Enhance Dialyzer's inference on comparisons

This patch makes Dialyzer aware of Erlang's total ordering of terms,
enabling discrepancy detection in cases where e.g. integer() < tuple()
is treated as a comparison that might also return false (when it is
certain to always return true).

3 files changed, 523 insertions, 4 deletions

diff --git a/lib/dialyzer/test/small_SUITE_data/results/comparisons b/lib/dialyzer/test/small_SUITE_data/results/comparisons
new file mode 100644
index 0000000000..642585d25e
--- /dev/null
+++ b/lib/dialyzer/test/small_SUITE_data/results/comparisons
@@ -0,0 +1,153 @@
+
+comparisons.erl:100: The pattern 'true' can never match the type 'false'
+comparisons.erl:101: The pattern 'true' can never match the type 'false'
+comparisons.erl:102: The pattern 'false' can never match the type 'true'
+comparisons.erl:103: The pattern 'false' can never match the type 'true'
+comparisons.erl:104: The pattern 'true' can never match the type 'false'
+comparisons.erl:105: The pattern 'true' can never match the type 'false'
+comparisons.erl:107: The pattern 'true' can never match the type 'false'
+comparisons.erl:108: The pattern 'true' can never match the type 'false'
+comparisons.erl:109: The pattern 'false' can never match the type 'true'
+comparisons.erl:110: The pattern 'false' can never match the type 'true'
+comparisons.erl:111: The pattern 'true' can never match the type 'false'
+comparisons.erl:112: The pattern 'true' can never match the type 'false'
+comparisons.erl:113: The pattern 'false' can never match the type 'true'
+comparisons.erl:114: The pattern 'false' can never match the type 'true'
+comparisons.erl:115: The pattern 'true' can never match the type 'false'
+comparisons.erl:116: The pattern 'true' can never match the type 'false'
+comparisons.erl:117: The pattern 'false' can never match the type 'true'
+comparisons.erl:118: The pattern 'false' can never match the type 'true'
+comparisons.erl:123: The pattern 'false' can never match the type 'true'
+comparisons.erl:124: The pattern 'false' can never match the type 'true'
+comparisons.erl:125: The pattern 'true' can never match the type 'false'
+comparisons.erl:126: The pattern 'true' can never match the type 'false'
+comparisons.erl:127: The pattern 'false' can never match the type 'true'
+comparisons.erl:128: The pattern 'false' can never match the type 'true'
+comparisons.erl:129: The pattern 'true' can never match the type 'false'
+comparisons.erl:130: The pattern 'true' can never match the type 'false'
+comparisons.erl:132: The pattern 'true' can never match the type 'false'
+comparisons.erl:133: The pattern 'true' can never match the type 'false'
+comparisons.erl:134: The pattern 'false' can never match the type 'true'
+comparisons.erl:135: The pattern 'false' can never match the type 'true'
+comparisons.erl:136: The pattern 'true' can never match the type 'false'
+comparisons.erl:137: The pattern 'true' can never match the type 'false'
+comparisons.erl:138: The pattern 'false' can never match the type 'true'
+comparisons.erl:139: The pattern 'false' can never match the type 'true'
+comparisons.erl:140: The pattern 'true' can never match the type 'false'
+comparisons.erl:141: The pattern 'true' can never match the type 'false'
+comparisons.erl:142: The pattern 'false' can never match the type 'true'
+comparisons.erl:143: The pattern 'false' can never match the type 'true'
+comparisons.erl:144: The pattern 'true' can never match the type 'false'
+comparisons.erl:145: The pattern 'true' can never match the type 'false'
+comparisons.erl:146: The pattern 'false' can never match the type 'true'
+comparisons.erl:147: The pattern 'false' can never match the type 'true'
+comparisons.erl:152: The pattern 'false' can never match the type 'true'
+comparisons.erl:153: The pattern 'false' can never match the type 'true'
+comparisons.erl:154: The pattern 'true' can never match the type 'false'
+comparisons.erl:155: The pattern 'true' can never match the type 'false'
+comparisons.erl:157: The pattern 'true' can never match the type 'false'
+comparisons.erl:158: The pattern 'true' can never match the type 'false'
+comparisons.erl:159: The pattern 'false' can never match the type 'true'
+comparisons.erl:160: The pattern 'false' can never match the type 'true'
+comparisons.erl:161: The pattern 'true' can never match the type 'false'
+comparisons.erl:162: The pattern 'true' can never match the type 'false'
+comparisons.erl:163: The pattern 'false' can never match the type 'true'
+comparisons.erl:164: The pattern 'false' can never match the type 'true'
+comparisons.erl:165: The pattern 'true' can never match the type 'false'
+comparisons.erl:166: The pattern 'true' can never match the type 'false'
+comparisons.erl:167: The pattern 'false' can never match the type 'true'
+comparisons.erl:168: The pattern 'false' can never match the type 'true'
+comparisons.erl:169: The pattern 'true' can never match the type 'false'
