%%
%% %CopyrightBegin%
%%
%% Copyright Ericsson AB 2001-2012. 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(sofs_SUITE).
%%-define(debug, true).
-ifdef(debug).
-define(format(S, A), io:format(S, A)).
-define(line, put(line, ?LINE), ).
-define(config(X,Y), foo).
-define(t, test_server).
-else.
-include_lib("common_test/include/ct.hrl").
-define(format(S, A), ok).
-endif.
-export([all/0, suite/0,groups/0,init_per_suite/1, end_per_suite/1,
init_per_group/2,end_per_group/2]).
-export([ from_term_1/1, set_1/1, from_sets_1/1, relation_1/1,
a_function_1/1, family_1/1, projection/1,
relation_to_family_1/1, domain_1/1, range_1/1, image/1,
inverse_image/1, inverse_1/1, converse_1/1, no_elements_1/1,
substitution/1, restriction/1, drestriction/1,
strict_relation_1/1, extension/1, weak_relation_1/1,
to_sets_1/1, specification/1, union_1/1, intersection_1/1,
difference/1, symdiff/1, symmetric_partition/1,
is_sofs_set_1/1, is_set_1/1, is_equal/1, is_subset/1,
is_a_function_1/1, is_disjoint/1, join/1, canonical/1,
composite_1/1, relative_product_1/1, relative_product_2/1,
product_1/1, partition_1/1, partition_3/1,
multiple_relative_product/1, digraph/1, constant_function/1,
misc/1]).
-export([ family_specification/1,
family_domain_1/1, family_range_1/1,
family_to_relation_1/1,
union_of_family_1/1, intersection_of_family_1/1,
family_projection/1, family_difference/1,
family_intersection_1/1, family_union_1/1,
family_intersection_2/1, family_union_2/1,
partition_family/1]).
-import(sofs,
[a_function/1, a_function/2, constant_function/2,
canonical_relation/1, composite/2,
converse/1, extension/3, from_term/1, from_term/2,
difference/2, domain/1, empty_set/0, family_difference/2,
family_intersection/1, family_intersection/2, family_union/1,
family_union/2, family/1, family/2, family_specification/2,
family_domain/1, family_range/1, family_field/1,
family_projection/2, family_to_relation/1, union_of_family/1,
field/1, from_external/2, image/2, intersection/1,
intersection/2, intersection_of_family/1, inverse/1,
inverse_image/2, is_disjoint/2, is_empty_set/1, is_equal/2,
is_a_function/1, is_set/1, is_sofs_set/1, is_subset/2,
join/4, from_sets/1, multiple_relative_product/2,
no_elements/1, partition/1, partition/2, partition/3,
partition_family/2, product/1, product/2, projection/2,
range/1, relation/1, relation/2, relation_to_family/1,
relative_product/1, relative_product/2, relative_product1/2,
strict_relation/1, weak_relation/1, restriction/2,
restriction/3, drestriction/2, drestriction/3, to_sets/1,
is_type/1, set/1, set/2, specification/2, substitution/2,
symdiff/2, symmetric_partition/2, to_external/1, type/1,
union/1, union/2, family_to_digraph/1, family_to_digraph/2,
digraph_to_family/1, digraph_to_family/2]).
-export([init_per_testcase/2, end_per_testcase/2]).
-compile({inline,[{eval,2}]}).
suite() ->
[{ct_hooks,[ts_install_cth]},
{timetrap,{minutes,2}}].
all() ->
[{group, sofs}, {group, sofs_family}].
groups() ->
[{sofs, [],
[from_term_1, set_1, from_sets_1, relation_1,
a_function_1, family_1, relation_to_family_1, domain_1,
range_1, image, inverse_image, inverse_1, converse_1,
no_elements_1, substitution, restriction, drestriction,
projection, strict_relation_1, extension,
weak_relation_1, to_sets_1, specification, union_1,
intersection_1, difference, symdiff,
symmetric_partition, is_sofs_set_1, is_set_1, is_equal,
is_subset, is_a_function_1, is_disjoint, join,
canonical, composite_1, relative_product_1,
relative_product_2, product_1, partition_1, partition_3,
multiple_relative_product, digraph, constant_function,
misc]},
{sofs_family, [],
[family_specification, family_domain_1, family_range_1,
family_to_relation_1, union_of_family_1,
intersection_of_family_1, family_projection,
family_difference, family_intersection_1,
family_intersection_2, family_union_1, family_union_2,
partition_family]}].
init_per_suite(Config) ->
Config.
end_per_suite(_Config) ->
ok.
init_per_group(_GroupName, Config) ->
Config.
end_per_group(_GroupName, Config) ->
Config.
init_per_testcase(_Case, Config) ->
Config.
end_per_testcase(_Case, _Config) ->
ok.
