-module(ask@equivalence).
-compile([no_auto_import, nowarn_unused_vars, nowarn_unused_function, nowarn_nomatch]).

-export([trivial/0, 'and'/2, 'or'/2, 'not'/1, list/1, pair/2, map_input/2]).

-spec trivial() -> fun((FLQ, FLQ) -> boolean()).
trivial() ->
    fun(_, _) -> true end.

-spec 'and'(fun((FLS, FLS) -> boolean()), fun((FLS, FLS) -> boolean())) -> fun((FLS, FLS) -> boolean()).
'and'(First, Second) ->
    fun(Value, Other) -> First(Value, Other) andalso Second(Value, Other) end.

-spec 'or'(fun((FLW, FLW) -> boolean()), fun((FLW, FLW) -> boolean())) -> fun((FLW, FLW) -> boolean()).
'or'(First, Second) ->
    fun(Value, Other) -> First(Value, Other) orelse Second(Value, Other) end.

-spec 'not'(fun((FMA, FMA) -> boolean())) -> fun((FMA, FMA) -> boolean()).
'not'(Eq) ->
    fun(Value, Other) -> not Eq(Value, Other) end.

-spec list(fun((FMD, FMD) -> boolean())) -> fun((list(FMD), list(FMD)) -> boolean()).
list(Eq) ->
    fun(Values, Others) -> case {Values, Others} of
            {[], []} ->
                true;

            {[Value | Values@1], [Other | Others@1]} ->
                Eq(Value, Other) andalso (list(Eq))(Values@1, Others@1);

            {_, _} ->
                false
        end end.

-spec pair(fun((FMH, FMH) -> boolean()), fun((FMJ, FMJ) -> boolean())) -> fun(({FMH,
    FMJ}, {FMH, FMJ}) -> boolean()).
pair(First, Second) ->
    fun(Value, Other) -> case {Value, Other} of
            {{Value1, Value2}, {Other1, Other2}} ->
                First(Value1, Other1) andalso Second(Value2, Other2)
        end end.

-spec map_input(fun((FMM, FMM) -> boolean()), fun((FMO) -> FMM)) -> fun((FMO, FMO) -> boolean()).
map_input(Eq, Fun) ->
    fun(Value, Other) -> Eq(Fun(Value), Fun(Other)) end.