File 5541-Property-based-tests-for-the-lists-module.... of Package erlang

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File 5541-Property-based-tests-for-the-lists-module.patch of Package erlang (Revision e0e016f64b94e78db3440770f914218d)

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From 87d80d23950dc8ef7249bdd58c84214096e9ddac Mon Sep 17 00:00:00 2001
From: Maria Scott <maria-12648430@hnc-agency.org>
Date: Tue, 5 Jul 2022 15:10:30 +0200
Subject: [PATCH] Property-based tests for the lists module
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

Co-authored-by: Jan Uhlig <juhlig@hnc-agency.org>
Co-authored-by: Björn Gustavsson <bgustavsson@gmail.com>
---
 lib/stdlib/test/Makefile                      |    1 +
 lib/stdlib/test/lists_property_test_SUITE.erl |  391 ++++
 lib/stdlib/test/property_test/lists_prop.erl  | 1807 +++++++++++++++++
 3 files changed, 2199 insertions(+)
 create mode 100644 lib/stdlib/test/lists_property_test_SUITE.erl
 create mode 100644 lib/stdlib/test/property_test/lists_prop.erl

diff --git a/lib/stdlib/test/Makefile b/lib/stdlib/test/Makefile
index b8e4d89996..9ccd48bcc7 100644
--- a/lib/stdlib/test/Makefile
+++ b/lib/stdlib/test/Makefile
@@ -49,6 +49,7 @@ MODULES= \
 	io_SUITE \
 	io_proto_SUITE \
 	lists_SUITE \
+	lists_property_test_SUITE \
 	log_mf_h_SUITE \
 	math_SUITE \
 	ms_transform_SUITE \
diff --git a/lib/stdlib/test/lists_property_test_SUITE.erl b/lib/stdlib/test/lists_property_test_SUITE.erl
new file mode 100644
index 0000000000..fee088a396
--- /dev/null
+++ b/lib/stdlib/test/lists_property_test_SUITE.erl
@@ -0,0 +1,391 @@
+%%
+%% %CopyrightBegin%
+%%
+%% Copyright Ericsson AB 2021. All Rights Reserved.
+%%
+%% Licensed under the Apache License, Version 2.0 (the "License");
+%% you may not use this file except in compliance with the License.
+%% You may obtain a copy of the License at
+%%
+%%     http://www.apache.org/licenses/LICENSE-2.0
+%%
+%% Unless required by applicable law or agreed to in writing, software
+%% distributed under the License is distributed on an "AS IS" BASIS,
+%% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+%% See the License for the specific language governing permissions and
+%% limitations under the License.
+%%
+%% %CopyrightEnd%
+%%
+-module(lists_property_test_SUITE).
+
+-include_lib("common_test/include/ct.hrl").
+-compile(export_all).
+
+all() ->
+    [
+        all_true_case, all_false_case,
+        any_true_case, any_false_case,
+        append_1_case,
+        append_2_case,
+        concat_case,
+        delete_case, delete_absent_case,
+        droplast_case,
+        dropwhile_case,
+        duplicate_case,
+        enumerate_1_case,
+        enumerate_2_case,
+        filter_case,
+        filtermap_case,
+        flatlength_case,
+        flatmap_case,
+        flatten_1_case,
+        flatten_2_case,
+        foldl_case,
+        foldr_case,
+        foreach_case,
+        join_case,
+        keydelete_case, keydelete_absent_case,
+        keyfind_case, keyfind_absent_case,
+        keymap_case,
+        keymember_case, keymember_absent_case,
+        keymerge_case,
+        keyreplace_case, keyreplace_absent_case,
+        keysearch_case, keysearch_absent_case,
+        keysort_case,
+        keystore_case, keystore_absent_case,
+        keytake_case, keytake_absent_case,
+        last_case,
+        map_case,
+        mapfoldl_case,
+        mapfoldr_case,
+        max_case,
+        member_case, member_absent_case,
+        merge_1_case,
+        merge_2_case,
+        merge_3_case,
+        merge3_case,
+        min_case,
+        nth_case, nth_outofrange_case,
+        nthtail_case, nthtail_outofrange_case,
+        partition_case,
+        prefix_case,
+        reverse_1_case,
+        reverse_2_case,
+        search_case, search_absent_case,
+        seq2_case,
+        seq3_case,
+        sort_1_case,
+        sort_2_case,
+        split_case, split_outofrange_case,
+        splitwith_case,
+        sublist_2_case,
+        sublist_3_case,
+        subtract_case,
+        suffix_case,
+        sum_case,
+        takewhile_case,
+        ukeymerge_case,
+        ukeysort_case,
+        umerge_1_case,
+        umerge_2_case,
+        umerge_3_case,
+        umerge3_case,
+        uniq_1_case,
+        uniq_2_case,
+        unzip_case,
+        unzip3_case,
+        usort_1_case,
+        usort_2_case,
+        zip_case,
+        zip3_case,
+        zipwith_case,
+        zipwith3_case
+    ].
+
+init_per_suite(Config) ->
+    ct_property_test:init_per_suite(Config).
+
+end_per_suite(Config) ->
+    persistent_term:erase({lists_prop, random_atoms}),
+    Config.
+
+do_proptest(Prop, Config) ->
+    ct_property_test:quickcheck(lists_prop:Prop(), Config).
+
+all_true_case(Config) ->
+    do_proptest(prop_all_true, Config).
+
+all_false_case(Config) ->
+    do_proptest(prop_all_false, Config).
+
+any_true_case(Config) ->
+    do_proptest(prop_any_true, Config).
+
+any_false_case(Config) ->
+    do_proptest(prop_any_false, Config).
+
+append_1_case(Config) ->
+    do_proptest(prop_append_1, Config).
+
+append_2_case(Config) ->
+    do_proptest(prop_append_2, Config).
+
+concat_case(Config) ->
+    do_proptest(prop_concat, Config).
+
+delete_case(Config) ->
+    do_proptest(prop_delete, Config).
+
+delete_absent_case(Config) ->
+    do_proptest(prop_delete_absent, Config).
+
+droplast_case(Config) ->
+    do_proptest(prop_droplast, Config).
+
+dropwhile_case(Config) ->
+    do_proptest(prop_dropwhile, Config).
+
+duplicate_case(Config) ->
+    do_proptest(prop_duplicate, Config).
+
+enumerate_1_case(Config) ->
+    do_proptest(prop_enumerate_1, Config).
+
+enumerate_2_case(Config) ->
+    do_proptest(prop_enumerate_2, Config).
+
+filter_case(Config) ->
+    do_proptest(prop_filter, Config).
+
+filtermap_case(Config) ->
+    do_proptest(prop_filtermap, Config).
+
+flatlength_case(Config) ->
+    do_proptest(prop_flatlength, Config).
+
+flatmap_case(Config) ->
+    do_proptest(prop_flatmap, Config).
+
+flatten_1_case(Config) ->
+    do_proptest(prop_flatten_1, Config).
+
+flatten_2_case(Config) ->
+    do_proptest(prop_flatten_2, Config).
+
+foldl_case(Config) ->
+    do_proptest(prop_foldl, Config).
+
+foldr_case(Config) ->
+    do_proptest(prop_foldr, Config).
+
+foreach_case(Config) ->
+    do_proptest(prop_foreach, Config).
+
+join_case(Config) ->
+    do_proptest(prop_join, Config).
+
+keydelete_case(Config) ->
+    do_proptest(prop_keydelete, Config).
+
+keydelete_absent_case(Config) ->
+    do_proptest(prop_keydelete_absent, Config).
+
+keyfind_case(Config) ->
+    do_proptest(prop_keyfind, Config).
+
+keyfind_absent_case(Config) ->
+    do_proptest(prop_keyfind_absent, Config).
+
+keymap_case(Config) ->
+    do_proptest(prop_keymap, Config).
+
+keymember_case(Config) ->
+    do_proptest(prop_keymember, Config).
+
+keymember_absent_case(Config) ->
+    do_proptest(prop_keymember_absent, Config).
+
+keymerge_case(Config) ->
+    do_proptest(prop_keymerge, Config).
+
+keyreplace_case(Config) ->
+    do_proptest(prop_keyreplace, Config).
+
+keyreplace_absent_case(Config) ->
+    do_proptest(prop_keyreplace_absent, Config).
+
+keysearch_case(Config) ->
+    do_proptest(prop_keysearch, Config).
+
+keysearch_absent_case(Config) ->
+    do_proptest(prop_keysearch_absent, Config).
+
+keysort_case(Config) ->
+    do_proptest(prop_keysort, Config).
+
+keystore_case(Config) ->
+    do_proptest(prop_keystore, Config).
+
+keystore_absent_case(Config) ->
+    do_proptest(prop_keystore_absent, Config).
+
+keytake_case(Config) ->
+    do_proptest(prop_keytake, Config).
