Add first draft of total order for FATE terms.

src/aeb_fate_data.erl

@@ -96,7 +96,10 @@
         , make_bits/1
         , make_unit/0
         ]).
--export([format/1]).
+-export([
+         elt/2
+        , lt/2
+        , format/1]).
 
 
 make_boolean(true)  -> ?FATE_TRUE;
@@ -193,3 +196,54 @@ format_list(List) ->
 
 format_kvs(List) ->
     lists:join(", ", [ [format(K), " => ",  format(V)] || {K, V} <- List]).
+
+
+%% Total order of FATE terms.
+%%  Integers < Booleans < Address < Channel < Contract < Name < Oracle
+%%   < Hash < Signature < Bits < Tuple < Map < List
+ordinal(T) when ?IS_FATE_INTEGER(T)   -> 0;
+ordinal(T) when ?IS_FATE_BOOLEAN(T)   -> 1;
+ordinal(T) when ?IS_FATE_ADDRESS(T)   -> 2;
+ordinal(T) when ?IS_FATE_CHANNEL(T)   -> 3;
+ordinal(T) when ?IS_FATE_CONTRACT(T)  -> 4;
+ordinal(T) when ?IS_FATE_NAME(T)      -> 5;
+ordinal(T) when ?IS_FATE_ORACLE(T)    -> 6;
+ordinal(T) when ?IS_FATE_HASH(T)      -> 7;
+ordinal(T) when ?IS_FATE_SIGNATURE(T) -> 8;
+ordinal(T) when ?IS_FATE_BITS(T)      -> 9;
+ordinal(T) when ?IS_FATE_TUPLE(T)     -> 10;
+ordinal(T) when ?IS_FATE_MAP(T)       -> 11;
+ordinal(T) when ?IS_FATE_LIST(T)      -> 12.
+
+
+-spec lt(fate_type(), fate_type()) -> boolean.
+%% This function assumes that all lists and maps are monomorphic,
+%% and only tests one element of a list or a map.
+%% If there is a risc that the term is not monomorphic,
+%% use safe_lt.
+lt(A, B) ->
+    O1 = ordinal(A),
+    O2 = ordinal(B),
+    if O1 == O2 -> lt(O1, A, B);
+       true -> O1 < O2
+    end.
+
+%% Integer is the smallest FATE type.
+%% Integers themselves are ordered as usual.
+lt(0, A, B) when ?IS_FATE_INTEGER(A), ?IS_FATE_INTEGER(B) ->
+    ?FATE_INTEGER_VALUE(A) < ?FATE_INTEGER_VALUE(B);
+%% Boolean is the second smallest FATE type.
+%% false is smaller than true (true also for erlang booleans).
+lt(1, A, B) when ?IS_FATE_BOOLEAN(A), ?IS_FATE_INTEGER(B) -> false;
+lt(1, A, B) when ?IS_FATE_BOOLEAN(A), ?IS_FATE_BOOLEAN(B) ->
+    ?FATE_BOOLEAN_VALUE(A) < ?FATE_BOOLEAN_VALUE(B);
+lt(_, A, B) -> A < B.
+
+
+-spec elt(fate_type(), fate_type()) -> boolean.
+elt(A, A) -> true;
+elt(A, B) ->
+    R = lt(A, B),
+    io:format("~w < ~w : ~w~n", [A, B, R]),
+    R.
+

src/aeb_fate_encoding.erl

@@ -1,21 +1,29 @@
 %% Fate data (and instruction) serialization.
 %%
-%% The FATE serialization has to fullfill the following properties:
-%% * There has to be 1 and only 1 byte sequence
-%%     representing each unique value in FATE.
-%% * A valid byte sequence has to be deserializable to a FATE value.
-%% * A valid byte sequence must not contain any trailing bytes.
-%% * A serialization is a sequence of 8-bit bytes.
-%%
-%% The serialization function should fullfill the following:
-%% * A valid FATE value should be serialized to a byte sequence.
-%% * Any other argument, not representing a valid FATE value should
+%% Assuming
+%%   S is seralize/1 (fate_type() -> binary())
+%%   D is deserialize/1 (binary) -> fate_type())
+%%   V, V1, V2 are of the type fate_type()
+%%   B is of the type binary()
+%% Then
+%%  The FATE serialization has to fullfill the following properties:
+%%   * For each value (V) in FATE there has to be a bytecode sequence (B)
+%%     representing that value.
+%%   * A valid byte sequence has to be deserializable to a FATE value.
+%%   * A valid byte sequence must not contain any trailing bytes.
+%%   * A serialization is a sequence of 8-bit bytes.
+%%  The serialization function (S) should fullfill the following:
+%%   * A valid FATE value should be serialized to a byte sequence.
+%%   * Any other argument, not representing a valid FATE value should
 %%     throw an exception
-%%
-%% The deserialization function should fullfill the following:
-%% * A valid byte sequence should be deserialized to a valid FATE value.
-%% * Any other argument, not representing a valid byte sequence should
+%%  The deserialization function (D) should fullfill the following:
+%%   * A valid byte sequence should be deserialized to a valid FATE value.
+%%   * Any other argument, not representing a valid byte sequence should
 %%     throw an exception
+%%  The following equalities should hold:
+%%   * D(S(V)) == V
+%%   * if V1 == V2 then S(V1) == S(V2)
+%%
 %%
 %% History
 %% * First draft of FATE serialization encoding/decoding.
@@ -421,7 +429,7 @@ deserialize_elements(N, Es) ->
     {[E|Tail], Rest2}.
 
 
-%% It is important to rem ove duplicated keys.
+%% It is important to remove duplicated keys.
 %% For deserialize this check is needed to observe illegal duplicates.
 sort_and_check(List) ->
     UniqKeyList =
@@ -439,7 +447,7 @@ sort_and_check(List) ->
 
 sort(KVList) ->
     SortFun = fun({K1, _}, {K2, _}) ->
-                      K1 =< K2
+                      aeb_fate_data:elt(K1, K2)
               end,
     lists:sort(SortFun, KVList).