+comparisons.erl:170: The pattern 'true' can never match the type 'false'
+comparisons.erl:171: The pattern 'false' can never match the type 'true'
+comparisons.erl:172: The pattern 'false' can never match the type 'true'
+comparisons.erl:173: The pattern 'true' can never match the type 'false'
+comparisons.erl:174: The pattern 'true' can never match the type 'false'
+comparisons.erl:175: The pattern 'false' can never match the type 'true'
+comparisons.erl:176: The pattern 'false' can never match the type 'true'
+comparisons.erl:186: The pattern 'false' can never match the type 'true'
+comparisons.erl:187: The pattern 'false' can never match the type 'true'
+comparisons.erl:188: The pattern 'true' can never match the type 'false'
+comparisons.erl:189: The pattern 'true' can never match the type 'false'
+comparisons.erl:190: The pattern 'false' can never match the type 'true'
+comparisons.erl:191: The pattern 'false' can never match the type 'true'
+comparisons.erl:192: The pattern 'true' can never match the type 'false'
+comparisons.erl:193: The pattern 'true' can never match the type 'false'
+comparisons.erl:203: The pattern 'false' can never match the type 'true'
+comparisons.erl:204: The pattern 'false' can never match the type 'true'
+comparisons.erl:205: The pattern 'true' can never match the type 'false'
+comparisons.erl:206: The pattern 'true' can never match the type 'false'
+comparisons.erl:208: The pattern 'true' can never match the type 'false'
+comparisons.erl:209: The pattern 'true' can never match the type 'false'
+comparisons.erl:210: The pattern 'false' can never match the type 'true'
+comparisons.erl:211: The pattern 'false' can never match the type 'true'
+comparisons.erl:221: The pattern 'true' can never match the type 'false'
+comparisons.erl:222: The pattern 'true' can never match the type 'false'
+comparisons.erl:223: The pattern 'false' can never match the type 'true'
+comparisons.erl:224: The pattern 'false' can never match the type 'true'
+comparisons.erl:225: The pattern 'true' can never match the type 'false'
+comparisons.erl:226: The pattern 'true' can never match the type 'false'
+comparisons.erl:227: The pattern 'false' can never match the type 'true'
+comparisons.erl:228: The pattern 'false' can never match the type 'true'
+comparisons.erl:242: The pattern 'false' can never match the type 'true'
+comparisons.erl:243: The pattern 'false' can never match the type 'true'
+comparisons.erl:244: The pattern 'true' can never match the type 'false'
+comparisons.erl:245: The pattern 'true' can never match the type 'false'
+comparisons.erl:246: The pattern 'false' can never match the type 'true'
+comparisons.erl:247: The pattern 'false' can never match the type 'true'
+comparisons.erl:248: The pattern 'true' can never match the type 'false'
+comparisons.erl:249: The pattern 'true' can never match the type 'false'
+comparisons.erl:251: The pattern 'true' can never match the type 'false'
+comparisons.erl:252: The pattern 'true' can never match the type 'false'
+comparisons.erl:253: The pattern 'false' can never match the type 'true'
+comparisons.erl:254: The pattern 'false' can never match the type 'true'
+comparisons.erl:263: The pattern 'false' can never match the type 'true'
+comparisons.erl:264: The pattern 'false' can never match the type 'true'
+comparisons.erl:265: The pattern 'true' can never match the type 'false'
+comparisons.erl:266: The pattern 'true' can never match the type 'false'
+comparisons.erl:268: The pattern 'true' can never match the type 'false'
+comparisons.erl:269: The pattern 'true' can never match the type 'false'
+comparisons.erl:270: The pattern 'false' can never match the type 'true'
+comparisons.erl:271: The pattern 'false' can never match the type 'true'
+comparisons.erl:272: The pattern 'true' can never match the type 'false'
+comparisons.erl:273: The pattern 'true' can never match the type 'false'
+comparisons.erl:274: The pattern 'false' can never match the type 'true'
+comparisons.erl:275: The pattern 'false' can never match the type 'true'
+comparisons.erl:293: The pattern 'false' can never match the type 'true'
+comparisons.erl:294: The pattern 'false' can never match the type 'true'
+comparisons.erl:295: The pattern 'true' can never match the type 'false'
+comparisons.erl:296: The pattern 'true' can never match the type 'false'
+comparisons.erl:311: The pattern 'true' can never match the type 'false'
+comparisons.erl:312: The pattern 'true' can never match the type 'false'
+comparisons.erl:313: The pattern 'false' can never match the type 'true'
+comparisons.erl:314: The pattern 'false' can never match the type 'true'
+comparisons.erl:44: The pattern 'false' can never match the type 'true'
+comparisons.erl:45: The pattern 'false' can never match the type 'true'
+comparisons.erl:46: The pattern 'true' can never match the type 'false'