+
+keytake_absent_case(Config) ->
+    do_proptest(prop_keytake_absent, Config).
+
+last_case(Config) ->
+    do_proptest(prop_last, Config).
+
+map_case(Config) ->
+    do_proptest(prop_map, Config).
+
+mapfoldl_case(Config) ->
+    do_proptest(prop_mapfoldl, Config).
+
+mapfoldr_case(Config) ->
+    do_proptest(prop_mapfoldr, Config).
+
+max_case(Config) ->
+    do_proptest(prop_max, Config).
+
+member_case(Config) ->
+    do_proptest(prop_member, Config).
+
+member_absent_case(Config) ->
+    do_proptest(prop_member_absent, Config).
+
+merge_1_case(Config) ->
+    do_proptest(prop_merge_1, Config).
+
+merge_2_case(Config) ->
+    do_proptest(prop_merge_2, Config).
+
+merge_3_case(Config) ->
+    do_proptest(prop_merge_3, Config).
+
+merge3_case(Config) ->
+    do_proptest(prop_merge3, Config).
+
+min_case(Config) ->
+    do_proptest(prop_min, Config).
+
+nth_case(Config) ->
+    do_proptest(prop_nth, Config).
+
+nth_outofrange_case(Config) ->
+    do_proptest(prop_nth_outofrange, Config).
+
+nthtail_case(Config) ->
+    do_proptest(prop_nthtail, Config).
+
+nthtail_outofrange_case(Config) ->
+    do_proptest(prop_nthtail_outofrange, Config).
+
+partition_case(Config) ->
+    do_proptest(prop_partition, Config).
+
+prefix_case(Config) ->
+    do_proptest(prop_prefix, Config).
+
+reverse_1_case(Config) ->
+    do_proptest(prop_reverse_1, Config).
+
+reverse_2_case(Config) ->
+    do_proptest(prop_reverse_2, Config).
+
+search_case(Config) ->
+    do_proptest(prop_search, Config).
+
+search_absent_case(Config) ->
+    do_proptest(prop_search_absent, Config).
+
+seq2_case(Config) ->
+    do_proptest(prop_seq2, Config).
+
+seq3_case(Config) ->
+    do_proptest(prop_seq3, Config).
+
+sort_1_case(Config) ->
+    do_proptest(prop_sort_1, Config).
+
+sort_2_case(Config) ->
+    do_proptest(prop_sort_2, Config).
+
+split_case(Config) ->
+    do_proptest(prop_split, Config).
+
+split_outofrange_case(Config) ->
+    do_proptest(prop_split_outofrange, Config).
+
+splitwith_case(Config) ->
+    do_proptest(prop_splitwith, Config).
+
+sublist_2_case(Config) ->
+    do_proptest(prop_sublist_2, Config).
+
+sublist_3_case(Config) ->
+    do_proptest(prop_sublist_3, Config).
+
+subtract_case(Config) ->
+    do_proptest(prop_subtract, Config).
+
+suffix_case(Config) ->
+    do_proptest(prop_suffix, Config).
+
+sum_case(Config) ->
+    do_proptest(prop_sum, Config).
+
+takewhile_case(Config) ->
+    do_proptest(prop_takewhile, Config).
+
+ukeymerge_case(Config) ->
+    do_proptest(prop_ukeymerge, Config).
+
+ukeysort_case(Config) ->
+    do_proptest(prop_ukeysort, Config).
+
+umerge_1_case(Config) ->
+    do_proptest(prop_umerge_1, Config).
+
+umerge_2_case(Config) ->
+    do_proptest(prop_umerge_2, Config).
+
+umerge_3_case(Config) ->
+    do_proptest(prop_umerge_3, Config).
+
+umerge3_case(Config) ->
+    do_proptest(prop_umerge3, Config).
+
+uniq_1_case(Config) ->
+    do_proptest(prop_uniq_1, Config).
+
+uniq_2_case(Config) ->
+    do_proptest(prop_uniq_2, Config).
+
+unzip_case(Config) ->
+    do_proptest(prop_unzip, Config).
+
+unzip3_case(Config) ->
+    do_proptest(prop_unzip3, Config).
+
+usort_1_case(Config) ->
+    do_proptest(prop_usort_1, Config).
+
+usort_2_case(Config) ->
+    do_proptest(prop_usort_2, Config).
+
+zip_case(Config) ->
+    do_proptest(prop_zip, Config).
+
+zip3_case(Config) ->
+    do_proptest(prop_zip3, Config).
+
+zipwith_case(Config) ->
+    do_proptest(prop_zipwith, Config).
+
+zipwith3_case(Config) ->
+    do_proptest(prop_zipwith3, Config).
+
diff --git a/lib/stdlib/test/property_test/lists_prop.erl b/lib/stdlib/test/property_test/lists_prop.erl
new file mode 100644
index 0000000000..6df00335c6
--- /dev/null
+++ b/lib/stdlib/test/property_test/lists_prop.erl
@@ -0,0 +1,1807 @@
+%%
+%% %CopyrightBegin%
+%%
+%% Copyright Ericsson AB 2021. All Rights Reserved.
+%%
+%% Licensed under the Apache License, Version 2.0 (the "License");
+%% you may not use this file except in compliance with the License.
+%% You may obtain a copy of the License at
+%%
+%%     http://www.apache.org/licenses/LICENSE-2.0
+%%
+%% Unless required by applicable law or agreed to in writing, software
+%% distributed under the License is distributed on an "AS IS" BASIS,
+%% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+%% See the License for the specific language governing permissions and
+%% limitations under the License.
+%%
+%% %CopyrightEnd%
+%%
+-module(lists_prop).
+
+-compile([export_all, nowarn_export_all]).
+
+-proptest(eqc).
+-proptest([triq, proper]).
+
+-ifndef(EQC).
+-ifndef(PROPER).
+-ifndef(TRIQ).
+-define(EQC, true).
+-endif.
+-endif.
+-endif.
+
+-ifdef(EQC).
+-include_lib("eqc/include/eqc.hrl").
+-define(MOD_eqc,eqc).
+
+-else.
+-ifdef(PROPER).
+-include_lib("proper/include/proper.hrl").
+-define(MOD_eqc,proper).
+
+-else.
+-ifdef(TRIQ).
+-define(MOD_eqc,triq).
+-include_lib("triq/include/triq.hrl").
+
+-endif.
+-endif.
+-endif.
+
+-define(RANDOM_ATOMS, 1000).
+
+%%%%%%%%%%%%%%%%%%
+%%% Properties %%%
+%%%%%%%%%%%%%%%%%%
+
+%% all/2
+prop_all_true() ->
+    ?FORALL(
+        InList,
+        gen_list(),
+        lists:all(fun(_) -> true end, InList)
+    ).
+
+prop_all_false() ->
+    ?FORALL(
+        {InList, Elem},
+        ?LET(
+            {F, R, E},
+            {gen_list(), gen_list(), make_ref()},
+            {F ++ [E|R], E}
+        ),
+        not lists:all(fun(T) -> T =/= Elem end, InList)
+    ).
+
+%% any/2
+prop_any_true() ->
+    ?FORALL(
+        {InList, Elem},
+        ?LET(
+            {F, R, E},
+            {gen_list(), gen_list(), make_ref()},
+            {F ++ [E|R], E}
+        ),
+        lists:any(fun(T) -> T =:= Elem end, InList)
+    ).
+
+prop_any_false() ->
+    ?FORALL(
+        InList,
+        gen_list(),
+        not lists:any(fun(_) -> false end, InList)
+    ).
+
+%% append/1
+prop_append_1() ->
+    ?FORALL(
+        InLists,
+        list(gen_list()),
+        check_appended(InLists, lists:append(InLists))
+    ).
+
+%% append/2
+prop_append_2() ->
+    ?FORALL(
+        {InList1, InList2},
+        {gen_list(), gen_list()},
+        lists:append(InList1, InList2) =:= InList1 ++ InList2
+    ).
+
+%% concat/1
+prop_concat() ->
+    ?FORALL(
+        {InList, ExpString},
+        gen_list_fold(
+            oneof([gen_atom(), number(), string()]),
+            fun
+                (A, Acc) when is_atom(A) -> Acc ++ atom_to_list(A);
+                (I, Acc) when is_integer(I) -> Acc ++ integer_to_list(I);
+                (F, Acc) when is_float(F) -> Acc ++ float_to_list(F);
+                (L, Acc) when is_list(L) -> Acc ++ L
+            end,
+            []
+        ),
+        lists:concat(InList) =:= ExpString
+    ).
+
+%% delete/2
+prop_delete() ->
+    ?FORALL(
+        {InList, DelElem},
+        ?LET(
+            {F, R, E},
+            {gen_list(), gen_list(), gen_any()},
+            {F ++ [E|R], E}
+        ),
+        begin
+            DeletedList = lists:delete(DelElem, InList),
+            length(DeletedList) =:= length(InList) - 1 andalso
+            check_deleted(DelElem, InList, DeletedList)
+        end
+    ).
