Example monoids.js

//-- Sum --------------------------------------------------------------
let
  identity = 0,
  mappend  = (x,y) => x + y, // +
  concatSum =
    xs => xs.reduce(mappend, identity)

concatSum([1,2,3,4,5]) // => 15

//-- Product ----------------------------------------------------------
let
  identity = 1,
  mappend  = (x,y) => x * y, // *
  concatProduct =
    xs => xs.reduce(mappend, identity)

concatProduct([1,2,3,4,5]) // => 120

//-- String -----------------------------------------------------------
let
  identity = '',
  mappend  = (x,y) => x + y, // +
  concatString =
    xs => xs.reduce(mappend, identity)

concatString(['Shoreditch',' ', 'JS']) // => 'Shoreditch JS'

//-- Array ------------------------------------------------------------
let
  identity = [],
  mappend  = (xs,ys) => xs.concat(ys), // Array.prototype.concat
  concatArray =
    xs => xs.reduce(mappend, identity)

concatArray([[1,2,3],[1,2,3]]) // => [ 1, 2, 3, 1, 2, 3 ]

//-- Function ---------------------------------------------------------
let
  identity = x => x,
  mappend  = (f,g) => x => f(g(x)), // f ∘ g 
  concatFunction =
    xs => xs.reduce(mappend, identity)

concatFunction([it => it+10, it => it *2])(5) // => 20