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Question

import { Magma } from 'fp-ts/Magma'

const MagmaSub: Magma<number> = {
  concat: (first, second) => first - second
}

The fact that concat is a closed operation isn't a trivial detail. If A is the set of natural numbers (defined as positive integers) instead of the JavaScript number type (a set of positive and negative floats), could we define a Magma<Natural> with concat implemented like in MagmaSub? Can you think of any other concat operation on natural numbers for which the closure property isn't valid?

Answer

With natural numbers, the substraction operation cannot define a Magma. a - b with b being greater than a results in a negative number which is not a natural number.

Here are other examples of concat operation on natural numbers for which the closure property isn't valid:

  • concat: (first, second) => first / second
  • concat: (first, second) => (first + second) / 2