+
+prop_delete_absent() ->
+    ?FORALL(
+        InList,
+        gen_list(),
+        lists:delete(make_ref(), InList) =:= InList
+    ).
+
+%% droplast/1
+prop_droplast() ->
+    ?FORALL(
+        InList,
+        gen_list(),
+        try
+            lists:droplast(InList) =:= lists:reverse(tl(lists:reverse(InList)))
+        catch
+            error:_ ->
+                InList =:= []
+        end
+    ).
+
+%% dropwhile/2
+prop_dropwhile() ->
+    ?FORALL(
+        {Pred, InList, ExpList},
+        ?LET(
+            Fn,
+            function1(boolean()),
+            ?LET(
+                {L, {_, DL}},
+                gen_list_fold(
+                    gen_any(),
+                    fun(E, {Drop, Acc}) ->
+                        case Drop andalso Fn(E) of
+                            true -> {true, Acc};
+                            false -> {false, Acc ++ [E]}
+                        end
+                    end,
+                    {true, []}
+                ),
+                {Fn, L, DL}
+            )
+        ),
+        lists:dropwhile(Pred, InList) =:= ExpList
+    ).
+
+%% duplicate/2
+prop_duplicate() ->
+    ?FORALL(
+        {N, Term, ExpList},
+        ?LET(
+            T,
+            gen_any(),
+            ?LET(L, list(T), {length(L), T, L})
+        ),
+        lists:duplicate(N, Term) =:= ExpList
+    ).
+
+%% enumerate/1
+prop_enumerate_1() ->
+    ?FORALL(
+        {InList, ExpList},
+        ?LET(
+            {L, {_, EL}},
+            gen_list_fold(
+                gen_any(),
+                fun(T, {I, Acc}) ->
+                    {I + 1, Acc ++ [{I, T}]}
+                end,
+                {1, []}
+            ),
+            {L, EL}
+        ),
+        lists:enumerate(InList) =:= ExpList
+    ).
+
+%% enumerate/2
+prop_enumerate_2() ->
+    ?FORALL(
+        {StartIndex, InList, ExpList},
+        ?LET(
+            N,
+            integer(),
+            ?LET(
+                {L, {_, EL}},
+                gen_list_fold(
+                    gen_any(),
+                    fun(T, {I, Acc}) ->
+                        {I + 1, Acc ++ [{I, T}]}
+                    end,
+                    {N, []}
+                ),
+                {N, L, EL}
+            )
+        ),
+        lists:enumerate(StartIndex, InList) =:= ExpList
+    ).
+
+%% filter/2
+prop_filter() ->
+    ?FORALL(
+        {Pred, InList, ExpList},
+        ?LET(
+            P,
+            function1(boolean()),
+            ?LET(
+                {L, F},
+                gen_list_fold(
+                    gen_any(),
+                    fun(T, Acc) ->
+                        case P(T) of
+                            true -> Acc ++ [T];
+                            false -> Acc
+                        end
+                    end,
+                    []
+                ),
+                {P, L, F}
+            )
+        ),
+        lists:filter(Pred, InList) =:= ExpList
+    ).
+
+%% filtermap/2
+prop_filtermap() ->
+    ?FORALL(
+        {FilterMapFn, InList, ExpList},
+        ?LET(
+            Fn,
+            function1(oneof([true, false, {true, gen_any()}])),
+            ?LET(
+                {L, FM},
+                gen_list_fold(
+                    gen_any(),
+                    fun(T, Acc) ->
+                        case Fn(T) of
+                            false -> Acc;
+                            true -> Acc ++ [T];
+                            {true, T1} -> Acc ++ [T1]
+                        end
+                    end,
+                    []
+                ),
+                {Fn, L, FM}
+            )
+        ),
+        lists:filtermap(FilterMapFn, InList) =:= ExpList
+    ).
+
+%% flatlength/1
+prop_flatlength() ->
+    ?FORALL(
+        {DeepList, Len},
+        gen_list_deepfold(fun(_, _, Cnt) -> Cnt + 1 end, 0),
+        lists:flatlength(DeepList) =:= Len
+    ).
+
+%% flatmap/2
+prop_flatmap() ->
+    ?FORALL(
+        {MapFn, InList, ExpList},
+        ?LET(
+            Fn,
+            function1(gen_list()),
+            ?LET(
+                {L, FlatMapped},
+                gen_list_fold(
+                    gen_any(),
+                    fun(T, Acc) ->
+                        Acc ++ Fn(T)
+                    end,
+                    []
+                ),
+                {Fn, L, FlatMapped}
+            )
+        ),
+        lists:flatmap(MapFn, InList) =:= ExpList
+    ).
+
+%% flatten/1
+prop_flatten_1() ->
+    ?FORALL(
+        {DeepList, FlatList},
+        gen_list_deepfold(fun(_, E, Acc) -> Acc ++ [E] end, []),
+        lists:flatten(DeepList) =:= FlatList
+    ).
+
+%% flatten/2
+prop_flatten_2() ->
+    ?FORALL(
+        {{DeepList, FlatList}, Tail},
+        {gen_list_deepfold(fun(_, E, Acc) -> Acc ++ [E] end, []), gen_list()},
+        lists:flatten(DeepList, Tail) =:= FlatList ++ Tail
+    ).
+
+%% foldl/3
+prop_foldl() ->
+    ?FORALL(
+        {FoldFn, InList, Acc0, Exp},
+        ?LET(
+            {Fn, Acc0},
+            {function2(gen_any()), gen_any()},
+            ?LET(
+                {L, V},
+                gen_list_fold(gen_any(), Fn, Acc0),
+                {Fn, L, Acc0, V}
+            )
+        ),
+        lists:foldl(FoldFn, Acc0, InList) =:= Exp
+    ).
+
+%% foldr/3
+prop_foldr() ->
+    ?FORALL(
+        {FoldFn, InList, Acc0, Exp},
+        ?LET(
+            {Fn, Acc0},
+            {function2(gen_any()), gen_any()},
+            ?LET(
+                {L, V},
+                gen_list_fold(gen_any(), Fn, Acc0),
+                {Fn, lists:reverse(L), Acc0, V}
+            )
+        ),
+        lists:foldr(FoldFn, Acc0, InList) =:= Exp
+    ).
+
+%% foreach/2
+prop_foreach() ->
+    ?FORALL(
+        InList,
+        gen_list(),
+        begin
+            Tag = make_ref(),
+            lists:foreach(fun(E) -> self() ! {Tag, E} end, InList),
+            [receive {Tag, T} -> T after 100 -> error(timeout) end || _ <- InList] =:= InList
+        end
+    ).
+
+%% join/2
+prop_join() ->
+    ?FORALL(
+        {Sep, InList},
+        {gen_any(), gen_list()},
+        check_joined(Sep, InList, lists:join(Sep, InList))
+    ).
+
+%% keydelete/3
+prop_keydelete() ->
+    ?FORALL(
+        {Key, N, InList},
+        ?LET(
+            {K, N},
+            {gen_any(), range(1, 5)},
+            ?LET(
+                {F, R, E},
+                {gen_list(), gen_list(), gen_keytuple(K, N, N + 3)},
+                {K, N, F ++ [E|R]}
+            )
+        ),
+        begin
+            DeletedL = lists:keydelete(Key, N, InList),
+            length(DeletedL) =:= length(InList) - 1 andalso
+            check_keydeleted(Key, N, InList, DeletedL)
+        end
+    ).
+
+prop_keydelete_absent() ->
+    ?FORALL(
+        {N, InList},
+        {pos_integer(), gen_list()},
+        lists:keydelete(make_ref(), N, InList) =:= InList
+    ).
+
+%% keyfind/3
+prop_keyfind() ->
+    ?FORALL(
+        {Key, N, InList},
+        ?LET(
+            {K, N},
+            {gen_any(), range(1, 5)},
+            ?LET(
+                {F, R, E},
+                {gen_list(), gen_list(), gen_keytuple(K, N, N + 3)},
+                {K, N, F ++ [E|R]}
+            )
+        ),
+        begin
+            Found = lists:keyfind(Key, N, InList),
+            is_tuple(Found) andalso
+            tuple_size(Found) >= N andalso
+            element(N, Found) == Key
+        end
+    ).
+
+prop_keyfind_absent() ->
+    ?FORALL(
+        {N, InList},
+        {pos_integer(), gen_list()},
+        not lists:keyfind(make_ref(), N, InList)
+    ).