%% [{2,b},{1,a,b}] == lists:sort([{2,b},{1,a,b}])
%% [{1,a,b},{2,b}] == lists:keysort(1,[{2,b},{1,a,b}])
from_term_1(Conf) when is_list(Conf) ->
%% would go wrong: projection(1,from_term([{2,b},{1,a,b}])),
?line {'EXIT', {badarg, _}} = (catch from_term([], {atom,'_',atom})),
?line {'EXIT', {badarg, _}} = (catch from_term([], [])),
?line {'EXIT', {badarg, _}} = (catch from_term([], [atom,atom])),
?line [] = to_external(from_term([])),
?line eval(from_term([]), empty_set()),
?line [] = to_external(from_term([], ['_'])),
?line eval(from_term([], ['_']), empty_set()),
?line [[]] = to_external(from_term([[]])),
?line [[['_']]] = type(from_term([[],[[]]])),
?line [[],[[]]] = to_external(from_term([[],[[]]])),
?line [[['_']]] = type(from_term([[],[[]]])),
?line eval(from_term([a],['_']), set([a])),
?line [[],[a]] = to_external(from_term([[],[a]])),
?line [[],[{a}]] = to_external(from_term([[{a}],[]])),
?line [{[],[{a,b,[d]}]},{[{a,b}],[]}] =
to_external(from_term([{[],[{a,b,[d]}]},{[{a,b}],[]}])),
?line [{[a,b],[c,d]}] = to_external(from_term([{[a,b],[c,d]}])),
?line [{{a,b},[a,b],{{a},{b}}}] =
to_external(from_term([{{a,b},[a,b],{{a},{b}}}])),
?line [{{a,{[a,b]},a}},{{z,{[y,z]},z}}] =
to_external(from_term([{{a,{[a,b,a]},a}},{{z,{[y,y,z]},z}}])),
?line {'EXIT', {badarg, _}} =
(catch from_term([{m1,[{m1,f1,1},{m1,f2,2}]},{m2,[]},{m3,[a]}])),
?line MS1 = [{m1,[{m1,f1,1},{m1,f2,2}]},{m2,[]},{m3,[{m3,f3,3}]}],
?line eval(to_external(from_term(MS1)), MS1),
?line eval(to_external(from_term(a)), a),
?line eval(to_external(from_term({a})), {a}),
?line eval(to_external(from_term([[a],[{b,c}]],[[atomic]])),
[[a],[{b,c}]]),
?line eval(type(from_term([[a],[{b,c}]],[[atomic]])),
[[atomic]]),
?line {'EXIT', {badarg, _}} = (catch from_term([[],[],a])),
?line {'EXIT', {badarg, _}} = (catch from_term([{[a,b],[c,{d}]}])),
?line {'EXIT', {badarg, _}} = (catch from_term([[],[a],[{a}]])),
?line {'EXIT', {badarg, _}} = (catch from_term([a,{a,b}])),
?line {'EXIT', {badarg, _}} = (catch from_term([[a],[{b,c}]],[['_']])),
?line {'EXIT', {badarg, _}} = (catch from_term([a | {a,b}])),
?line {'EXIT', {badarg, _}} =
(catch from_term([{{a},b,c},{d,e,f}],[{{atom},atom,atom}])),
?line {'EXIT', {badarg, _}} =
(catch from_term([{a,{b,c}} | tail], [{atom,{atom,atom}}])),
?line {'EXIT', {badarg, _}} = (catch from_term({})),
?line {'EXIT', {badarg, _}} = (catch from_term([{}])),
?line [{foo,bar},[b,a]] =
to_external(from_term([[b,a],{foo,bar},[b,a]], [atom])),
?line [{[atom],{atom,atom}}] =
type(from_term([{[], {a,b}},{[a,b],{e,f}}])),
?line [{[atom],{atom,atom}}] =
type(from_term([{[], {a,b}},{[a,b],{e,f}}], [{[atom],{atom,atom}}])),
?line [[atom]] = type(from_term([[a],[{b,c}]],[[atom]])),
?line {atom, atom} = type(from_term({a,b}, {atom, atom})),
?line atom = type(from_term(a, atom)),
?line {'EXIT', {badarg, _}} = (catch from_term({a,b},{atom})),
?line [{{a},b,c},{{d},e,f}] =
to_external(from_term([{{a},b,c},{{a},b,c},{{d},e,f}],
[{{atom},atom,atom}])),
%% from_external too...
?line e = to_external(from_external(e, atom)),
?line {e} = to_external(from_external({e}, {atom})),
?line [e] = to_external(from_external([e], [atom])),
%% and is_type...
?line true = is_type(['_']),
?line false = is_type('_'),
?line true = is_type([['_']]),
?line false = is_type({atom,[],atom}),
?line false = is_type({atom,'_',atom}),
?line true = is_type({atom,atomic,atom}),
?line true = is_type({atom,atom}),
?line true = is_type(atom),
?line true = is_type([atom]),
?line true = is_type(type),
ok.
set_1(Conf) when is_list(Conf) ->
%% set/1
?line {'EXIT', {badarg, _}} = (catch set(a)),
?line {'EXIT', {badarg, _}} = (catch set({a})),
?line eval(set([]), from_term([],[atom])),
?line eval(set([a,b,c]), from_term([a,b,c])),
?line eval(set([a,b,a,a,b]), from_term([a,b])),
?line eval(set([a,b,c,a,d,d,c,1]), from_term([1,a,b,c,d])),
?line eval(set([a,b,d,a,c]), from_term([a,b,c,d])),
?line eval(set([f,e,d,c,d]), from_term([c,d,e,f])),
?line eval(set([h,f,d,g,g,d,c]), from_term([c,d,f,g,h])),
?line eval(set([h,e,d,k,l]), from_term([d,e,h,k,l])),
?line eval(set([h,e,c,k,d]), from_term([c,d,e,h,k])),
%% set/2
?line {'EXIT', {badarg, _}} = (catch set(a, [a])),
?line {'EXIT', {badarg, _}} = (catch set({a}, [a])),
?line {'EXIT', {badarg, _}} = (catch set([a], {a})),
?line {'EXIT', {badarg, _}} = (catch set([a], a)),
?line {'EXIT', {badarg, _}} = (catch set([a], [a,b])),
?line {'EXIT', {badarg, _}} = (catch set([a | b],[foo])),
?line {'EXIT', {badarg, _}} = (catch set([a | b],['_'])),
?line {'EXIT', {badarg, _}} = (catch set([a | b],[[atom]])),
?line {'EXIT', {badarg, _}} = (catch set([{}],[{}])),
?line eval(set([a],['_']), from_term([a],['_'])),
?line eval(set([], ['_']), empty_set()),
?line eval(set([a,b,a,b],[foo]), from_term([a,b],[foo])),
ok.
from_sets_1(Conf) when is_list(Conf) ->
?line E = empty_set(),
%% unordered
?line eval(from_sets([]), E),
?line {'EXIT', {type_mismatch, _}} =
(catch from_sets([from_term([{a,b}]),
E,
from_term([{a,b,c}])])),
?line eval(from_sets([from_term([{a,b}]), E]),
from_term([[],[{a,b}]])),
?line eval(from_sets([from_term({a,b},{atom,atom}),
from_term({b,c},{atom,atom})]),
relation([{a,b}, {b,c}])),
?line {'EXIT', {type_mismatch, _}} =
(catch from_sets([from_term({a,b},{atom,atom}),
from_term({a,b,c},{atom,atom,atom})])),
?line {'EXIT', {badarg, _}} = (catch from_sets(foo)),
?line eval(from_sets([E]), from_term([[]])),
?line eval(from_sets([E,E]), from_term([[]])),
?line eval(from_sets([E,set([a])]), from_term([[],[a]])),
?line {'EXIT', {badarg, _}} = (catch from_sets([E,{a}])),
?line {'EXIT', {type_mismatch, _}} =
(catch from_sets([E,from_term({a}),E])),
?line {'EXIT', {type_mismatch, _}} = (catch from_sets([from_term({a}),E])),
%% ordered
?line O = {from_term(a,atom), from_term({b}, {atom}), set([c,d])},
?line eval(from_sets(O), from_term({a,{b},[c,d]}, {atom,{atom},[atom]})),
?line {'EXIT', {badarg, _}} = (catch from_sets([a,b])),
?line {'EXIT', {badarg, _}} = (catch from_sets({a,b})),
?line eval(from_sets({from_term({a}),E}), from_term({{a},[]})),
ok.
