Catamorphism

Catamorphism is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

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
• Catamorphism

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>

Perl 6

Any infix operator, either built-in or user-defined, may be turned into a reduce operator by putting it into square brackets (known as "the reduce metaoperator") and using it as a list operator. The operations will work left-to-right or right-to-left automatically depending on the natural associativity of the base operator. <lang perl6>my @list = 1..10; say [+] @list; say [*] @list; say [~] @list;</lang>

Output:

55
3628800
12345678910

In addition to the reduce metaoperator, a general higher-order function, reduce, can apply any appropriate function. Reproducing the above in this form, using the function names of those operators, we have: <lang perl6>say reduce &infix:<+>, @list; say reduce &infix:<*>, @list; say reduce &infix:<~>, @list;</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>

Additional example

<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>