+
+%% keymap/3
+prop_keymap() ->
+    ?FORALL(
+        {MapFn, N, InList, ExpList},
+        ?LET(
+            Fn,
+            function([gen_any()], gen_any()),
+            ?LET(
+                N,
+                range(1, 5),
+                ?LET(
+                    {L, M},
+                    gen_list_fold(
+                        gen_tuple(N, N + 3),
+                        fun(T, Acc) ->
+                            Acc ++ [setelement(N, T, Fn(element(N, T)))]
+                        end,
+                        []
+                    ),
+                    {Fn, N, L, M}
+                )
+            )
+        ),
+        lists:keymap(MapFn, N, InList) =:= ExpList
+    ).
+
+%% keymember/3
+prop_keymember() ->
+    ?FORALL(
+        {Key, N, InList},
+        ?LET(
+            {K, N},
+            {gen_any(), range(1, 5)},
+            ?LET(
+                {F, R, E},
+                {gen_list(), gen_list(), gen_keytuple(K, N, N + 3)},
+                {K, N, F ++ [E|R]}
+            )
+        ),
+        lists:keymember(Key, N, InList)
+    ).
+
+prop_keymember_absent() ->
+    ?FORALL(
+        {N, InList},
+        {pos_integer(), gen_list()},
+        not lists:keymember(make_ref(), N, InList)
+    ).
+
+%% keymerge/3
+prop_keymerge() ->
+    ?FORALL(
+        {N, InList1, InList2},
+        ?LET(
+            N,
+            range(1, 5),
+            ?LET(
+                {L1, L2},
+                {list(gen_tuple(N, N+3)), list(gen_tuple(N, N+3))},
+                {N, lists:sort(L1), lists:sort(L2)}
+            )
+        ),
+        check_merged(
+            fun (E1, E2) -> element(N, E1) =< element(N, E2) end,
+            [InList1, InList2],
+            lists:keymerge(N, InList1, InList2)
+        )
+    ).
+
+%% keyreplace/4
+prop_keyreplace() ->
+    ?FORALL(
+        {Key, N, InList, Replacement},
+        ?LET(
+            {K, N},
+            {gen_any(), range(1, 5)},
+            ?LET(
+                {F, R, E0, E1},
+                {gen_list(), gen_list(), gen_keytuple(K, N, N + 3), gen_tuple()},
+                {K, N, F ++ [E0|R], E1}
+            )
+        ),
+        check_keyreplaced(Key, N, Replacement, InList, lists:keyreplace(Key, N, InList, Replacement))
+    ).
+
+prop_keyreplace_absent() ->
+    ?FORALL(
+        {N, InList, Replacement},
+        {pos_integer(), gen_list(), gen_tuple()},
+        lists:keyreplace(make_ref(), N, InList, Replacement) =:= InList
+    ).
+
+%% keysearch/3
+prop_keysearch() ->
+    ?FORALL(
+        {Key, N, InList},
+        ?LET(
+            {K, N},
+            {gen_any(), range(1, 5)},
+            ?LET(
+                {F, R, E},
+                {gen_list(), gen_list(), gen_keytuple(K, N, N + 3)},
+                {K, N, F ++ [E|R]}
+            )
+        ),
+        begin
+            {value, Found} = lists:keysearch(Key, N, InList),
+            is_tuple(Found) andalso
+            tuple_size(Found) >= N andalso
+            element(N, Found) == Key
+        end
+    ).
+
+prop_keysearch_absent() ->
+    ?FORALL(
+        {N, InList},
+        {pos_integer(), gen_list()},
+        not lists:keysearch(make_ref(), N, InList)
+    ).
+
+%% keysort/2
+prop_keysort() ->
+    ?FORALL(
+        {N, InList},
+        ?LET(
+            N,
+            range(1, 5),
+            {N, list(gen_tuple(N, N + 3))}
+        ),
+        begin
+            Sorted = lists:keysort(N, InList),
+            length(Sorted) =:= length(InList) andalso
+            check_sorted(fun(E1, E2) -> element(N, E1) =< element(N, E2) end, InList, Sorted)
+        end
+    ).
+
+%% keystore/4
+prop_keystore() ->
+    ?FORALL(
+        {Key, N, InList, ToStore},
+        ?LET(
+            {K, N},
+            {gen_any(), range(1, 5)},
+            ?LET(
+                {F, R, E0, E1},
+                {gen_list(), gen_list(), gen_keytuple(K, N, N + 3), gen_tuple()},
+                {K, N, F ++ [E0|R], E1}
+            )
+        ),
+        check_keyreplaced(Key, N, ToStore, InList, lists:keystore(Key, N, InList, ToStore))
+    ).
+
+prop_keystore_absent() ->
+    ?FORALL(
+        {N, InList, ToStore},
+        {pos_integer(), gen_list(), gen_tuple()},
+        lists:keystore(make_ref(), N, InList, ToStore) =:= InList ++ [ToStore]
+    ).
+
+%% keytake/3
+prop_keytake() ->
+    ?FORALL(
+        {Key, N, InList, ExpList, ExpElem},
+        ?LET(
+           {K, N},
+           {make_ref(), range(1, 5)},
+           ?LET(
+               {F, R, E},
+            {gen_list(), gen_list(), gen_keytuple(K, N, N + 3)},
+            {K, N, F ++ [E|R], F ++ R, E}
+           )
+        ),
+        lists:keytake(Key, N, InList) =:= {value, ExpElem, ExpList}
+    ).
+
+prop_keytake_absent() ->
+    ?FORALL(
+        {N, InList},
+        {pos_integer(), gen_list()},
+        lists:keytake(make_ref(), N, InList) =:= false
+    ).
+
+%% last/1
+prop_last() ->
+    ?FORALL(
+        InList,
+        gen_list(),
+        try
+            lists:last(InList) =:= hd(lists:reverse(InList))
+        catch
+            error:_ ->
+                InList =:= []
+        end
+    ).
+
+%% map/2
+prop_map() ->
+    ?FORALL(
+        {MapFn, InList, ExpList},
+        ?LET(
+            Fn,
+            function1(gen_any()),
+            ?LET(
+                {L, M},
+                gen_list_fold(
+                    gen_any(),
+                    fun(T, Acc) ->
+                        Acc ++ [Fn(T)]
+                    end,
+                    []
+                ),
+                {Fn, L, M}
+            )
+        ),
+        lists:map(MapFn, InList) =:= ExpList
+    ).
+
+%% mapfoldl/3
+prop_mapfoldl() ->
+    ?FORALL(
+        {MapFoldFn, InList, Acc0, Exp},
+        ?LET(
+            {MapFn, FoldFn, Acc0},
+            {function1(gen_any()), function2(gen_any()), gen_any()},
+            ?LET(
+                {L, MV},
+                gen_list_fold(
+                    gen_any(),
+                    fun(T, {AccM, AccF}) ->
+                        {AccM ++ [MapFn(T)], FoldFn(T, AccF)}
+                    end,
+                    {[], Acc0}
+                ),
+                {fun(T, Acc) -> {MapFn(T), FoldFn(T, Acc)} end, L, Acc0, MV}
+            )
+        ),
+        lists:mapfoldl(MapFoldFn, Acc0, InList) =:= Exp
+    ).
+
+%% mapfoldr/3
+prop_mapfoldr() ->
+    ?FORALL(
+        {MapFoldFn, InList, Acc0, Exp},
+        ?LET(
+            {MapFn, FoldFn, Acc0},
+            {function1(gen_any()), function2(gen_any()), gen_any()},
+            ?LET(
+                {L, MV},
+                gen_list_fold(
+                    gen_any(),
+                    fun(T, {AccM, AccF}) ->
+                        {[MapFn(T)|AccM], FoldFn(T, AccF)}
+                    end,
+                    {[], Acc0}
+                ),
+                {fun(T, Acc) -> {MapFn(T), FoldFn(T, Acc)} end, lists:reverse(L), Acc0, MV}
+            )
+        ),
+        lists:mapfoldr(MapFoldFn, Acc0, InList) =:= Exp
+    ).
+
+%% max/1
+prop_max() ->
+    ?FORALL(
+        {InList, ExpMax},
+        gen_list_fold(gen_any(), fun erlang:max/2),
+        try
+            lists:max(InList) == ExpMax
+        catch
+            error:_ ->
+                InList =:= []
+        end
+    ).
+
+%% member/2
+prop_member() ->
+    ?FORALL(
+        {InList, Member},
+        ?LET(
+            {F, R, E},
+            {gen_list(), gen_list(), gen_any()},
+            {F ++ [E|R], E}
+        ),
+        lists:member(Member, InList)
+    ).
+
+prop_member_absent() ->
+    ?FORALL(
+        InList,
+        gen_list(),
+        not lists:member(make_ref(), InList)
+    ).
+
+%% merge/1
+prop_merge_1() ->
+    ?FORALL(
+        InLists,
+        list(?LET(L, gen_list(), lists:sort(L))),
+        check_merged(fun erlang:'=<'/2, InLists, lists:merge(InLists))
+    ).