relation_1(Conf) when is_list(Conf) ->
%% relation/1
?line eval(relation([]), from_term([], [{atom,atom}])),
?line eval(from_term([{a}]), relation([{a}])),
?line {'EXIT', {badarg, _}} = (catch relation(a)),
?line {'EXIT', {badarg, _}} = (catch relation([{a} | a])),
?line {'EXIT', {badarg, _}} = (catch relation([{}])),
?line {'EXIT', {badarg, _}} = (catch relation([],0)),
?line {'EXIT', {badarg, _}} = (catch relation([{a}],a)),
%% relation/2
?line eval(relation([{a},{b}], 1), from_term([{a},{b}])),
?line eval(relation([{1,a},{2,b},{1,a}], [{x,y}]),
from_term([{1,a},{2,b}], [{x,y}])),
?line eval(relation([{[1,2],a},{[2,1],b},{[2,1],a}], [{[x],y}]),
from_term([{[1,2],a},{[1,2],b}], [{[x],y}])),
?line {'EXIT', {badarg, _}} = (catch relation([{1,a},{2,b}], [{[x],y}])),
?line {'EXIT', {badarg, _}} = (catch relation([{1,a},{1,a,b}], [{x,y}])),
?line {'EXIT', {badarg, _}} = (catch relation([{a}], 2)),
?line {'EXIT', {badarg, _}} = (catch relation([{a},{b},{c,d}], 1)),
?line eval(relation([{{a},[{foo,bar}]}], ['_']),
from_term([{{a},[{foo,bar}]}], ['_'])),
?line eval(relation([], ['_']), from_term([], ['_'])),
?line {'EXIT', {badarg, _}} = (catch relation([[a]],['_'])),
?line eval(relation([{[a,b,a]}], [{[atom]}]), from_term([{[a,b,a]}])),
?line eval(relation([{[a,b,a],[[d,e,d]]}], [{[atom],[[atom]]}]),
from_term([{[a,b,a],[[d,e,d]]}])),
?line eval(relation([{[a,b,a],[[d,e,d]]}], [{atom,[[atom]]}]),
from_term([{[a,b,a],[[d,e,d]]}], [{atom,[[atom]]}])),
ok.
a_function_1(Conf) when is_list(Conf) ->
%% a_function/1
?line eval(a_function([]), from_term([], [{atom,atom}])),
?line eval(a_function([{a,b},{a,b},{b,c}]), from_term([{a,b},{b,c}])),
?line {'EXIT', {badarg, _}} = (catch a_function([{a}])),
?line {'EXIT', {badarg, _}} = (catch a_function([{a},{b},{c,d}])),
?line {'EXIT', {badarg, _}} = (catch a_function(a)),
?line {'EXIT', {badarg, _}} = (catch a_function([{a,b} | a])),
?line {'EXIT', {bad_function, _}} =
(catch a_function([{a,b},{b,c},{a,c}])),
F = 0.0, I = round(F),
if
F == I -> % term ordering
?line {'EXIT', {bad_function, _}} =
(catch a_function([{I,a},{F,b}])),
?line {'EXIT', {bad_function, _}} =
(catch a_function([{[I],a},{[F],b}],[{[a],b}]));
true ->
?line 2 = no_elements(a_function([{I,a},{F,b}])),
?line 2 = no_elements(a_function([{[I],a},{[F],b}],[{[a],b}]))
end,
%% a_function/2
FT = [{atom,atom}],
?line eval(a_function([], FT), from_term([], FT)),
?line eval(a_function([{a,b},{b,c},{b,c}], FT),
from_term([{a,b},{b,c}], FT)),
?line {'EXIT', {badarg, _}} = (catch a_function([{a,b}], [{a}])),
?line {'EXIT', {badarg, _}} = (catch a_function([{a,b}], [{a,[b,c]}])),
?line {'EXIT', {badarg, _}} = (catch a_function([{a}], FT)),
?line {'EXIT', {badarg, _}} = (catch a_function([{a},{b},{c,d}], FT)),
?line {'EXIT', {badarg, _}} = (catch a_function(a, FT)),
?line {'EXIT', {badarg, _}} = (catch a_function([{a,b} | a], FT)),
?line eval(a_function([{{a},[{foo,bar}]}], ['_']),
from_term([{{a},[{foo,bar}]}], ['_'])),
?line eval(a_function([], ['_']), from_term([], ['_'])),
?line {'EXIT', {badarg, _}} = (catch a_function([[a]],['_'])),
?line {'EXIT', {bad_function, _}} =
(catch a_function([{a,b},{b,c},{a,c}], FT)),
?line eval(a_function([{a,[a]},{a,[a,a]}], [{atom,[atom]}]),
from_term([{a,[a]}])),
?line eval(a_function([{[b,a],c},{[a,b],c}], [{[atom],atom}]),
from_term([{[a,b],c}])),
ok.
