% @doc
% library of truth tables
-module(wfc_tts).

-export_type([
    bit/0,
    tt1/0,
    tt2/0
]).

-export([
    % porcelains
    lnot/1,
    lxor/2,
    land/2,
    lior/2,
    limplies/2,
    limpliedby/2,
    liff/2,
    % basic truth tables arity 1
    tt1_r1/1, tt1_r2/1,
    % basic truth tables arity 2
    tt2_r1/2, tt2_r2/2, tt2_r3/2, tt2_r4/2
]).

-type bit() :: 0 | 1.
-type tt1() :: fun(( bit() ) -> bit() ).
-type tt2() :: fun(( bit() ) -> bit)( ).

%% convert truth tables to fixed-arity sentence-functions
%% easiest approach is to use boole-mobius transform


tt1_r1(0) -> 1;
tt1_r1(1) -> 0.

tt1_r2(0) -> 0;
tt1_r2(1) -> 1.

tt2_r1(0, 0) -> 1;
tt2_r1(1, 0) -> 0;
tt2_r1(0, 1) -> 0;
tt2_r1(1, 1) -> 0.

tt2_r2(0, 0) -> 0;
tt2_r2(1, 0) -> 1;
tt2_r2(0, 1) -> 0;
tt2_r2(1, 1) -> 0.

tt2_r3(0, 0) -> 0;
tt2_r3(1, 0) -> 0;
tt2_r3(0, 1) -> 1;
tt2_r3(1, 1) -> 0.

tt2_r4(0, 0) -> 0;
tt2_r4(1, 0) -> 0;
tt2_r4(0, 1) -> 0;
tt2_r4(1, 1) -> 1.

lnot(0) -> 1;
lnot(1) -> 0.

lxor(0, 0) -> 0;
lxor(1, 0) -> 1;
lxor(0, 1) -> 1;
lxor(1, 1) -> 0.

land(0, 0) -> 0;
land(1, 0) -> 0;
land(0, 1) -> 0;
land(1, 1) -> 1.

lior(0, 0) -> 0;
lior(1, 0) -> 1;
lior(0, 1) -> 1;
lior(1, 1) -> 1.

limplies(0, 0) -> 1;
limplies(1, 0) -> 0;
limplies(0, 1) -> 1;
limplies(1, 1) -> 1.

limpliedby(X, Y) ->
    limplies(Y, X).

liff(X, Y) ->
    land(limplies(X, Y), limpliedby(X, Y)).