+
+%% merge/2
+prop_merge_2() ->
+    ?FORALL(
+        {InList1, InList2},
+        ?LET(
+            {L1, L2},
+            {gen_list(), gen_list()},
+            {lists:sort(L1), lists:sort(L2)}
+        ),
+        check_merged(fun erlang:'=<'/2, [InList1, InList2], lists:merge(InList1, InList2))
+    ).
+
+%% merge/3
+prop_merge_3() ->
+    ?FORALL(
+        {SortFn, InList1, InList2},
+        ?LET(
+            {Fn, L1, L2},
+            {gen_ordering_fun(), gen_list(), gen_list()},
+            {Fn, lists:sort(Fn, L1), lists:sort(Fn, L2)}
+        ),
+        check_merged(SortFn, [InList1, InList2], lists:merge(SortFn, InList1, InList2))
+    ).
+
+%% merge3/3
+prop_merge3() ->
+    ?FORALL(
+        {InList1, InList2, InList3},
+        ?LET(
+            {L1, L2, L3},
+            {gen_list(), gen_list(), gen_list()},
+            {lists:sort(L1), lists:sort(L2), lists:sort(L3)}
+        ),
+        check_merged(fun erlang:'=<'/2, [InList1, InList2, InList3], lists:merge3(InList1, InList2, InList3))
+    ).
+
+%% min/1
+prop_min() ->
+    ?FORALL(
+        {InList, ExpMin},
+        gen_list_fold(gen_any(), fun erlang:min/2),
+        try
+            lists:min(InList) == ExpMin
+        catch
+            error:_ ->
+                InList =:= []
+        end
+    ).
+
+%% nth/2
+prop_nth() ->
+    ?FORALL(
+        {InList, N, ExpElem},
+        ?LET(
+            {F, R, E},
+            {gen_list(), gen_list(), gen_any()},
+            {F ++ [E|R], length(F)+1, E}
+        ),
+        lists:nth(N, InList) =:= ExpElem
+    ).
+
+prop_nth_outofrange() ->
+    ?FORALL(
+        {N, InList},
+        ?LET(
+            {L, Offset},
+            {gen_list(), pos_integer()},
+            {length(L) + Offset, L}
+        ),
+        try
+            lists:nth(N, InList)
+        of
+            _ ->
+                false
+        catch
+            error:_ ->
+                true
+        end
+    ).
+
+%% nthtail/2
+prop_nthtail() ->
+    ?FORALL(
+        {InList, N, ExpTail},
+        ?LET(
+            {F, R},
+            {gen_list(), gen_list()},
+            {F ++ R, length(F), R}
+        ),
+        lists:nthtail(N, InList) =:= ExpTail
+    ).
+
+prop_nthtail_outofrange() ->
+    ?FORALL(
+        {N, InList},
+        ?LET(
+            {L, Offset},
+            {gen_list(), pos_integer()},
+            {length(L) + Offset, L}
+        ),
+        try
+            lists:nthtail(N, InList)
+        of
+            _ ->
+                false
+        catch
+            error:_ ->
+                true
+        end
+    ).
+
+%% partition/2
+prop_partition() ->
+    ?FORALL(
+        {Pred, InList},
+        {function1(boolean()), gen_list()},
+        begin
+            {Group1, Group2} = lists:partition(Pred, InList),
+            check_partitioned(Pred, InList, Group1, Group2)
+        end
+    ).
+
+%% prefix/2
+prop_prefix() ->
+    ?FORALL(
+        {InList, Prefix},
+        ?LET(
+            {F, R},
+            {gen_list(), gen_list()},
+            {F ++ R, F}
+        ),
+        lists:prefix(Prefix, InList) andalso
+        not lists:prefix([make_ref()|Prefix], InList) andalso
+        not lists:prefix(Prefix ++ [make_ref()], InList) andalso
+        (not lists:prefix(Prefix, [make_ref()|InList]) orelse Prefix =:= [])
+    ).
+
+%% reverse/1
+prop_reverse_1() ->
+    ?FORALL(
+        InList,
+        gen_list(),
+        check_reversed(InList, lists:reverse(InList)) andalso
+        lists:reverse(lists:reverse(InList)) =:= InList
+    ).
+
+%% reverse/2
+prop_reverse_2() ->
+    ?FORALL(
+        {InList, InTail},
+        {gen_list(), gen_list()},
+        check_reversed(InList, lists:reverse(InList, InTail), InTail)
+    ).
+
+%% search/2
+prop_search() ->
+    ?FORALL(
+        {Pred, InList, ExpElem},
+        ?LET(
+            {F, R, E},
+            {gen_list(), gen_list(), make_ref()},
+            {fun(T) -> T =:= E end, F ++ [E|R], E}
+        ),
+        lists:search(Pred, InList) =:= {value, ExpElem}
+    ).
+
+prop_search_absent() ->
+    ?FORALL(
+        InList,
+        gen_list(),
+        lists:search(fun(_) -> false end, InList) =:= false
+    ).
+
+%% seq/2
+prop_seq2() ->
+    ?FORALL(
+        {From, To},
+        {integer(), integer()},
+        try
+            lists:seq(From, To)
+        of
+            Seq ->
+                To >= From - 1 andalso
+                check_seq(Seq, From, To, 1)
+        catch
+            error:_ ->
+                To < From - 1
+        end
+    ).
+
+%% seq/3
+prop_seq3() ->
+    ?FORALL(
+        {From, To, Step},
+        {integer(), integer(), integer()},
+        try
+            lists:seq(From, To, Step)
+        of
+            Seq when Step > 0 ->
+                To >= From - Step andalso
+                check_seq(Seq, From, To, Step);
+            Seq when Step < 0 ->
+                To =< From - Step andalso
+                check_seq(Seq, From, To, Step);
+            Seq when Step =:= 0 ->
+                From =:= To andalso
+                check_seq(Seq, From, To, Step)
+        catch
+            error:_ when Step > 0 ->
+                To < From - Step;
+            error:_ when Step < 0 ->
+                To > From - Step;
+            error:_ when Step =:= 0 ->
+                From =/= To
+        end
+    ).
+
+%% sort/1
+prop_sort_1() ->
+    ?FORALL(
+        InList,
+        gen_list(),
+        begin
+            Sorted = lists:sort(InList),
+            length(Sorted) =:= length(InList) andalso
+            check_sorted(InList, Sorted)
+        end
+    ).
+
+%% sort/2
+prop_sort_2() ->
+    ?FORALL(
+        {SortFn, InList},
+        {gen_ordering_fun(), gen_list()},
+        begin
+            Sorted = lists:sort(SortFn, InList),
+            length(Sorted) =:= length(InList) andalso
+            check_sorted(SortFn, InList, Sorted)
+        end
+    ).
+
+%% split/2
+prop_split() ->
+    ?FORALL(
+        {N, InList, ExpList1, ExpList2},
+        ?LET(
+            {F, R},
+            {gen_list(), gen_list()},
+            {length(F), F ++ R, F, R}
+        ),
+        lists:split(N, InList) =:= {ExpList1, ExpList2}
+    ).
+
+prop_split_outofrange() ->
+    ?FORALL(
+        {N, InList},
+        ?LET(
+            {L, Offset},
+            {gen_list(), pos_integer()},
+            {length(L) + Offset, L}
+        ),
+        try
+            lists:split(N, InList)
+        of
+            _ ->
+                false
+        catch
+            error:_ ->
+                true
+        end
+    ).
+
+%% splitwith/2
+prop_splitwith() ->
+    ?FORALL(
+        {Pred, InList},
+        {function1(boolean()), gen_list()},
+        begin
+            {Part1, Part2} = lists:splitwith(Pred, InList),
+            check_splitwithed(Pred, InList, Part1, Part2)
+        end
+    ).
+
+%% sublist/2
+prop_sublist_2() ->
+    ?FORALL(
+        {Len, InList, ExpList},
+        ?LET(
+            {F, R},
+            {gen_list(), gen_list()},
+            {length(F), F ++ R, F}
+        ),
+        lists:sublist(InList, Len) =:= ExpList
+    ).
+
+%% sublist/3
+prop_sublist_3() ->
+    ?FORALL(
+        {Start, Len, InList, ExpList},
+        ?LET(
+            {F, M, R},
+            {gen_list(), gen_list(), gen_list()},
+            {length(F)+1, length(M), F ++ M ++ R, M}
+        ),
+        lists:sublist(InList, Start, Len) =:= ExpList
+    ).
+
+%% subtract/2
+prop_subtract() ->
+    ?FORALL(
+        {InList, SubtractList},
+        ?LET(
+            {L, B, S},
+            {gen_list(), gen_list(), gen_list()},
+            {L ++ B, S ++ B}
+        ),
+        lists:subtract(InList, SubtractList) =:= InList -- SubtractList
+    ).
