hacky as fuck truth table <-> sentence-fun logic works

src/wfc.erl

@@ -114,3 +114,7 @@ mul([Arg | Rest]) ->
     end;
 mul([]) ->
     {ok, wfc_sentence:one()}.
+
+
+zero() -> wfc_sentence:zero().
+one() -> wfc_sentence:one().

src/wfc_bm.erl

@@ -27,6 +27,7 @@
     blocks/1,
     %% fancier constructors
     from_list/1, bmt/1,
+    row/1, col/1,
     %% useful operations
     transpose/1, from_bitfun/2,
     to_list/1
@@ -117,7 +118,7 @@ rth(RowIdx1, {bm, _Shape = {rc, NR, NC}, Bits})
     RowIdx0        = RowIdx1 - 1,
     RowLength      = NC,
     SkipToGetToRow = RowIdx0 * RowLength,
-    <<_:SkipToGetToRow, RowBits:RowLength, _/bits>> = Bits,
+    <<_:SkipToGetToRow, RowBits:RowLength/bits, _/bits>> = Bits,
     {bm, NewShape, RowBits}.
 
 
@@ -213,7 +214,8 @@ mulfold({rc, R, C}, Shape, AccBits, M1, M2) ->
 dot({bm, {rc, 1, Same}, Bits1}, {bm, {rc, Same, 1}, Bits2}) ->
     <<Int1:Same>> = Bits1,
     <<Int2:Same>> = Bits2,
-    SummandBits   = Int1 band Int2,
+    SummandInt    = Int1 band Int2,
+    SummandBits   = <<SummandInt:Same>>,
     parity(SummandBits).
 
 
@@ -322,6 +324,18 @@ bitsy([Bit | Rest], Acc)    -> bitsy(Rest, <<Acc/bits, Bit:1>>);
 bitsy([],           Result) -> Result.
 
 
+-spec row([bit()]) -> bm().
+
+row(Row) ->
+    from_list([Row]).
+
+
+-spec col([bit()]) -> bm().
+
+col(Col) ->
+    transpose(row(Col)).
+
+
 -spec bmt(Arity :: pos_integer()) -> bm().
 % @doc Boole-Mobius transform
 %
@@ -329,8 +343,8 @@ bitsy([],           Result) -> Result.
 
 bmt(N) when N > 0 ->
     %% this might be backwards...
-    blocks([[bmt(N-1), bmt(N-1)],
-            [ztn(N-1), bmt(N-1)]]);
+    blocks([[bmt(N-1), ztn(N-1)],
+            [bmt(N-1), bmt(N-1)]]);
 bmt(0) ->
     from_list([[1]]).
 