+comparisons.erl:47: The pattern 'true' can never match the type 'false'
+comparisons.erl:48: The pattern 'false' can never match the type 'true'
+comparisons.erl:49: The pattern 'false' can never match the type 'true'
+comparisons.erl:50: The pattern 'true' can never match the type 'false'
+comparisons.erl:51: The pattern 'true' can never match the type 'false'
+comparisons.erl:52: The pattern 'false' can never match the type 'true'
+comparisons.erl:53: The pattern 'false' can never match the type 'true'
+comparisons.erl:54: The pattern 'true' can never match the type 'false'
+comparisons.erl:55: The pattern 'true' can never match the type 'false'
+comparisons.erl:69: The pattern 'false' can never match the type 'true'
+comparisons.erl:70: The pattern 'false' can never match the type 'true'
+comparisons.erl:71: The pattern 'true' can never match the type 'false'
+comparisons.erl:72: The pattern 'true' can never match the type 'false'
+comparisons.erl:73: The pattern 'false' can never match the type 'true'
+comparisons.erl:74: The pattern 'false' can never match the type 'true'
+comparisons.erl:75: The pattern 'true' can never match the type 'false'
+comparisons.erl:76: The pattern 'true' can never match the type 'false'
+comparisons.erl:77: The pattern 'false' can never match the type 'true'
+comparisons.erl:78: The pattern 'false' can never match the type 'true'
+comparisons.erl:79: The pattern 'true' can never match the type 'false'
+comparisons.erl:80: The pattern 'true' can never match the type 'false'
+comparisons.erl:94: The pattern 'false' can never match the type 'true'
+comparisons.erl:95: The pattern 'false' can never match the type 'true'
+comparisons.erl:96: The pattern 'true' can never match the type 'false'
+comparisons.erl:97: The pattern 'true' can never match the type 'false'
+comparisons.erl:98: The pattern 'false' can never match the type 'true'
+comparisons.erl:99: The pattern 'false' can never match the type 'true'
diff --git a/lib/dialyzer/test/small_SUITE_data/src/comparisons.erl b/lib/dialyzer/test/small_SUITE_data/src/comparisons.erl
new file mode 100644
index 0000000000..70e3cb6af4
--- /dev/null
+++ b/lib/dialyzer/test/small_SUITE_data/src/comparisons.erl
@@ -0,0 +1,322 @@
+-module(comparisons).
+
+-compile(export_all).
+
+-define(r, get(r)).
+
+integer() -> integer(?r).
+integer(X) when is_integer(X) -> X.
+
+mfloat() -> float(?r).
+mfloat(X) when is_float(X) -> X.
+
+atom() -> atom(?r).
+atom(X) when is_atom(X) -> X.
+
+tuple() -> tuple(?r).
+tuple(X) when is_tuple(X) -> X.
+
+list() -> list(?r).
+list(X) when is_list(X) -> X.
+
+i() -> integer().
+f() -> mfloat().
+n() -> case ?r of 1 -> i(); 2 -> f() end.
+a() -> atom().
+t() -> tuple().
+l() -> list().
+na() -> case ?r of 1 -> n(); 2 -> a() end.
+at() -> case ?r of 1 -> t(); 2 -> a() end.
+tl() -> case ?r of 1 -> t(); 2 -> l() end.
+
+test_i_ll_i() -> case i()  < i() of true -> maybe; false -> maybe_too end.
+test_i_le_i() -> case i() =< i() of true -> maybe; false -> maybe_too end.
+test_i_gg_i() -> case i()  > i() of true -> maybe; false -> maybe_too end.
+test_i_ge_i() -> case i() >= i() of true -> maybe; false -> maybe_too end.
+test_i_ll_f() -> case i()  < f() of true -> maybe; false -> maybe_too end.
+test_i_le_f() -> case i() =< f() of true -> maybe; false -> maybe_too end.
+test_i_gg_f() -> case i()  > f() of true -> maybe; false -> maybe_too end.
+test_i_ge_f() -> case i() >= f() of true -> maybe; false -> maybe_too end.
+test_i_ll_n() -> case i()  < n() of true -> maybe; false -> maybe_too end.
+test_i_le_n() -> case i() =< n() of true -> maybe; false -> maybe_too end.
+test_i_gg_n() -> case i()  > n() of true -> maybe; false -> maybe_too end.
+test_i_ge_n() -> case i() >= n() of true -> maybe; false -> maybe_too end.
+test_i_ll_a() -> case i()  < a() of true -> always; false -> never end.
+test_i_le_a() -> case i() =< a() of true -> always; false -> never end.
+test_i_gg_a() -> case i()  > a() of true -> never; false -> always end.
+test_i_ge_a() -> case i() >= a() of true -> never; false -> always end.
+test_i_ll_t() -> case i()  < t() of true -> always; false -> never end.
+test_i_le_t() -> case i() =< t() of true -> always; false -> never end.
+test_i_gg_t() -> case i()  > t() of true -> never; false -> always end.
+test_i_ge_t() -> case i() >= t() of true -> never; false -> always end.
+test_i_ll_l() -> case i()  < l() of true -> always; false -> never end.
+test_i_le_l() -> case i() =< l() of true -> always; false -> never end.
+test_i_gg_l() -> case i()  > l() of true -> never; false -> always end.
+test_i_ge_l() -> case i() >= l() of true -> never; false -> always end.
+
+test_f_ll_i() -> case f()  < i() of true -> maybe; false -> maybe_too end.
+test_f_le_i() -> case f() =< i() of true -> maybe; false -> maybe_too end.
+test_f_gg_i() -> case f()  > i() of true -> maybe; false -> maybe_too end.
+test_f_ge_i() -> case f() >= i() of true -> maybe; false -> maybe_too end.