+
+%% suffix/2
+prop_suffix() ->
+    ?FORALL(
+        {InList, Suffix},
+        ?LET(
+            {F, R},
+            {gen_list(), gen_list()},
+            {F ++ R, R}
+        ),
+        lists:suffix(Suffix, InList) andalso
+        not lists:suffix([make_ref()|Suffix], InList) andalso
+        not lists:suffix(Suffix ++ [make_ref()], InList) andalso
+        (not lists:suffix(Suffix, InList ++ [make_ref()]) orelse Suffix =:= [])
+    ).
+
+%% sum/1
+prop_sum() ->
+    ?FORALL(
+        {InList, ExpSum},
+        gen_list_fold(number(), fun erlang:'+'/2, 0),
+        lists:sum(InList) =:= ExpSum
+    ).
+
+%% takewhile/2
+prop_takewhile() ->
+    ?FORALL(
+        {Pred, InList, ExpList},
+        ?LET(
+            Fn,
+            function1(boolean()),
+            ?LET(
+                {L, {_, TL}},
+                gen_list_fold(
+                    gen_any(),
+                    fun(E, {Take, Acc}) ->
+                        case Take andalso Fn(E) of
+                            true -> {true, Acc ++ [E]};
+                            false -> {false, Acc}
+                        end
+                    end,
+                    {true, []}
+                ),
+                {Fn, L, TL}
+            )
+        ),
+        lists:takewhile(Pred, InList) =:= ExpList
+    ).
+
+%% ukeymerge/3
+prop_ukeymerge() ->
+    ?FORALL(
+        {N, InList1, InList2},
+        ?LET(
+            N,
+            range(1, 5),
+            ?LET(
+                {L1, L2},
+                {list(gen_tuple(N, N+3)), list(gen_tuple(N, N+3))},
+                {N, lists:ukeysort(N, L1), lists:ukeysort(N, L2)}
+            )
+        ),
+        check_umerged(
+            fun(E1, E2) -> element(N, E1) =< element(N, E2) end,
+            [InList1, InList2],
+            lists:ukeymerge(N, InList1, InList2)
+        )
+    ).
+
+%% ukeysort/2
+prop_ukeysort() ->
+    ?FORALL(
+        {N, InList},
+        ?LET(
+            N,
+            range(1, 5),
+            {N, list(gen_tuple(N, N + 3))}
+        ),
+        begin
+            Sorted = lists:ukeysort(N, InList),
+            length(Sorted) =< length(InList) andalso
+            check_usorted(fun(E1, E2) -> element(N, E1) =< element(N, E2) end, InList, Sorted)
+        end
+    ).
+
+%% umerge/1
+prop_umerge_1() ->
+    ?FORALL(
+        InLists,
+        list(?LET(L, gen_list(), lists:usort(L))),
+        check_umerged(InLists, lists:umerge(InLists))
+    ).
+
+%% umerge/2
+prop_umerge_2() ->
+    ?FORALL(
+        {InList1, InList2},
+        ?LET(
+            {L1, L2},
+            {gen_list(), gen_list()},
+            {lists:usort(L1), lists:usort(L2)}
+        ),
+        check_umerged([InList1, InList2], lists:umerge(InList1, InList2))
+    ).
+
+%% umerge/3
+prop_umerge_3() ->
+    ?FORALL(
+        {SortFn, InList1, InList2},
+        ?LET(
+            {Fn, L1, L2},
+            {gen_ordering_fun(), gen_list(), gen_list()},
+            {Fn, lists:usort(Fn, L1), lists:usort(Fn, L2)}
+        ),
+        check_umerged(SortFn, [InList1, InList2], lists:umerge(SortFn, InList1, InList2))
+    ).
+
+%% umerge3/3
+prop_umerge3() ->
+    ?FORALL(
+        {InList1, InList2, InList3},
+        ?LET(
+            {L1, L2, L3},
+            {gen_list(), gen_list(), gen_list()},
+            {lists:usort(L1), lists:usort(L2), lists:usort(L3)}
+        ),
+        check_umerged([InList1, InList2, InList3], lists:umerge3(InList1, InList2, InList3))
+    ).
+
+%% uniq/1
+prop_uniq_1() ->
+    ?FORALL(
+        InList,
+        ?LET(
+            {L, M},
+            {gen_list(), gen_list()},
+	    ?LET(
+	        S,
+		vector(length(L) + 2 * length(M), integer()),
+	        [E || {_, E} <- lists:sort(lists:zip(S, L ++ M ++ M))]
+	    )
+        ),
+        check_uniqed(InList, lists:uniq(InList))
+    ).
+
+%% uniq/2
+prop_uniq_2() ->
+    ?FORALL(
+        {UniqFn, InList},
+        {function1(oneof([a, b, c])), gen_list()},
+        check_uniqed(UniqFn, InList, lists:uniq(UniqFn, InList))
+    ).
+
+%% unzip/1
+prop_unzip() ->
+    ?FORALL(
+        {InList, {ExpList1, ExpList2}},
+        gen_list_fold(
+            {gen_any(), gen_any()},
+            fun({T1, T2}, {L1, L2}) ->
+                {L1 ++ [T1], L2 ++ [T2]}
+            end,
+            {[], []}
+        ),
+        lists:unzip(InList) =:= {ExpList1, ExpList2}
+    ).
+
+%% unzip3/1
+prop_unzip3() ->
+    ?FORALL(
+        {InList, {ExpList1, ExpList2, ExpList3}},
+        gen_list_fold(
+            {gen_any(), gen_any(), gen_any()},
+            fun({T1, T2, T3}, {L1, L2, L3}) ->
+                {L1 ++ [T1], L2 ++ [T2], L3 ++ [T3]}
+            end,
+            {[], [], []}
+        ),
+        lists:unzip3(InList) =:= {ExpList1, ExpList2, ExpList3}
+    ).
+
+%% usort/1
+prop_usort_1() ->
+    ?FORALL(
+        InList,
+        gen_list(),
+        begin
+            Sorted = lists:usort(InList),
+            length(Sorted) =< length(InList) andalso
+            check_usorted(InList, Sorted)
+        end
+    ).
+
+%% usort/2
+prop_usort_2() ->
+    ?FORALL(
+        {SortFn, InList},
+        {gen_ordering_fun(), gen_list()},
+        begin
+            Sorted = lists:usort(SortFn, InList),
+            length(Sorted) =< length(InList) andalso
+            check_usorted(SortFn, InList, Sorted)
+        end
+    ).
+
+%% zip/2
+prop_zip() ->
+    ?FORALL(
+        {ExpList, {InList1, InList2}},
+        gen_list_fold(
+            {gen_any(), gen_any()},
+            fun({T1, T2}, {L1, L2}) ->
+                {L1 ++ [T1], L2 ++ [T2]}
+            end,
+            {[], []}
+        ),
+        lists:zip(InList1, InList2) =:= ExpList
+    ).
+
+%% zip3/3
+prop_zip3() ->
+    ?FORALL(
+        {ExpList, {InList1, InList2, InList3}},
+        gen_list_fold(
+            {gen_any(), gen_any(), gen_any()},
+            fun({T1, T2, T3}, {L1, L2, L3}) ->
+                {L1 ++ [T1], L2 ++ [T2], L3 ++ [T3]}
+            end,
+            {[], [], []}
+        ),
+        lists:zip3(InList1, InList2, InList3) =:= ExpList
+    ).
+
+%% zipwith/3
+prop_zipwith() ->
+    ?FORALL(
+        {ZipFn, InList1, InList2, ExpList},
+        ?LET(
+            Fn,
+            function2(gen_any()),
+            ?LET(
+                {_, {L1, L2, Z}},
+                gen_list_fold(
+                    {gen_any(), gen_any()},
+                    fun({T1, T2}, {L1, L2, Z}) ->
+                        {L1 ++ [T1], L2 ++ [T2], Z ++ [Fn(T1, T2)]}
+                    end,
+                    {[], [], []}
+                ),
+                {Fn, L1, L2, Z}
+            )
+        ),
+        lists:zipwith(ZipFn, InList1, InList2) =:= ExpList
+    ).
+
+%% zipwith3/4
+prop_zipwith3() ->
+    ?FORALL(
+        {ZipFn, InList1, InList2, InList3, ExpList},
+        ?LET(
+            Fn,
+            function3(gen_any()),
+            ?LET(
+                {_, {L1, L2, L3, Z}},
+                gen_list_fold(
+                    {gen_any(), gen_any(), gen_any()},
+                    fun({T1, T2, T3}, {L1, L2, L3, Z}) ->
+                        {L1 ++ [T1], L2 ++ [T2], L3 ++ [T3], Z ++ [Fn(T1, T2, T3)]}
+                    end,
+                    {[], [], [], []}
+                ),
+                {Fn, L1, L2, L3, Z}
+            )
+        ),
+        lists:zipwith3(ZipFn, InList1, InList2, InList3) =:= ExpList
+    ).