family_1(Conf) when is_list(Conf) ->
%% family/1
?line eval(family([]), from_term([],[{atom,[atom]}])),
?line {'EXIT', {badarg, _}} = (catch family(a)),
?line {'EXIT', {badarg, _}} = (catch family([a])),
?line {'EXIT', {badarg, _}} = (catch family([{a,b}])),
?line {'EXIT', {badarg, _}} = (catch family([{a,[]} | a])),
?line {'EXIT', {badarg, _}} = (catch family([{a,[a|b]}])),
?line {'EXIT', {bad_function, _}} =
(catch family([{a,[a]},{a,[]}])),
?line {'EXIT', {bad_function, _}} =
(catch family([{a,[]},{b,[]},{a,[a]}])),
F = 0.0, I = round(F),
if
F == I -> % term ordering
?line {'EXIT', {bad_function, _}} =
(catch family([{I,[a]},{F,[b]}])),
?line true = (1 =:= no_elements(family([{a,[I]},{a,[F]}])));
true ->
?line {'EXIT', {bad_function, _}} =
(catch family([{a,[I]},{a,[F]}]))
end,
?line eval(family([{a,[]},{b,[b]},{a,[]}]), from_term([{a,[]},{b,[b]}])),
?line eval(to_external(family([{b,[{hej,san},tjo]},{a,[]}])),
[{a,[]},{b,[tjo,{hej,san}]}]),
?line eval(family([{a,[a]},{a,[a,a]}]), family([{a,[a]}])),
%% family/2
FT = [{a,[a]}],
?line eval(family([], FT), from_term([],FT)),
?line {'EXIT', {badarg, _}} = (catch family(a,FT)),
?line {'EXIT', {badarg, _}} = (catch family([a],FT)),
?line {'EXIT', {badarg, _}} = (catch family([{a,b}],FT)),
?line {'EXIT', {badarg, _}} = (catch family([{a,[]} | a],FT)),
?line {'EXIT', {badarg, _}} = (catch family([{a,[a|b]}], FT)),
?line {'EXIT', {bad_function, _}} =
(catch family([{a,[a]},{a,[]}], FT)),
?line {'EXIT', {bad_function, _}} =
(catch family([{a,[]},{b,[]},{a,[a]}], FT)),
?line eval(family([{a,[]},{b,[b,b]},{a,[]}], FT),
from_term([{a,[]},{b,[b]}], FT)),
?line eval(to_external(family([{b,[{hej,san},tjo]},{a,[]}], FT)),
[{a,[]},{b,[tjo,{hej,san}]}]),
?line eval(family([{{a},[{foo,bar}]}], ['_']),
from_term([{{a},[{foo,bar}]}], ['_'])),
?line eval(family([], ['_']), from_term([], ['_'])),
?line {'EXIT', {badarg, _}} = (catch family([[a]],['_'])),
?line {'EXIT', {badarg, _}} = (catch family([{a,b}],['_'])),
?line {'EXIT', {badarg, _}} =
(catch family([{a,[foo]}], [{atom,atom}])),
?line eval(family([{{a},[{foo,bar}]}], [{{dt},[{r1,t2}]}]),
from_term([{{a},[{foo,bar}]}], [{{dt},[{r1,t2}]}])),
?line eval(family([{a,[a]},{a,[a,a]}],[{atom,[atom]}]),
family([{a,[a]}])),
?line eval(family([{[a,b],[a]},{[b,a],[a,a]}],[{[atom],[atom]}]),
from_term([{[a,b],[a]},{[b,a],[a,a]}])),
ok.
projection(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line ER = relation([]),
%% set of ordered sets
?line S1 = relation([{a,1},{b,2},{b,22},{c,0}]),
?line S2 = relation([{a,1},{a,2},{a,3},{b,4},{b,5},{b,6}]),
?line eval(projection(1, E), E),
?line eval(projection(1, ER), set([])),
?line eval(projection(1, relation([{a,1}])), set([a])),
?line eval(projection(1, S1), set([a,b,c])),
?line eval(projection(1, S2), set([a,b])),
?line eval(projection(2, S1), set([0,1,2,22])),
?line eval(projection(2, relation([{1,a},{2,a},{3,b}])), set([a,b])),
?line eval(projection(1, relation([{a},{b},{c}])), set([a,b,c])),
Fun1 = {external, fun({A,B,C}) -> {A,{B,C}} end},
?line eval(projection(Fun1, E), E),
%% No check here:
?line eval(projection(3, projection(Fun1, empty_set())), E),
?line E2 = relation([], 3),
?line eval(projection(Fun1, E2), from_term([], [{atom,{atom,atom}}])),
Fun2 = {external, fun({A,_B}) -> {A} end},
?line eval(projection(Fun2, ER), from_term([], [{atom}])),
?line eval(projection(Fun2, relation([{a,1}])), relation([{a}])),
?line eval(projection(Fun2, relation([{a,1},{b,3},{a,2}])),
relation([{a},{b}])),
Fun3 = {external, fun({A,_B,C}) -> {C,{A},C} end},
?line eval(projection(Fun3, relation([{a,1,x},{b,3,y},{a,2,z}])),
from_term([{x,{a},x},{y,{b},y},{z,{a},z}])),
Fun4 = {external, fun(A={B,_C,_D}) -> {B, A} end},
?line eval(projection(Fun4, relation([{a,1,x},{b,3,y},{a,2,z}])),
from_term([{a,{a,1,x}},{b,{b,3,y}},{a,{a,2,z}}])),
?line eval(projection({external, fun({A,B,_C,D}) -> {A,B,A,D} end},
relation([{1,1,1,2}, {1,1,3,1}])),
relation([{1,1,1,1}, {1,1,1,2}])),
?line {'EXIT', {badarg, _}} = (catch projection(1, set([]))),
?line {'EXIT', {function_clause, _}} =
(catch projection({external, fun({A}) -> A end}, S1)),
?line {'EXIT', {badarg, _}} =
(catch projection({external, fun({A,_}) -> {A,0} end},
from_term([{1,a}]))),
%% {} is not an ordered set
?line {'EXIT', {badarg, _}} =
(catch projection({external, fun(_) -> {} end}, ER)),
?line {'EXIT', {badarg, _}} =
(catch projection({external, fun(_) -> {{}} end}, ER)),
?line eval(projection({external, fun({T,_}) -> T end},
relation([{{},a},{{},b}])),
set([{}])),
?line eval(projection({external, fun({T}) -> T end}, relation([{{}}])),
set([{}])),
?line eval(projection({external, fun(A) -> {A} end},
relation([{1,a},{2,b}])),
from_term([{{1,a}},{{2,b}}])),
?line eval(projection({external, fun({A,B}) -> {B,A} end},
relation([{1,a},{2,b}])),
relation([{a,1},{b,2}])),