+test_f_ll_f() -> case f()  < f() of true -> maybe; false -> maybe_too end.
+test_f_le_f() -> case f() =< f() of true -> maybe; false -> maybe_too end.
+test_f_gg_f() -> case f()  > f() of true -> maybe; false -> maybe_too end.
+test_f_ge_f() -> case f() >= f() of true -> maybe; false -> maybe_too end.
+test_f_ll_n() -> case f()  < n() of true -> maybe; false -> maybe_too end.
+test_f_le_n() -> case f() =< n() of true -> maybe; false -> maybe_too end.
+test_f_gg_n() -> case f()  > n() of true -> maybe; false -> maybe_too end.
+test_f_ge_n() -> case f() >= n() of true -> maybe; false -> maybe_too end.
+test_f_ll_a() -> case f()  < a() of true -> always; false -> never end.
+test_f_le_a() -> case f() =< a() of true -> always; false -> never end.
+test_f_gg_a() -> case f()  > a() of true -> never; false -> always end.
+test_f_ge_a() -> case f() >= a() of true -> never; false -> always end.
+test_f_ll_t() -> case f()  < t() of true -> always; false -> never end.
+test_f_le_t() -> case f() =< t() of true -> always; false -> never end.
+test_f_gg_t() -> case f()  > t() of true -> never; false -> always end.
+test_f_ge_t() -> case f() >= t() of true -> never; false -> always end.
+test_f_ll_l() -> case f()  < l() of true -> always; false -> never end.
+test_f_le_l() -> case f() =< l() of true -> always; false -> never end.
+test_f_gg_l() -> case f()  > l() of true -> never; false -> always end.
+test_f_ge_l() -> case f() >= l() of true -> never; false -> always end.
+
+test_n_ll_i() -> case n()  < i() of true -> maybe; false -> maybe_too end.
+test_n_le_i() -> case n() =< i() of true -> maybe; false -> maybe_too end.
+test_n_gg_i() -> case n()  > i() of true -> maybe; false -> maybe_too end.
+test_n_ge_i() -> case n() >= i() of true -> maybe; false -> maybe_too end.
+test_n_ll_f() -> case n()  < f() of true -> maybe; false -> maybe_too end.
+test_n_le_f() -> case n() =< f() of true -> maybe; false -> maybe_too end.
+test_n_gg_f() -> case n()  > f() of true -> maybe; false -> maybe_too end.
+test_n_ge_f() -> case n() >= f() of true -> maybe; false -> maybe_too end.
+test_n_ll_n() -> case n()  < n() of true -> maybe; false -> maybe_too end.
+test_n_le_n() -> case n() =< n() of true -> maybe; false -> maybe_too end.
+test_n_gg_n() -> case n()  > n() of true -> maybe; false -> maybe_too end.
+test_n_ge_n() -> case n() >= n() of true -> maybe; false -> maybe_too end.
+test_n_ll_a() -> case n()  < a() of true -> always; false -> never end.
+test_n_le_a() -> case n() =< a() of true -> always; false -> never end.
+test_n_gg_a() -> case n()  > a() of true -> never; false -> always end.
+test_n_ge_a() -> case n() >= a() of true -> never; false -> always end.
+test_n_ll_t() -> case n()  < t() of true -> always; false -> never end.
+test_n_le_t() -> case n() =< t() of true -> always; false -> never end.
+test_n_gg_t() -> case n()  > t() of true -> never; false -> always end.
+test_n_ge_t() -> case n() >= t() of true -> never; false -> always end.
+test_n_ll_l() -> case n()  < l() of true -> always; false -> never end.
+test_n_le_l() -> case n() =< l() of true -> always; false -> never end.
+test_n_gg_l() -> case n()  > l() of true -> never; false -> always end.
+test_n_ge_l() -> case n() >= l() of true -> never; false -> always end.
+
+test_a_ll_i() -> case a()  < i() of true -> never; false -> always end.
+test_a_le_i() -> case a() =< i() of true -> never; false -> always end.
+test_a_gg_i() -> case a()  > i() of true -> always; false -> never end.
+test_a_ge_i() -> case a() >= i() of true -> always; false -> never end.
+test_a_ll_f() -> case a()  < f() of true -> never; false -> always end.
+test_a_le_f() -> case a() =< f() of true -> never; false -> always end.
+test_a_gg_f() -> case a()  > f() of true -> always; false -> never end.
+test_a_ge_f() -> case a() >= f() of true -> always; false -> never end.
+test_a_ll_n() -> case a()  < n() of true -> never; false -> always end.
+test_a_le_n() -> case a() =< n() of true -> never; false -> always end.
+test_a_gg_n() -> case a()  > n() of true -> always; false -> never end.
+test_a_ge_n() -> case a() >= n() of true -> always; false -> never end.
+test_a_ll_a() -> case a()  < a() of true -> maybe; false -> maybe_too end.
+test_a_le_a() -> case a() =< a() of true -> maybe; false -> maybe_too end.
+test_a_gg_a() -> case a()  > a() of true -> maybe; false -> maybe_too end.
+test_a_ge_a() -> case a() >= a() of true -> maybe; false -> maybe_too end.