+
+%%%%%%%%%%%%%%%%%%
+%%% Generators %%%
+%%%%%%%%%%%%%%%%%%
+
+%% Generator for lists of the given type, folding the given function
+%% over values on the top level as they are generated. The first generated
+%% value serves as the initial accumulator.
+gen_list_fold(Gen, FoldFn) ->
+    ?SIZED(
+        Size,
+        ?LET(
+            T,
+            Gen,
+            if
+                Size =< 1 ->
+                    {[], T};
+                true ->
+                    gen_list_fold(max(0, Size - 1), Gen, [T], FoldFn, T)
+            end
+        )
+    ).
+
+%% Generator for lists of the given type, folding the given function
+%% over values on the top level as they are generated.
+gen_list_fold(Gen, FoldFn, Acc0) ->
+    ?SIZED(
+        Size,
+        gen_list_fold(max(0, Size - 1), Gen, [], FoldFn, Acc0)
+    ).
+
+gen_list_fold(0, _Gen, L, _FoldFn, Acc) ->
+    {L, Acc};
+gen_list_fold(N, Gen, L, FoldFn, Acc) ->
+    ?LET(
+        E,
+        Gen,
+        gen_list_fold(N - 1, Gen, L ++ [E], FoldFn, FoldFn(E, Acc))
+    ).
+
+%% Generator for key tuples of the given size,
+%% with the given key in the given (ie, last) position.
+gen_keytuple(Key, Size) ->
+    gen_keytuple(Key, Size, Size).
+
+%% Generator for key tuples of the given minimum and maximum
+%% sizes, with the given key in the given minimum position.
+gen_keytuple(Key, MinSize, MaxSize) ->
+    ?LET(
+        Tuple,
+        gen_tuple(MinSize, MaxSize),
+        setelement(MinSize, Tuple, Key)
+    ).
+
+%% Generator for tuples of random size.
+gen_tuple() ->
+    ?LET(
+        N,
+        non_neg_integer(),
+        gen_tuple(N)
+    ).
+
+%% Generator for tuples of the given size.
+gen_tuple(Size) ->
+    ?LET(
+        V,
+        vector(Size, gen_any()),
+        list_to_tuple(V)
+    ).
+
+%% Generator for tuples of the given minimum and
+%% maximum sizes.
+gen_tuple(MinSize, MaxSize) ->
+    ?LET(
+        N,
+        range(MinSize, MaxSize),
+        ?LET(
+            V,
+            vector(N, gen_any()),
+            list_to_tuple(V)
+        )
+    ).
+
+%% Generator for lists of anything.
+gen_list() ->
+    list(gen_any()).
+
+%% Generator for lists of anything, folding the given function
+%% over values on all levels of list-nesting as they are generated.
+gen_list_deepfold(FoldFn, Acc0) ->
+    ?SIZED(
+        Size,
+        ?LET(
+            {_, L, Acc},
+            gen_list_deepfold(max(0, Size - 1), 0, [], FoldFn, Acc0),
+            {L, Acc}
+        )
+    ).
+
+gen_list_deepfold(N, _Level, L, _FoldFn, Acc) when N =< 0 ->
+    {N, lists:reverse(L), Acc};
+gen_list_deepfold(N, Level, L, FoldFn, Acc) ->
+    ?LET(
+        X,
+        frequency([
+            {4, {term, gen_any_simple()}},
+            {1, deeplist},
+            {1, tuple},
+            {2, stop}
+        ]),
+        case X of
+            deeplist ->
+                ?LET(
+                    {N1, L1, Acc1},
+                    gen_list_deepfold(N, Level + 1, [], FoldFn, Acc),
+                    gen_list_deepfold(N1, Level, [L1|L], FoldFn, Acc1)
+                );
+            tuple ->
+                ?LET(
+                    {N1, L1, _},
+                    gen_list_deepfold(N, Level + 1, [], fun(_, _, _) -> undefined end, undefined),
+                    begin
+                        E = list_to_tuple(L1),
+                        gen_list_deepfold(N1, Level, [E|L], FoldFn, FoldFn(Level, E, Acc))
+                    end
+                );
+            stop ->
+                {N, lists:reverse(L), Acc};
+            {term, E} ->
+                gen_list_deepfold(N - 1, Level, [E|L], FoldFn, FoldFn(Level, E, Acc))
+        end
+    ).
+
+%% Generator for simple and composite (lists and tuples) types.
+gen_any() ->
+    frequency(
+        [
+            {4, gen_any_simple()},
+            {1, ?LET({L, _}, gen_list_deepfold(fun(_, _, Acc) -> Acc end, undefined), L)},
+            {1, ?LET({L, _}, gen_list_deepfold(fun(_, _, Acc) -> Acc end, undefined), list_to_tuple(L))}
+        ]
+    ).
+
+%% Generator for simple types:
+%%   - atoms
+%%   - integers
+%%   - floats
+%%   - bitstrings
+gen_any_simple() ->
+    oneof([gen_atom(), integer(), float(), bitstring()]).
+
+%% Generator for interesting atoms:
+%%   - well-known atoms like `ok', `undefined', `infinity'...
+%%   - randomly generated "weird" atoms
+gen_atom() ->
+    oneof(
+        [
+            oneof([ok, error, true, false, undefined, infinity]),
+            oneof(['', '"', '\'', '(', ')', '()', '[', '[', '[]', '{', '}', '{}']),
+            gen_random_atom()
+        ]
+    ).
+
+%% Generator for a limited set of random atoms. The number of
+%% atoms that will be generated is set in `?RANDOM_ATOMS'.
+gen_random_atom() ->
+    ?LAZY(
+        ?LET(
+            N,
+            range(1, ?RANDOM_ATOMS),
+            try
+                persistent_term:get({?MODULE, random_atoms})
+            of
+                Atoms ->
+                    maps:get(N, Atoms)
+            catch
+                error:badarg ->
+                    ?LET(
+                        AtomsList,
+                        vector(?RANDOM_ATOMS, ?SIZED(Size, resize(Size * 100, atom()))),
+                        begin
+                            Fn = fun
+                                F(_, [], Acc) ->
+                                    Acc;
+                                F(Index, [A|As], Acc) ->
+                                    F(Index + 1, As, Acc#{Index => A})
+                            end,
+                            Atoms = Fn(1, AtomsList, #{}),
+                            persistent_term:put({?MODULE, random_atoms}, Atoms),
+                            maps:get(N, Atoms)
+                        end
+                    )
+            end
+        )
+    ).
+
+%% Generator for ordering functions, to be used for sorting and merging.
+%% The generated ordering functions are designed to fulfill the requirements given
+%% at the top of the `lists' documentation, namely to be antisymmetric, transitive,
+%% and total. Further, the chances that two terms compare equal, less or greater
+%% are equal.
+gen_ordering_fun() ->
+    ?LET(
+        F,
+        function1(range(1, 3)),
+        fun(T1, T2) ->
+            F(T1) =< F(T2)
+        end
+    ).
+
+%%%%%%%%%%%%%%%
+%%% Helpers %%%
+%%%%%%%%%%%%%%%
+
+%% --------------------------------------------------------------------
+check_appended([], []) ->
+    true;
+check_appended([[]|Ls], AL) ->
+    check_appended(Ls, AL);
+check_appended([L], AL) ->
+    L =:= AL;
+check_appended([[E1|L]|Ls], [E2|AL]) ->
+    E1 =:= E2 andalso
+    check_appended([L|Ls], AL);
+check_appended(_Ls, _AL) ->
+    false.
+
+%% --------------------------------------------------------------------
+check_deleted(E, [E|L], DL) ->
+    L =:= DL;
+check_deleted(E, [_|L], [_|DL]) ->
+    check_deleted(E, L, DL);
+check_deleted(_E, [], []) ->
+    true;
+check_deleted(_E, _L, _DL) ->
+    false.
+
+%% --------------------------------------------------------------------
+check_joined(Sep, [E|L], [E, Sep|JL]) ->
+    check_joined(Sep, L, JL);
+check_joined(_Sep, [E], [E]) ->
+    true;
+check_joined(_Sep, [], []) ->
+    true;
+check_joined(_Sep, _L, _JL) ->
+    false.
+
+%% --------------------------------------------------------------------
+check_keydeleted(K, N, [E|L], KDL) when element(N, E) == K ->
+    L =:= KDL;
+check_keydeleted(K, N, [_|L], [_|KDL]) ->
+    check_keydeleted(K, N, L, KDL);
+check_keydeleted(_K, _N, _L, _KDL) ->
+    false.
+
+%% --------------------------------------------------------------------
+check_keyreplaced(K, N, R, [E1|L], [E2|KRL]) when element(N, E1) == K ->
+    E2 =:= R andalso L =:= KRL;
+check_keyreplaced(K, N, R, [_|L], [_|KRL]) ->
+    check_keyreplaced(K, N, R, L, KRL);
+check_keyreplaced(_K, _N, _R, _L, _KRL) ->
+    false.
