Describe semigroups about fantasy-land HOT 6 CLOSED

Perhaps a simple example?

from fantasy-land.

Yeah, I want to include a description of each class. See #3.

from fantasy-land.

Set of nonempty strings might be slightly interesting, though I think when you get less structure than a monoid you are usually taking a "normal" programming structure and restricting it.

from fantasy-land.

How about Either? It seems to be one of the few semigroups that's not just a monoid missing zero.

function Either(left, right) {
  if ((typeof left !== 'undefined' && typeof right !== 'undefined') ||
      (typeof left === 'undefined' && typeof right === 'undefined'))
    throw new Error();
  this.left  = left;
  this.right = right;
  return this;
}

// "Takes the first `right`."
Either.prototype.concat = function(a) {
  if (typeof this.right !== 'undefined')
    return new Either(undefined, this.right);
  else
    return new Either(a.left, a.right);
};

from fantasy-land.

We don't have to only work with structures that are strictly semigroups. If it's a monoid, then it's a semigroup by definition, and there's a whole mess of those. You just don't worry about what the identity does if you come in contact with it.

from fantasy-land.

Is this still going to be the intention or we happy to close this one?

from fantasy-land.