?line eval(projection({external, fun(X=Y=A) -> {X,Y,A} end}, set([a,b,c])),
relation([{a,a,a},{b,b,b},{c,c,c}])),
?line eval(projection({external, fun({A,{_},B}) -> {A,B} end},
from_term([{a,{a},b},{a,{b},c}])),
relation([{a,b},{a,c}])),
?line eval(projection({external, fun({A,_,B}) -> {A,B} end},
relation([{a,{},b},{a,{},c}])),
relation([{a,b},{a,c}])),
Fun5 = fun(S) -> from_term({to_external(S),0}, {type(S),atom}) end,
?line eval(projection(Fun5, E), E),
?line eval(projection(Fun5, set([a,b])), from_term([{a,0},{b,0}])),
?line eval(projection(Fun5, relation([{a,1},{b,2}])),
from_term([{{a,1},0},{{b,2},0}])),
?line eval(projection(Fun5, from_term([[a],[b]])),
from_term([{[a],0},{[b],0}])),
F = 0.0, I = round(F),
?line FR = relation([{I},{F}]),
if
F == I -> % term ordering
true = (no_elements(projection(1, FR)) =:= 1);
true ->
eval(projection(1, FR), set([I,F]))
end,
%% set of sets
?line {'EXIT', {badarg, _}} =
(catch projection({external, fun(X) -> X end},
from_term([], [[atom]]))),
?line {'EXIT', {badarg, _}} =
(catch projection({external, fun(X) -> X end}, from_term([[a]]))),
?line eval(projection(fun sofs:union/1,
from_term([[[1,2],[2,3]], [[a,b],[b,c]]])),
from_term([[1,2,3], [a,b,c]])),
?line eval(projection(fun(_) -> from_term([a]) end,
from_term([[b]], [[a]])),
from_term([[a]])),
?line eval(projection(fun(_) -> from_term([a]) end,
from_term([[1,2],[3,4]])),
from_term([[a]])),
Fun10 = fun(S) ->
%% Cheating a lot...
case to_external(S) of
[1] -> from_term({1,1});
_ -> S
end
end,
?line eval(projection(Fun10, from_term([[1]])), from_term([{1,1}])),
?line eval(projection(fun(_) -> from_term({a}) end, from_term([[a]])),
from_term([{a}])),
?line {'EXIT', {badarg, _}} =
(catch projection(fun(_) -> {a} end, from_term([[a]]))),
ok.
substitution(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line ER = relation([]),
%% set of ordered sets
?line S1 = relation([{a,1},{b,2},{b,22},{c,0}]),
?line S2 = relation([{a,1},{a,2},{a,3},{b,4},{b,5},{b,6}]),
?line eval(substitution(1, E), E),
%% No check here:
Fun0 = {external, fun({A,B,C}) -> {A,{B,C}} end},
?line eval(substitution(3, substitution(Fun0, empty_set())), E),
?line eval(substitution(1, ER), from_term([],[{{atom,atom},atom}])),
?line eval(substitution(1, relation([{a,1}])), from_term([{{a,1},a}])),
?line eval(substitution(1, S1),
from_term([{{a,1},a},{{b,2},b},{{b,22},b},{{c,0},c}])),
?line eval(substitution(1, S2),
from_term([{{a,1},a},{{a,2},a},{{a,3},a},{{b,4},b},
{{b,5},b},{{b,6},b}])),
?line eval(substitution(2, S1),
from_term([{{a,1},1},{{b,2},2},{{b,22},22},{{c,0},0}])),
Fun1 = fun({A,_B}) -> {A} end,
XFun1 = {external, Fun1},
?line eval(substitution(XFun1, E), E),
?line eval(substitution(Fun1, E), E),
?line eval(substitution(XFun1, ER), from_term([], [{{atom,atom},{atom}}])),
?line eval(substitution(XFun1, relation([{a,1}])),
from_term([{{a,1},{a}}])),
?line eval(substitution(XFun1, relation([{a,1},{b,3},{a,2}])),
from_term([{{a,1},{a}},{{a,2},{a}},{{b,3},{b}}])),
?line eval(substitution({external, fun({A,_B,C}) -> {C,A,C} end},
relation([{a,1,x},{b,3,y},{a,2,z}])),
from_term([{{a,1,x},{x,a,x}},{{a,2,z},{z,a,z}},
{{b,3,y},{y,b,y}}])),
Fun2 = fun(S) -> {A,_B} = to_external(S), from_term({A}) end,
?line eval(substitution(Fun2, ER), E),
?line eval(substitution(Fun2, relation([{a,1}])),
from_term([{{a,1},{a}}])),
Fun3 = fun(S) -> from_term({to_external(S),0}, {type(S),atom}) end,
?line eval(substitution(Fun3, E), E),
?line eval(substitution(Fun3, set([a,b])),
from_term([{a,{a,0}},{b,{b,0}}])),
?line eval(substitution(Fun3, relation([{a,1},{b,2}])),
from_term([{{a,1},{{a,1},0}},{{b,2},{{b,2},0}}])),
?line eval(substitution(Fun3, from_term([[a],[b]])),
from_term([{[a],{[a],0}},{[b],{[b],0}}])),
?line eval(substitution(fun(_) -> E end, from_term([[a],[b]])),
from_term([{[a],[]},{[b],[]}])),
?line {'EXIT', {badarg, _}} = (catch substitution(1, set([]))),
?line eval(substitution(1, ER), from_term([], [{{atom,atom},atom}])),
?line {'EXIT', {function_clause, _}} =
(catch substitution({external, fun({A,_}) -> A end}, set([]))),
?line {'EXIT', {badarg, _}} =
(catch substitution({external, fun({A,_}) -> {A,0} end},
from_term([{1,a}]))),
%% set of sets
?line {'EXIT', {badarg, _}} =
(catch substitution({external, fun(X) -> X end},
from_term([], [[atom]]))),
?line {'EXIT', {badarg, _}} =
(catch substitution({external, fun(X) -> X end}, from_term([[a]]))),
?line eval(substitution(fun(X) -> X end, from_term([], [[atom]])), E),
?line eval(substitution(fun sofs:union/1,
from_term([[[1,2],[2,3]], [[a,b],[b,c]]])),
from_term([{[[1,2],[2,3]],[1,2,3]}, {[[a,b],[b,c]],[a,b,c]}])),
?line eval(substitution(fun(_) -> from_term([a]) end,
from_term([[b]], [[a]])),
from_term([{[b],[a]}], [{[a],[atom]}])),
?line eval(substitution(fun(_) -> from_term([a]) end,
from_term([[1,2],[3,4]])),
from_term([{[1,2],[a]},{[3,4],[a]}])),
Fun10 = fun(S) ->
%% Cheating a lot...