+test_a_ll_t() -> case a()  < t() of true -> always; false -> never end.
+test_a_le_t() -> case a() =< t() of true -> always; false -> never end.
+test_a_gg_t() -> case a()  > t() of true -> never; false -> always end.
+test_a_ge_t() -> case a() >= t() of true -> never; false -> always end.
+test_a_ll_l() -> case a()  < l() of true -> always; false -> never end.
+test_a_le_l() -> case a() =< l() of true -> always; false -> never end.
+test_a_gg_l() -> case a()  > l() of true -> never; false -> always end.
+test_a_ge_l() -> case a() >= l() of true -> never; false -> always end.
+
+test_t_ll_i() -> case t()  < i() of true -> never; false -> always end.
+test_t_le_i() -> case t() =< i() of true -> never; false -> always end.
+test_t_gg_i() -> case t()  > i() of true -> always; false -> never end.
+test_t_ge_i() -> case t() >= i() of true -> always; false -> never end.
+test_t_ll_f() -> case t()  < f() of true -> never; false -> always end.
+test_t_le_f() -> case t() =< f() of true -> never; false -> always end.
+test_t_gg_f() -> case t()  > f() of true -> always; false -> never end.
+test_t_ge_f() -> case t() >= f() of true -> always; false -> never end.
+test_t_ll_n() -> case t()  < n() of true -> never; false -> always end.
+test_t_le_n() -> case t() =< n() of true -> never; false -> always end.
+test_t_gg_n() -> case t()  > n() of true -> always; false -> never end.
+test_t_ge_n() -> case t() >= n() of true -> always; false -> never end.
+test_t_ll_a() -> case t()  < a() of true -> never; false -> always end.
+test_t_le_a() -> case t() =< a() of true -> never; false -> always end.
+test_t_gg_a() -> case t()  > a() of true -> always; false -> never end.
+test_t_ge_a() -> case t() >= a() of true -> always; false -> never end.
+test_t_ll_t() -> case t()  < t() of true -> maybe; false -> maybe_too end.
+test_t_le_t() -> case t() =< t() of true -> maybe; false -> maybe_too end.
+test_t_gg_t() -> case t()  > t() of true -> maybe; false -> maybe_too end.
+test_t_ge_t() -> case t() >= t() of true -> maybe; false -> maybe_too end.
+test_t_ll_l() -> case t()  < l() of true -> always; false -> never end.
+test_t_le_l() -> case t() =< l() of true -> always; false -> never end.
+test_t_gg_l() -> case t()  > l() of true -> never; false -> always end.
+test_t_ge_l() -> case t() >= l() of true -> never; false -> always end.
+
+test_l_ll_i() -> case l()  < i() of true -> never; false -> always end.
+test_l_le_i() -> case l() =< i() of true -> never; false -> always end.
+test_l_gg_i() -> case l()  > i() of true -> always; false -> never end.
+test_l_ge_i() -> case l() >= i() of true -> always; false -> never end.
+test_l_ll_f() -> case l()  < f() of true -> never; false -> always end.
+test_l_le_f() -> case l() =< f() of true -> never; false -> always end.
+test_l_gg_f() -> case l()  > f() of true -> always; false -> never end.
+test_l_ge_f() -> case l() >= f() of true -> always; false -> never end.
+test_l_ll_n() -> case l()  < n() of true -> never; false -> always end.
+test_l_le_n() -> case l() =< n() of true -> never; false -> always end.
+test_l_gg_n() -> case l()  > n() of true -> always; false -> never end.
+test_l_ge_n() -> case l() >= n() of true -> always; false -> never end.
+test_l_ll_a() -> case l()  < a() of true -> never; false -> always end.
+test_l_le_a() -> case l() =< a() of true -> never; false -> always end.
+test_l_gg_a() -> case l()  > a() of true -> always; false -> never end.
+test_l_ge_a() -> case l() >= a() of true -> always; false -> never end.
+test_l_ll_t() -> case l()  < t() of true -> never; false -> always end.
+test_l_le_t() -> case l() =< t() of true -> never; false -> always end.
+test_l_gg_t() -> case l()  > t() of true -> always; false -> never end.
+test_l_ge_t() -> case l() >= t() of true -> always; false -> never end.
+test_l_ll_l() -> case l()  < l() of true -> maybe; false -> maybe_too end.
+test_l_le_l() -> case l() =< l() of true -> maybe; false -> maybe_too end.
+test_l_gg_l() -> case l()  > l() of true -> maybe; false -> maybe_too end.
+test_l_ge_l() -> case l() >= l() of true -> maybe; false -> maybe_too end.
+
+test_n_ll_na() -> case n()  < na() of true -> maybe; false -> maybe_too end.
+test_n_le_na() -> case n() =< na() of true -> maybe; false -> maybe_too end.
+test_n_gg_na() -> case n()  > na() of true -> maybe; false -> maybe_too end.
+test_n_ge_na() -> case n() >= na() of true -> maybe; false -> maybe_too end.
+test_n_ll_at() -> case n()  < at() of true -> always; false -> never end.
+test_n_le_at() -> case n() =< at() of true -> always; false -> never end.