+
+%% --------------------------------------------------------------------
+check_merged(Ls, ML) ->
+    check_merged(fun erlang:'=<'/2, Ls, ML).
+
+check_merged(Fn, [[]|Ls], ML) ->
+    check_merged(Fn, Ls, ML);
+check_merged(_Fn, [], ML) ->
+    ML =:= [];
+check_merged(_Fn, [L], ML) ->
+    ML =:= L;
+check_merged(Fn, Ls, [E|ML]) ->
+    case find_in_heads(Fn, E, Ls) of
+        {true, Ls1} ->
+            check_merged(Fn, Ls1, ML);
+        false ->
+            false
+    end;
+check_merged(_Fn, _Ls, _ML) ->
+    false.
+
+find_in_heads(Fn, E, Ls) ->
+    find_in_heads(Fn, E, Ls, []).
+
+find_in_heads(Fn, E, [[]|Ls], Seen) ->
+    find_in_heads(Fn, E, Ls, Seen);
+find_in_heads(Fn, E, [[E1|LRest]=L|Ls], Seen) ->
+    case Fn(E, E1) andalso Fn(E1, E) of
+        true ->
+            {true, lists:reverse(Seen, [LRest|Ls])};
+        false ->
+            find_in_heads(Fn, E, Ls, [L|Seen])
+    end;
+find_in_heads(_Fn, _E, _Ls, _Seen) ->
+    false.
+
+%% --------------------------------------------------------------------
+check_partitioned(Pred, [E|L], P1, P2) ->
+    case {Pred(E), P1, P2} of
+        {true, [E|Rest], _} ->
+            check_partitioned(Pred, L, Rest, P2);
+        {false, _, [E|Rest]}  ->
+            check_partitioned(Pred, L, P1, Rest);
+        _ ->
+            false
+    end;
+check_partitioned(_Pred, [], [], []) ->
+    true;
+check_partitioned(_Pred, _L, _P1, _P2) ->
+    false.
+
+%% --------------------------------------------------------------------
+check_reversed(L1, L2) ->
+    check_reversed(L1, L2, []).
+
+check_reversed(L1, L2, Tail) ->
+    check_reversed1(L1, L2) =:= Tail.
+
+check_reversed1([], L2) ->
+    L2;
+check_reversed1([E|L1], L2) ->
+    case check_reversed1(L1, L2) of
+        [E|L2Rest] -> L2Rest;
+        _ -> false
+    end.
+
+%% --------------------------------------------------------------------
+check_seq([F|Seq], F, T, S) ->
+    check_seq(Seq, F + S, T, S);
+check_seq([], F, T, S) when S >= 0 ->
+    F >= T;
+check_seq([], F, T, S) when S < 0 ->
+    F =< T;
+check_seq(_Seq, _F, _T, _S) ->
+    false.
+
+%% --------------------------------------------------------------------
+check_sorted(L, Sorted) ->
+    check_sorted(fun erlang:'=<'/2, L, Sorted).
+
+check_sorted(SortFun, L, Sorted) ->
+    ExpElems = count_elems(L),
+    check_sorted(SortFun, Sorted, ExpElems, #{}).
+
+check_sorted(_SortFun, [], ExpElems, FoundElems) ->
+    ExpElems =:= FoundElems;
+check_sorted(SortFun, [E], ExpElems, FoundElems) ->
+    maps:is_key(E, ExpElems) andalso
+    check_sorted(SortFun, [], ExpElems, maps:update_with(E, fun(Cnt) -> Cnt + 1 end, 1, FoundElems));
+check_sorted(SortFun, [E1|[E2|_]=L], ExpElems, FoundElems) ->
+    SortFun(E1, E2) andalso
+    maps:is_key(E1, ExpElems) andalso
+    check_sorted(SortFun, L, ExpElems, maps:update_with(E1, fun(Cnt) -> Cnt + 1 end, 1, FoundElems));
+check_sorted(_SortFun, _L, _ExpElems, _FoundElems) ->
+    false.
+
+count_elems(L) ->
+    count_elems(L, #{}).
+
+count_elems([E|Es], Acc) ->
+    count_elems(Es, maps:update_with(E, fun(Cnt) -> Cnt + 1 end, 1, Acc));
+count_elems([], Acc) ->
+    Acc.
+
+%% --------------------------------------------------------------------
+check_splitwithed(Pred, [E|L], [E|P1], P2) ->
+    Pred(E) andalso
+    check_splitwithed(Pred, L, P1, P2);
+check_splitwithed(Pred, [E|_]=L, [], P2) ->
+    not Pred(E) andalso L =:= P2;
+check_splitwithed(_Pred, [], [], []) ->
+    true;
+check_splitwithed(_Pred, _L, _P1, _P2) ->
+    false.
+
+%% --------------------------------------------------------------------
+check_umerged(Ls, ML) ->
+    check_umerged(fun erlang:'=<'/2, Ls, ML).
+
+check_umerged(Fn, [[]|Ls], ML) ->
+    check_umerged(Fn, Ls, ML);
+check_umerged(_Fn, [L], ML) ->
+    ML =:= L;
+check_umerged(_Fn, [], ML) ->
+    ML =:= [];
+check_umerged(Fn, Ls, [E|ML]) ->
+    case find_and_remove_from_heads(Fn, E, Ls) of
+        {true, Ls1} ->
+            check_umerged(Fn, Ls1, ML);
+        false ->
+            false
+    end;
+check_umerged(_Fn, _Ls, _ML) ->
+    false.
+
+find_and_remove_from_heads(Fn, E, Ls) ->
+    find_and_remove_from_heads(false, Fn, E, Ls, []).
+
+find_and_remove_from_heads(Found, Fn, E, [[]|Ls], Seen) ->
+    find_and_remove_from_heads(Found, Fn, E, Ls, Seen);
+find_and_remove_from_heads(false, _Fn, _E, [], _Seen) ->
+    false;
+find_and_remove_from_heads(true, _Fn, _E, [], Seen) ->
+    {true, lists:reverse(Seen)};
+find_and_remove_from_heads(Found, Fn, E, [[E1|LRest]=L|Ls], Seen) ->
+    case Fn(E, E1) andalso Fn(E1, E) of
+        true ->
+            find_and_remove_from_heads(true, Fn, E, Ls, [LRest|Seen]);
+        false ->
+            find_and_remove_from_heads(Found, Fn, E, Ls, [L|Seen])
+    end.
+
+%% --------------------------------------------------------------------
+check_uniqed(L, UL) ->
+    check_uniqed(fun(X) -> X end, L, UL).
+
+check_uniqed(Fn, L, UL) ->
+    check_uniqed1(Fn, L, UL, sets:new([{version, 2}])).
+
+check_uniqed1(Fn, [E|L], [], Seen) ->
+    sets:is_element(Fn(E), Seen) andalso
+    check_uniqed1(Fn, L, [], Seen);
+check_uniqed1(Fn, [E1|L], [E2|URest]=U, Seen) ->
+    X1 = Fn(E1),
+    X2 = Fn(E2),
+    case sets:is_element(X1, Seen) of
+        true ->
+            X1 =/= X2 andalso
+            check_uniqed1(Fn, L, U, Seen);
+        false ->
+            X1 =:= X2 andalso
+            check_uniqed1(Fn, L, URest, sets:add_element(X1, Seen))
+    end;
+check_uniqed1(_Fn, [], [], _Seen) ->
+    true;
+check_uniqed1(_Fn, _L, _UL, _Seen) ->
+    false.
+
+%% --------------------------------------------------------------------
+check_usorted(L, Sorted) ->
+    check_usorted(fun erlang:'=<'/2, L, Sorted).
+
+check_usorted(SortFun, L, Sorted) ->
+    ExpElems = ucount_elems(SortFun, L),
+    check_sorted(SortFun, Sorted, ExpElems, #{}).
+
+ucount_elems(SortFun, L) ->
+    ucount_elems(SortFun, L, #{}).
+
+ucount_elems(SortFun, [E|Es], Acc) ->
+    K = ufind_key(SortFun, E, maps:keys(Acc)),
+    ucount_elems(SortFun, Es, maps:put(K, 1, Acc));
+ucount_elems(_SortFun, [], Acc) ->
+    Acc.
+
+ufind_key(SortFun, E, [K|Keys]) ->
+    case SortFun(E, K) andalso SortFun(K, E) of
+        true ->
+            K;
+        false ->
+            ufind_key(SortFun, E, Keys)
+    end;
+ufind_key(_SortFun, E, []) ->
+    E.
-- 
2.35.3

Places

File 5541-Property-based-tests-for-the-lists-module.patch of Package erlang (Revision e0e016f64b94e78db3440770f914218d)

Places