semigroup-second

Question

Is the following semigroup instance lawful (does it respect semigroup laws)?

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

/** Always return the last argument */
const last = <A>(): Semigroup<A> => ({
  concat: (_first, second) => second
})

Answer

Yes:

• first, second and the result of concat (which is second) are all of the same type A
• concat is associative:
  • concat(concat(first, second), third) evaluates to concat(second, third) which then evaluates to third
  • concat(first, concat(second, third)) evaluates to concat(first, third) which then evaluates to third