+test_n_gg_at() -> case n()  > at() of true -> never; false -> always end.
+test_n_ge_at() -> case n() >= at() of true -> never; false -> always end.
+test_n_ll_tl() -> case n()  < tl() of true -> always; false -> never end.
+test_n_le_tl() -> case n() =< tl() of true -> always; false -> never end.
+test_n_gg_tl() -> case n()  > tl() of true -> never; false -> always end.
+test_n_ge_tl() -> case n() >= tl() of true -> never; false -> always end.
+
+test_a_ll_na() -> case a()  < na() of true -> maybe; false -> maybe_too end.
+test_a_le_na() -> case a() =< na() of true -> maybe; false -> maybe_too end.
+test_a_gg_na() -> case a()  > na() of true -> maybe; false -> maybe_too end.
+test_a_ge_na() -> case a() >= na() of true -> maybe; false -> maybe_too end.
+test_a_ll_at() -> case a()  < at() of true -> maybe; false -> maybe_too end.
+test_a_le_at() -> case a() =< at() of true -> maybe; false -> maybe_too end.
+test_a_gg_at() -> case a()  > at() of true -> maybe; false -> maybe_too end.
+test_a_ge_at() -> case a() >= at() of true -> maybe; false -> maybe_too end.
+test_a_ll_tl() -> case a()  < tl() of true -> always; false -> never end.
+test_a_le_tl() -> case a() =< tl() of true -> always; false -> never end.
+test_a_gg_tl() -> case a()  > tl() of true -> never; false -> always end.
+test_a_ge_tl() -> case a() >= tl() of true -> never; false -> always end.
+
+test_t_ll_na() -> case t()  < na() of true -> never; false -> always end.
+test_t_le_na() -> case t() =< na() of true -> never; false -> always end.
+test_t_gg_na() -> case t()  > na() of true -> always; false -> never end.
+test_t_ge_na() -> case t() >= na() of true -> always; false -> never end.
+test_t_ll_at() -> case t()  < at() of true -> maybe; false -> maybe_too end.
+test_t_le_at() -> case t() =< at() of true -> maybe; false -> maybe_too end.
+test_t_gg_at() -> case t()  > at() of true -> maybe; false -> maybe_too end.
+test_t_ge_at() -> case t() >= at() of true -> maybe; false -> maybe_too end.
+test_t_ll_tl() -> case t()  < tl() of true -> maybe; false -> maybe_too end.
+test_t_le_tl() -> case t() =< tl() of true -> maybe; false -> maybe_too end.
+test_t_gg_tl() -> case t()  > tl() of true -> maybe; false -> maybe_too end.
+test_t_ge_tl() -> case t() >= tl() of true -> maybe; false -> maybe_too end.
+
+test_l_ll_na() -> case l()  < na() of true -> never; false -> always end.
+test_l_le_na() -> case l() =< na() of true -> never; false -> always end.
+test_l_gg_na() -> case l()  > na() of true -> always; false -> never end.
+test_l_ge_na() -> case l() >= na() of true -> always; false -> never end.
+test_l_ll_at() -> case l()  < at() of true -> never; false -> always end.
+test_l_le_at() -> case l() =< at() of true -> never; false -> always end.
+test_l_gg_at() -> case l()  > at() of true -> always; false -> never end.
+test_l_ge_at() -> case l() >= at() of true -> always; false -> never end.
+test_l_ll_tl() -> case l()  < tl() of true -> maybe; false -> maybe_too end.
+test_l_le_tl() -> case l() =< tl() of true -> maybe; false -> maybe_too end.
+test_l_gg_tl() -> case l()  > tl() of true -> maybe; false -> maybe_too end.
+test_l_ge_tl() -> case l() >= tl() of true -> maybe; false -> maybe_too end.
+
+test_na_ll_n() -> case na()  < n() of true -> maybe; false -> maybe_too end.
+test_na_le_n() -> case na() =< n() of true -> maybe; false -> maybe_too end.
+test_na_gg_n() -> case na()  > n() of true -> maybe; false -> maybe_too end.
+test_na_ge_n() -> case na() >= n() of true -> maybe; false -> maybe_too end.
+test_na_ll_a() -> case na()  < a() of true -> maybe; false -> maybe_too end.
+test_na_le_a() -> case na() =< a() of true -> maybe; false -> maybe_too end.
+test_na_gg_a() -> case na()  > a() of true -> maybe; false -> maybe_too end.
+test_na_ge_a() -> case na() >= a() of true -> maybe; false -> maybe_too end.
+test_na_ll_t() -> case na()  < t() of true -> always; false -> never end.
+test_na_le_t() -> case na() =< t() of true -> always; false -> never end.
+test_na_gg_t() -> case na()  > t() of true -> never; false -> always end.
+test_na_ge_t() -> case na() >= t() of true -> never; false -> always end.
+test_na_ll_l() -> case na()  < l() of true -> always; false -> never end.
+test_na_le_l() -> case na() =< l() of true -> always; false -> never end.
+test_na_gg_l() -> case na()  > l() of true -> never; false -> always end.
+test_na_ge_l() -> case na() >= l() of true -> never; false -> always end.
