-module(fp2@ord).
-compile(no_auto_import).

-export([min/1, max/1, get_semigroup/0, get_monoid/0]).

-spec min(fp2@models:ord(ELQ)) -> fun((ELQ, ELQ) -> ELQ).
min(O) ->
    fun(First, Second) -> case (erlang:element(2, O))(First, Second) of
            eq ->
                First;

            lt ->
                First;

            gt ->
                Second
        end end.

-spec max(fp2@models:ord(ELT)) -> fun((ELT, ELT) -> ELT).
max(O) ->
    fun(First, Second) -> case (erlang:element(2, O))(First, Second) of
            eq ->
                First;

            lt ->
                Second;

            gt ->
                First
        end end.

-spec get_semigroup() -> fp2@models:semigroup(fp2@models:ord(any())).
get_semigroup() ->
    {semigroup,
     fun(First, Second) ->
         {ord,
          fun(A, B) ->
              First_res = (erlang:element(2, First))(A, B),
              case First_res of
                  eq ->
                      (erlang:element(2, Second))(A, B);

                  _@1 ->
                      First_res
              end
          end}
     end}.

-spec get_monoid() -> fp2@models:monoid(fp2@models:ord(any())).
get_monoid() ->
    {monoid, erlang:element(2, get_semigroup()), {ord, fun(_, _) -> eq end}}.