case to_external(S) of
[1] -> from_term({1,1});
_ -> S
end
end,
?line eval(substitution(Fun10, from_term([[1]])),
from_term([{[1],{1,1}}])),
?line {'EXIT', {type_mismatch, _}} =
(catch substitution(Fun10, from_term([[1],[2]]))),
?line {'EXIT', {type_mismatch, _}} =
(catch substitution(Fun10, from_term([[1],[0]]))),
?line eval(substitution(fun(_) -> from_term({a}) end, from_term([[a]])),
from_term([{[a],{a}}])),
?line {'EXIT', {badarg, _}} =
(catch substitution(fun(_) -> {a} end, from_term([[a]]))),
ok.
restriction(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line ER = relation([], 2),
%% set of ordered sets
?line S1 = relation([{a,1},{b,2},{b,22},{c,0}]),
?line eval(restriction(S1, set([a,b])),
relation([{a,1},{b,2},{b,22}])),
?line eval(restriction(2, S1, set([1,2])),
relation([{a,1},{b,2}])),
?line eval(restriction(S1, set([a,b,c])), S1),
?line eval(restriction(1, S1, set([0,1,d,e])), ER),
?line eval(restriction(1, S1, E), ER),
?line eval(restriction({external, fun({_A,B,C}) -> {B,C} end},
relation([{a,aa,1},{b,bb,2},{c,cc,3}]),
relation([{bb,2},{cc,3}])),
relation([{b,bb,2},{c,cc,3}])),
R1 = relation([],[{a,b}]),
?line eval(restriction(2, R1,sofs:set([],[b])), R1),
Id = fun(X) -> X end,
XId = {external, Id},
?line eval(restriction(XId, relation([{a,b}]), E), ER),
?line eval(restriction(XId, E, relation([{b,d}])), E),
Fun1 = fun(S) -> {_A,B,C} = to_external(S), from_term({B,C}) end,
?line eval(restriction(Fun1,
relation([{a,aa,1},{b,bb,2},{c,cc,3}]),
relation([{bb,2},{cc,3}])),
relation([{b,bb,2},{c,cc,3}])),
?line eval(restriction({external, fun({_,{A},B}) -> {A,B} end},
from_term([{a,{aa},1},{b,{bb},2},{c,{cc},3}]),
from_term([{bb,2},{cc,3}])),
from_term([{b,{bb},2},{c,{cc},3}])),
S5 = relation([{1,a},{2,b},{3,c}]),
?line eval(restriction(2, S5, set([b,c])), relation([{2,b},{3,c}])),
S4 = relation([{a,1},{b,2},{b,27},{c,0}]),
?line eval(restriction(2, S4, E), ER),
S6 = relation([{1,a},{2,c},{3,b}]),
?line eval(restriction(2, S6, set([d,e])), ER),
?line eval(restriction(2,
relation([{1,d},{2,c},{3,b},{4,a},{5,e}]),
set([c])),
relation([{2,c}])),
?line eval(restriction(XId,
relation([{1,a},{3,b},{4,c},{4,d}]),
relation([{2,a},{2,c},{4,c}])),
relation([{4,c}])),
?line eval(restriction(2, relation([{a,b}]), E), ER),
?line eval(restriction(2, E, relation([{b,d}])), E),
?line eval(restriction(2, relation([{b,d}]), E), ER),
?line eval(restriction(XId, E, set([a])), E),
?line eval(restriction(1, S1, E), ER),
?line {'EXIT', {badarg, _}} =
(catch restriction(3, relation([{a,b}]), E)),
?line {'EXIT', {badarg, _}} =
(catch restriction(3, relation([{a,b}]), relation([{b,d}]))),
?line {'EXIT', {badarg, _}} =
(catch restriction(3, relation([{a,b}]), set([{b,d}]))),
?line {'EXIT', {type_mismatch, _}} =
(catch restriction(2, relation([{a,b}]), relation([{b,d}]))),
?line {'EXIT', {type_mismatch, _}} =
(catch restriction({external, fun({A,_B}) -> A end},
relation([{a,b}]), relation([{b,d}]))),
?line {'EXIT', {badarg, _}} =
(catch restriction({external, fun({A,_}) -> {A,0} end},
from_term([{1,a}]),
from_term([{1,0}]))),
?line eval(restriction(2, relation([{a,d},{b,e},{c,b},{d,c}]), set([b,d])),
relation([{a,d},{c,b}])),
?line {'EXIT', {function_clause, _}} =
(catch restriction({external, fun({A,_B}) -> A end}, set([]), E)),
Fun3 = fun(S) -> from_term({to_external(S),0}, {type(S),atom}) end,
?line eval(restriction(Fun3, set([1,2]), from_term([{1,0}])),
from_term([1])),
%% set of sets
?line {'EXIT', {badarg, _}} =
(catch restriction({external, fun(X) -> X end},
from_term([], [[atom]]), set([a]))),
S2 = from_term([], [[atom]]),
?line eval(restriction(Id, S2, E), E),
S3 = from_term([[a],[b]], [[atom]]),
?line eval(restriction(Id, S3, E), E),
?line eval(restriction(Id, from_term([], [[atom]]), set([a])),
from_term([], [[atom]])),
?line eval(restriction(fun sofs:union/1,
from_term([[[a],[b]], [[b],[c]],
[[], [a,b]], [[1],[2]]]),
from_term([[a,b],[1,2,3],[b,c]])),
from_term([[[],[a,b]], [[a],[b]],[[b],[c]]])),
?line eval(restriction(fun(_) -> from_term([a]) end,
from_term([], [[atom]]),
from_term([], [[a]])),
from_term([], [[atom]])),
?line {'EXIT', {type_mismatch, _}} =
(catch restriction(fun(_) -> from_term([a]) end,
from_term([[1,2],[3,4]]),
from_term([], [atom]))),
Fun10 = fun(S) ->
%% Cheating a lot...