+
+test_at_ll_n() -> case at()  < n() of true -> never; false -> always end.
+test_at_le_n() -> case at() =< n() of true -> never; false -> always end.
+test_at_gg_n() -> case at()  > n() of true -> always; false -> never end.
+test_at_ge_n() -> case at() >= n() of true -> always; false -> never end.
+test_at_ll_a() -> case at()  < a() of true -> maybe; false -> maybe_too end.
+test_at_le_a() -> case at() =< a() of true -> maybe; false -> maybe_too end.
+test_at_gg_a() -> case at()  > a() of true -> maybe; false -> maybe_too end.
+test_at_ge_a() -> case at() >= a() of true -> maybe; false -> maybe_too end.
+test_at_ll_t() -> case at()  < t() of true -> maybe; false -> maybe_too end.
+test_at_le_t() -> case at() =< t() of true -> maybe; false -> maybe_too end.
+test_at_gg_t() -> case at()  > t() of true -> maybe; false -> maybe_too end.
+test_at_ge_t() -> case at() >= t() of true -> maybe; false -> maybe_too end.
+test_at_ll_l() -> case at()  < l() of true -> always; false -> never end.
+test_at_le_l() -> case at() =< l() of true -> always; false -> never end.
+test_at_gg_l() -> case at()  > l() of true -> never; false -> always end.
+test_at_ge_l() -> case at() >= l() of true -> never; false -> always end.
+
+test_tl_ll_n() -> case tl()  < n() of true -> never; false -> always end.
+test_tl_le_n() -> case tl() =< n() of true -> never; false -> always end.
+test_tl_gg_n() -> case tl()  > n() of true -> always; false -> never end.
+test_tl_ge_n() -> case tl() >= n() of true -> always; false -> never end.
+test_tl_ll_a() -> case tl()  < a() of true -> never; false -> always end.
+test_tl_le_a() -> case tl() =< a() of true -> never; false -> always end.
+test_tl_gg_a() -> case tl()  > a() of true -> always; false -> never end.
+test_tl_ge_a() -> case tl() >= a() of true -> always; false -> never end.
+test_tl_ll_t() -> case tl()  < t() of true -> maybe; false -> maybe_too end.
+test_tl_le_t() -> case tl() =< t() of true -> maybe; false -> maybe_too end.
+test_tl_gg_t() -> case tl()  > t() of true -> maybe; false -> maybe_too end.
+test_tl_ge_t() -> case tl() >= t() of true -> maybe; false -> maybe_too end.
+test_tl_ll_l() -> case tl()  < l() of true -> maybe; false -> maybe_too end.
+test_tl_le_l() -> case tl() =< l() of true -> maybe; false -> maybe_too end.
+test_tl_gg_l() -> case tl()  > l() of true -> maybe; false -> maybe_too end.
+test_tl_ge_l() -> case tl() >= l() of true -> maybe; false -> maybe_too end.
+
+test_na_ll_na() -> case na()  < na() of true -> maybe; false -> maybe_too end.
+test_na_le_na() -> case na() =< na() of true -> maybe; false -> maybe_too end.
+test_na_gg_na() -> case na()  > na() of true -> maybe; false -> maybe_too end.
+test_na_ge_na() -> case na() >= na() of true -> maybe; false -> maybe_too end.
+test_na_ll_at() -> case na()  < at() of true -> maybe; false -> maybe_too end.
+test_na_le_at() -> case na() =< at() of true -> maybe; false -> maybe_too end.
+test_na_gg_at() -> case na()  > at() of true -> maybe; false -> maybe_too end.
+test_na_ge_at() -> case na() >= at() of true -> maybe; false -> maybe_too end.
+test_na_ll_tl() -> case na()  < tl() of true -> always; false -> never end.
+test_na_le_tl() -> case na() =< tl() of true -> always; false -> never end.
+test_na_gg_tl() -> case na()  > tl() of true -> never; false -> always end.
+test_na_ge_tl() -> case na() >= tl() of true -> never; false -> always end.
+
+test_at_ll_na() -> case at()  < na() of true -> maybe; false -> maybe_too end.
+test_at_le_na() -> case at() =< na() of true -> maybe; false -> maybe_too end.
+test_at_gg_na() -> case at()  > na() of true -> maybe; false -> maybe_too end.
+test_at_ge_na() -> case at() >= na() of true -> maybe; false -> maybe_too end.
+test_at_ll_at() -> case at()  < at() of true -> maybe; false -> maybe_too end.
+test_at_le_at() -> case at() =< at() of true -> maybe; false -> maybe_too end.
+test_at_gg_at() -> case at()  > at() of true -> maybe; false -> maybe_too end.
+test_at_ge_at() -> case at() >= at() of true -> maybe; false -> maybe_too end.
+test_at_ll_tl() -> case at()  < tl() of true -> maybe; false -> maybe_too end.
+test_at_le_tl() -> case at() =< tl() of true -> maybe; false -> maybe_too end.
+test_at_gg_tl() -> case at()  > tl() of true -> maybe; false -> maybe_too end.
+test_at_ge_tl() -> case at() >= tl() of true -> maybe; false -> maybe_too end.
+
+test_tl_ll_na() -> case tl()  < na() of true -> never; false -> always end.