src/wfc_sftt.erl

@@ -0,0 +1,149 @@
+% @doc
+% sentence-fun <-> truth table logic
+-module(wfc_sftt).
+
+-export_type([
+    sf/0, tt/0
+]).
+
+-export([
+    arity/1,
+    tt/1, sf/1,
+    sf_to_tt/1, tt_to_sf/1,
+    eval/2,
+    bfls/1,
+    bfl/2
+]).
+
+-type bit() :: 0 | 1.
+-opaque sf() :: {sf, wfc_bm:bm()}.
+-opaque tt() :: {tt, wfc_bm:bm()}.
+
+-spec arity(sf() | tt()) -> pos_integer().
+
+arity({sf, BM}) -> matrix_arity(BM);
+arity({tt, BM}) -> matrix_arity(BM).
+
+matrix_arity(Matrix) ->
+    {rc, Height, _} = wfc_bm:shape(Matrix),
+    log2(Height).
+
+log2(N) when N > 1 ->
+    1 + log2(N div 2);
+log2(1) ->
+    0.
+
+
+-spec sf_to_tt(sf()) -> tt().
+sf_to_tt({sf, SFBM}) ->
+    {tt, apply_bmt(SFBM)}.
+
+
+-spec tt_to_sf(tt()) -> sf().
+tt_to_sf({tt, SFBM}) ->
+    {sf, apply_bmt(SFBM)}.
+
+
+apply_bmt(Matrix) ->
+    BMT = wfc_bm:bmt(matrix_arity(Matrix)),
+    wfc_bm:mul(BMT, Matrix).
+
+
+tt(List) ->
+    {tt, wfc_bm:col(List)}.
+
+sf(List) ->
+    {sf, wfc_bm:col(List)}.
+
+
+-spec eval(sf() | tt(), [wfc:sentence()]) -> wfc:sentence().
+
+eval(TT = {tt, _}, Sentences) ->
+    eval(tt_to_sf(TT), Sentences);
+eval(SF = {sf, SFBM}, Sentences) ->
+    Arity = arity(SF),
+    Arity = length(Sentences),
+    % [0, 0, 0], [1, 0, 0], ...
+    BitFlagLists = bfls(Arity),
+    io:format("bfls: ~p~n", [BitFlagLists]),
+    % an SFBM is a Nx1 matrix where N = two_to_the(Arity)
+    % hacky but works
+    [Row] = wfc_bm:to_list(wfc_bm:transpose(SFBM)),
+    io:format("row: ~p~n", [Row]),
+    % filter by whether or not we're including
+    Included = filter_included(BitFlagLists, Row),
+    io:format("included: ~p~n", [Included]),
+    AlmostSummands = inseminate(Included, Sentences),
+    io:format("Almost: ~p~n", [AlmostSummands]),
+    collapse(AlmostSummands).
+
+
+filter_included([_ | Rest], [0 | Rest2]) ->
+    filter_included(Rest, Rest2);
+filter_included([Item | Rest], [1 | Rest2]) ->
+    [Item | filter_included(Rest, Rest2)];
+filter_included([], []) ->
+    [].
+
+
+-spec collapse([[wfc:sentence()]]) -> wfc:sentence().
+
+collapse(AlmostSummands) ->
+    Summands = lists:map(fun(Args) -> {ok,X} = wfc:mul(Args), X end, AlmostSummands),
+    {ok, Y} = wfc:add(Summands),
+    Y.
+
+
+-spec inseminate(BFLs :: [[bit()]], Sentences :: [wfc:sentence()]) -> [[wfc:sentence()]].
+
+inseminate(BFLs, Sentences) ->
+    lists:map(fun(BFL) -> inseminate2(BFL, Sentences) end, BFLs).
+
+
+-spec inseminate2(BFL :: [bit()], Sentences :: [wfc:sentence()]) -> [wfc:sentence()].
+inseminate2(BFL, Sentences) ->
+    lists:zipwith(fun pair/2, BFL, Sentences).
+
+pair(0, _) -> wfc_sentence:one();
+pair(1, S) -> S.
+
+
+-spec bfls(Arity :: non_neg_integer()) -> [[bit()]].
+% @doc get all bit-flag lists for 0..(2^Arity - 1)
+
+bfls(Arity) when Arity >= 0 ->
+    [bfl(Arity, N) || N <- lists:seq(0, two_to_the(Arity) - 1)].
+
+two_to_the(N) ->
+    1 bsl N.
+
+
+-spec bfl(Length :: pos_integer(), N :: non_neg_integer()) -> [bit()].
+% @doc
+% get the little-endian representation of N as binary, as a
+% list of bits.
+
+bfl(Length, N) when Length > 0, N >= 0 ->
+    %% hacky but logically straightforward
+    bfl2(Length, lists:reverse(integer_to_list(N, 2))).
+
+%% we're chopping digits off the end here
+bfl2(Length, Bits_Str) when Length =< length(Bits_Str) ->
+    bfl3(take(Length, Bits_Str));
+bfl2(Length, Bits_Str) when Length > length(Bits_Str) ->
+    % make more zeros than needed because about to circumcise
+    % them.
+    Zeros = [$0 || _ <- lists:seq(1, Length)],
+    bfl2(Length, Bits_Str ++ Zeros).
+
+
+take(0, _) ->
+    [];
+take(N, [Item | Rest]) when N >= 1 ->
+    [Item | take(N-1, Rest)].
+
+bfl3(BitsText) ->
+   lists:map(fun unfuck_char/1, BitsText).
+
+unfuck_char($0) -> 0;
+unfuck_char($1) -> 1.

src/wfc_tts.erl

@@ -24,8 +24,8 @@
 ]).
 
 -type bit() :: 0 | 1.
--type tt1() :: fun(( bit() ) -> bit() ).
--type tt2() :: fun(( bit() ) -> bit)( ).
+-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