case to_external(S) of
[1] -> from_term({1,1});
_ -> S
end
end,
?line {'EXIT', {type_mismatch, _}} =
(catch restriction(Fun10, from_term([[1]]), from_term([], [[atom]]))),
?line {'EXIT', {type_mismatch, _}} =
(catch restriction(fun(_) -> from_term({a}) end,
from_term([[a]]),
from_term([], [atom]))),
?line {'EXIT', {badarg, _}} =
(catch restriction(fun(_) -> {a} end,
from_term([[a]]),
from_term([], [atom]))),
ok.
drestriction(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line ER = relation([], 2),
%% set of ordered sets
?line S1 = relation([{a,1},{b,2},{b,22},{c,0}]),
?line eval(drestriction(S1, set([a,b])), relation([{c,0}])),
?line eval(drestriction(2, S1, set([1,2])),
relation([{b,22},{c,0}])),
?line eval(drestriction(S1, set([a,b,c])), ER),
?line eval(drestriction(2, ER, set([a,b])), ER),
?line eval(drestriction(1, S1, set([0,1,d,e])), S1),
?line eval(drestriction(1, S1, E), S1),
?line eval(drestriction({external, fun({_A,B,C}) -> {B,C} end},
relation([{a,aa,1},{b,bb,2},{c,cc,3}]),
relation([{bb,2},{cc,3}])),
relation([{a,aa,1}])),
Id = fun(X) -> X end,
XId = {external, Id},
?line eval(drestriction(XId, relation([{a,b}]), E), relation([{a,b}])),
?line eval(drestriction(XId, E, relation([{b,d}])), E),
Fun1 = fun(S) -> {_A,B,C} = to_external(S), from_term({B,C}) end,
?line eval(drestriction(Fun1,
relation([{a,aa,1},{b,bb,2},{c,cc,3}]),
relation([{bb,2},{cc,3}])),
relation([{a,aa,1}])),
?line eval(drestriction({external, fun({_,{A},B}) -> {A,B} end},
from_term([{a,{aa},1},{b,{bb},2},{c,{cc},3}]),
from_term([{bb,2},{cc,3}])),
from_term([{a,{aa},1}])),
S5 = relation([{1,a},{2,b},{3,c}]),
?line eval(drestriction(2, S5, set([b,c])), relation([{1,a}])),
S4 = relation([{a,1},{b,2},{b,27},{c,0}]),
?line eval(drestriction(2, S4, set([])), S4),
S6 = relation([{1,a},{2,c},{3,b}]),
?line eval(drestriction(2, S6, set([d,e])), S6),
?line eval(drestriction(2,
relation([{1,d},{2,c},{3,b},{4,a},{5,e}]),
set([c])),
relation([{1,d},{3,b},{4,a},{5,e}])),
?line eval(drestriction(XId,
relation([{1,a},{3,b},{4,c},{4,d}]),
relation([{2,a},{2,c},{4,c}])),
relation([{1,a},{3,b},{4,d}])),
?line eval(drestriction(2, relation([{a,b}]), E), relation([{a,b}])),
?line eval(drestriction(2, E, relation([{b,d}])), E),
?line eval(drestriction(2, relation([{b,d}]), E), relation([{b,d}])),
?line eval(drestriction(XId, E, set([a])), E),
?line eval(drestriction(1, S1, E), S1),
?line {'EXIT', {badarg, _}} =
(catch drestriction(3, relation([{a,b}]), E)),
?line {'EXIT', {badarg, _}} =
(catch drestriction(3, relation([{a,b}]), relation([{b,d}]))),
?line {'EXIT', {badarg, _}} =
(catch drestriction(3, relation([{a,b}]), set([{b,d}]))),
?line {'EXIT', {type_mismatch, _}} =
(catch drestriction(2, relation([{a,b}]), relation([{b,d}]))),
?line {'EXIT', {type_mismatch, _}} =
(catch drestriction({external, fun({A,_B}) -> A end},
relation([{a,b}]), relation([{b,d}]))),
?line {'EXIT', {badarg, _}} =
(catch drestriction({external, fun({A,_}) -> {A,0} end},
from_term([{1,a}]),
from_term([{1,0}]))),
?line eval(drestriction(2, relation([{a,d},{b,e},{c,b},{d,c}]), set([b,d])),
relation([{b,e},{d,c}])),
?line {'EXIT', {function_clause, _}} =
(catch drestriction({external, fun({A,_B}) -> A end}, set([]), E)),
Fun3 = fun(S) -> from_term({to_external(S),0}, {type(S),atom}) end,
?line eval(drestriction(Fun3, set([1,2]), from_term([{1,0}])),
from_term([2])),
%% set of sets
?line {'EXIT', {badarg, _}} =
(catch drestriction({external, fun(X) -> X end},
from_term([], [[atom]]), set([a]))),
S2 = from_term([], [[atom]]),
?line eval(drestriction(Id, S2, E), S2),
S3 = from_term([[a],[b]], [[atom]]),
?line eval(drestriction(Id, S3, E), S3),
?line eval(drestriction(Id, from_term([], [[atom]]), set([a])),
from_term([], [[atom]])),
?line eval(drestriction(fun sofs:union/1,
from_term([[[a],[b]], [[b],[c]],
[[], [a,b]], [[1],[2]]]),
from_term([[a,b],[1,2,3],[b,c]])),
from_term([[[1],[2]]])),
?line eval(drestriction(fun(_) -> from_term([a]) end,
from_term([], [[atom]]),
from_term([], [[a]])),
from_term([], [[atom]])),
?line {'EXIT', {type_mismatch, _}} =
(catch drestriction(fun(_) -> from_term([a]) end,
from_term([[1,2],[3,4]]),
from_term([], [atom]))),
Fun10 = fun(S) ->
%% Cheating a lot...
case to_external(S) of
[1] -> from_term({1,1});
_ -> S
end
end,
?line {'EXIT', {type_mismatch, _}} =
(catch drestriction(Fun10, from_term([[1]]), from_term([], [[atom]]))),
?line {'EXIT', {type_mismatch, _}} =
(catch drestriction(fun(_) -> from_term({a}) end,
from_term([[a]]),
from_term([], [atom]))),
?line {'EXIT', {badarg, _}} =
(catch drestriction(fun(_) -> {a} end,
from_term([[a]]),
from_term([], [atom]))),
ok.
