sf <-> tt logic seems done

2025-10-11 06:55:16 -06:00
parent 7560ee9151
commit 25bcfda65c
2 changed files with 18 additions and 1 deletions
@@ -0,0 +1,87 @@
+% @doc
+% library of truth tables
+-module(wfc_ttfuns).
+
+-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()) -> 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)).