fp_gl

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

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

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

            lt ->
                First;

            gt ->
                Second
        end end.

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

            lt ->
                Second;

            gt ->
                First
        end end.

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