, mul

nums = range(1,11)

summation = reduce(add, nums)

product = reduce(mul, nums)

concatenation = reduce(lambda a, b: str(a) + str(b), nums)

print(summation, product, concatenation) </lang>