too fucking tired... going to bed

src/wfc_sentence.erl

@@ -13,11 +13,14 @@
 
 -export([
     %% constructors
-    zero/0,
+    zero/0, one/0,
     validate/1,
     from_list/1, to_list/1,
     %% ops
-    add/2, add/1
+    add/2, add/1,
+    mul/2, mul_wxs/2, mul/1,
+    %%% from_
+    from_ltr/1, from_word/1
 ]).
 
 -opaque sentence() :: {s, ordsets:ordset(wfc_word:word())}.
@@ -27,11 +30,21 @@
 %%--------------------------
 
 -spec zero() -> sentence().
+% @doc the 0-sentence is the empty sentence
 
 zero() ->
     {s, []}.
 
 
+
+-spec one() -> sentence().
+% @doc the 1-sentence is the sentence that contains only the 1-word
+
+one() ->
+    {s, [wfc_word:one()]}.
+
+
+
 -spec from_list(Words) -> Result
     when Words  :: [wfc_word:word()],
          Result :: {ok, sentence()}
@@ -91,3 +104,54 @@ symdiff(X, Y) ->
 
 add([S | Rest]) -> add(S, add(Rest));
 add([])         -> zero().
+
+
+%%---------------------------
+%% spec ops
+%%---------------------------
+
+-spec mul(sentence(), sentence()) -> sentence().
+
+mul({s, [W | Rest]}, S) ->
+    %% (W + Rest) * S = W*S + Rest*S
+    add(mul_wxs(W, S),
+        mul({s, Rest}, S));
+mul({s, []}, _) ->
+    %% first arg 0 = result 0
+    zero().
+
+
+-spec mul([sentence()]) -> sentence().
+% @doc
+% multiply a list of sentences together; mul([]) = {s, {w, []}}
+
+mul([S | Rest]) -> mul(S, mul(Rest));
+mul([])         -> one().
+
+-spec mul_wxs(wfc_word:word(), sentence()) -> sentence().
+
+mul_wxs(W, {s, [X | Rest]}) ->
+    % W * (X + Rest) = W*X + W*Rest
+    add({s, [wfc_word:mul(W, X)]},
+        mul_wxs(W, {s, Rest}));
+mul_wxs(_, {s, []}) ->
+    zero().
+
+
+%%---------------------------
+%% from_
+%%---------------------------
+
+-spec from_ltr(term()) -> {ok, sentence()} | {error, string()}.
+
+from_ltr(Ltr) ->
+    case wfc_word:from_ltr(Ltr) of
+        {ok, Word} -> from_word(Word);
+        Error      -> Error
+    end.
+
+
+-spec from_word(term()) -> {ok, sentence()} | {error, string()}.
+
+from_word(Word) ->
+    from_list([Word]).