+test_tl_le_na() -> case tl() =< na() of true -> never; false -> always end.
+test_tl_gg_na() -> case tl()  > na() of true -> always; false -> never end.
+test_tl_ge_na() -> case tl() >= na() of true -> always; false -> never end.
+test_tl_ll_at() -> case tl()  < at() of true -> maybe; false -> maybe_too end.
+test_tl_le_at() -> case tl() =< at() of true -> maybe; false -> maybe_too end.
+test_tl_gg_at() -> case tl()  > at() of true -> maybe; false -> maybe_too end.
+test_tl_ge_at() -> case tl() >= at() of true -> maybe; false -> maybe_too end.
+test_tl_ll_tl() -> case tl()  < tl() of true -> maybe; false -> maybe_too end.
+test_tl_le_tl() -> case tl() =< tl() of true -> maybe; false -> maybe_too end.
+test_tl_gg_tl() -> case tl()  > tl() of true -> maybe; false -> maybe_too end.
+test_tl_ge_tl() -> case tl() >= tl() of true -> maybe; false -> maybe_too end.
diff --git a/lib/hipe/cerl/erl_bif_types.erl b/lib/hipe/cerl/erl_bif_types.erl
index 82e3675938..cd5d23c50c 100644
--- a/lib/hipe/cerl/erl_bif_types.erl
+++ b/lib/hipe/cerl/erl_bif_types.erl
@@ -366,7 +366,7 @@ type(erlang, '>', 2, Xs = [Lhs, Rhs]) ->
 	  is_integer(LhsMax), is_integer(RhsMin), RhsMin >= LhsMax -> F;
 	  true -> t_boolean()
 	end;
-      false -> t_boolean()
+      false -> compare('>', Lhs, Rhs)
     end,
   strict(Xs, Ans);
 type(erlang, '>=', 2, Xs = [Lhs, Rhs]) ->
@@ -384,7 +384,7 @@ type(erlang, '>=', 2, Xs = [Lhs, Rhs]) ->
 	  is_integer(LhsMax), is_integer(RhsMin), RhsMin > LhsMax -> F;
 	  true -> t_boolean()
 	end;
-      false -> t_boolean()
+      false -> compare('>=', Lhs, Rhs)
     end,
   strict(Xs, Ans);
 type(erlang, '<', 2, Xs = [Lhs, Rhs]) ->
@@ -402,7 +402,7 @@ type(erlang, '<', 2, Xs = [Lhs, Rhs]) ->
 	  is_integer(LhsMin), is_integer(RhsMax), RhsMax =< LhsMin -> F;
 	  true -> t_boolean()
 	end;
-      false -> t_boolean()
+      false -> compare('<', Lhs, Rhs)
     end,
   strict(Xs, Ans);
 type(erlang, '=<', 2, Xs = [Lhs, Rhs]) ->
@@ -420,7 +420,7 @@ type(erlang, '=<', 2, Xs = [Lhs, Rhs]) ->
 	  is_integer(LhsMin), is_integer(RhsMax), RhsMax < LhsMin -> F;
 	  true -> t_boolean()
 	end;
-      false -> t_boolean()
+      false -> compare('=<', Lhs, Rhs)
     end,
   strict(Xs, Ans);
 type(erlang, '+', 1, Xs) ->
@@ -3178,6 +3178,50 @@ arith(Op, X1, X2) ->
   end.
 
 %%=============================================================================
+%% Comparison of terms
+%%=============================================================================
+
+compare(Op, Lhs, Rhs) ->
+  case t_is_none(t_inf(Lhs, Rhs)) of
+    false -> t_boolean();
+    true ->
+      case Op of
+	'<' -> always_smaller(Lhs, Rhs);
+	'>' -> always_smaller(Rhs, Lhs);
+	'=<' -> always_smaller(Lhs, Rhs);
+	'>=' -> always_smaller(Rhs, Lhs)
+      end
+  end.
+
+always_smaller(Type1, Type2) ->
+  {Min1, Max1} = type_ranks(Type1),
+  {Min2, Max2} = type_ranks(Type2),
+  if Max1 < Min2 -> t_atom('true');
+     Min1 > Max2 -> t_atom('false');
+     true        -> t_boolean()
+  end.
+
+type_ranks(Type) ->
+  type_ranks(Type, 1, 0, 0, type_order()).
+
+type_ranks(_Type, _I, Min, Max, []) -> {Min, Max};
+type_ranks(Type, I, Min, Max, [TypeClass|Rest]) ->
+  {NewMin, NewMax} =
+    case t_is_none(t_inf(Type, TypeClass)) of
+      true  -> {Min, Max};
+      false -> case Min of
+		 0 -> {I, I};
+		 _ -> {Min, I}
+	       end
+    end,
+  type_ranks(Type, I+1, NewMin, NewMax, Rest).
+
+type_order() ->
+  [t_number(), t_atom(), t_reference(), t_fun(), t_port(), t_pid(), t_tuple(),
+   t_list(), t_binary()].
+
+
+%%=============================================================================
 
 -spec arg_types(atom(), atom(), arity()) -> [erl_types:erl_type()] | 'unknown'.