strict_relation_1(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line ER = relation([], 2),
?line eval(strict_relation(E), E),
?line eval(strict_relation(ER), ER),
?line eval(strict_relation(relation([{1,a},{a,a},{2,b}])),
relation([{1,a},{2,b}])),
?line {'EXIT', {badarg, _}} =
(catch strict_relation(relation([{1,2,3}]))),
F = 0.0, I = round(F),
?line FR = relation([{F,I}]),
if
F == I -> % term ordering
eval(strict_relation(FR), ER);
true ->
eval(strict_relation(FR), FR)
end,
ok.
extension(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line ER = relation([], 2),
?line EF = family([]),
?line C1 = from_term(3),
?line C2 = from_term([3]),
?line {'EXIT', {function_clause, _}} = (catch extension(foo, E, C1)),
?line {'EXIT', {function_clause, _}} = (catch extension(ER, foo, C1)),
?line {'EXIT', {{case_clause, _},_}} = (catch extension(ER, E, foo)),
?line {'EXIT', {type_mismatch, _}} = (catch extension(ER, E, E)),
?line {'EXIT', {badarg, _}} = (catch extension(C2, E, E)),
?line eval(E, extension(E, E, E)),
?line eval(EF, extension(EF, E, E)),
?line eval(family([{3,[]}]), extension(EF, set([3]), E)),
?line eval(ER, extension(ER, E, C1)),
?line eval(E, extension(E, ER, E)),
?line eval(from_term([],[{{atom,atom},type(ER)}]), extension(E, ER, ER)),
?line R1 = relation([{c,7},{c,9},{c,11},{d,17},{f,20}]),
?line S1 = set([a,c,d,e]),
?line eval(extension(R1, S1, C1), lextension(R1, S1, C1)),
?line S2 = set([1,2,3]),
?line eval(extension(ER, S2, C1), lextension(ER, S2, C1)),
?line R3 = relation([{4,a},{8,b}]),
?line S3 = set([1,2,3,4,5,6,7,8,9,10,11]),
?line eval(extension(R3, S3, C1), lextension(R3, S3, C1)),
?line R4 = relation([{2,b},{4,d},{6,f}]),
?line S4 = set([1,3,5,7]),
?line eval(extension(R4, S4, C1), lextension(R4, S4, C1)),
?line F1 = family([{a,[1]},{c,[2]}]),
?line S5 = set([a,b,c,d]),
?line eval(extension(F1, S5, C2), lextension(F1, S5, C2)),
ok.
lextension(R, S, C) ->
union(R, drestriction(1, constant_function(S, C), domain(R))).
weak_relation_1(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line ER = relation([], 2),
?line eval(weak_relation(E), E),
?line eval(weak_relation(ER), ER),
?line eval(weak_relation(relation([{a,1},{a,2},{b,2},{c,c}])),
relation([{1,1},{2,2},{a,1},{a,2},{a,a},{b,2},{b,b},{c,c}])),
?line eval(weak_relation(relation([{a,1},{a,a},{a,b}])),
relation([{1,1},{a,1},{a,a},{a,b},{b,b}])),
?line eval(weak_relation(relation([{a,1},{a,b},{7,w}])),
relation([{1,1},{7,7},{7,w},{a,1},{a,a},{a,b},{b,b},{w,w}])),
?line {'EXIT', {badarg, _}} =
(catch weak_relation(from_term([{{a},a}]))),
?line {'EXIT', {badarg, _}} =
(catch weak_relation(from_term([{a,a}],[{d,r}]))),
?line {'EXIT', {badarg, _}} = (catch weak_relation(relation([{1,2,3}]))),
F = 0.0, I = round(F),
if
F == I -> % term ordering
?line FR1 = relation([{F,I}]),
eval(weak_relation(FR1), FR1),
?line FR2 = relation([{F,2},{I,1}]),
true = no_elements(weak_relation(FR2)) =:= 5,
?line FR3 = relation([{1,0},{1.0,1}]),
true = no_elements(weak_relation(FR3)) =:= 3;
true ->
ok
end,
ok.
to_sets_1(Conf) when is_list(Conf) ->
?line {'EXIT', {badarg, _}} = (catch to_sets(from_term(a))),
?line {'EXIT', {function_clause, _}} = (catch to_sets(a)),
%% unordered
?line [] = to_sets(empty_set()),
?line eval(to_sets(from_term([a])), [from_term(a)]),
?line eval(to_sets(from_term([[]],[[atom]])), [set([])]),
?line L = [from_term([a,b]),from_term([c,d])],
?line eval(to_sets(from_sets(L)), L),
?line eval(to_sets(relation([{a,1},{b,2}])),
[from_term({a,1},{atom,atom}), from_term({b,2},{atom,atom})]),
%% ordered
?line O = {from_term(a,atom), from_term({b}, {atom}), set([c,d])},
?line eval(to_sets(from_sets(O)), O),
ok.
specification(Conf) when is_list(Conf) ->
Fun = {external, fun(I) when is_integer(I) -> true; (_) -> false end},
?line [1,2,3] = to_external(specification(Fun, set([a,1,b,2,c,3]))),
Fun2 = fun(S) -> is_subset(S, set([1,3,5,7,9])) end,
S2 = from_term([[1],[2],[3],[4],[5],[6],[7]]),
?line eval(specification(Fun2, S2), from_term([[1],[3],[5],[7]])),
Fun2x = fun([1]) -> true;
([3]) -> true;
(_) -> false
end,
?line eval(specification({external,Fun2x}, S2), from_term([[1],[3]])),
Fun3 = fun(_) -> neither_true_nor_false end,
?line {'EXIT', {badarg, _}} =
(catch specification(Fun3, set([a]))),
?line {'EXIT', {badarg, _}} =
(catch specification({external, Fun3}, set([a]))),
?line {'EXIT', {badarg, _}} =
(catch specification(Fun3, from_term([[a]]))),
?line {'EXIT', {function_clause, _}} =
(catch specification(Fun, a)),
ok.
union_1(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line ER = relation([], 2),
?line {'EXIT', {badarg, _}} = (catch union(ER)),
?line {'EXIT', {type_mismatch, _}} =
(catch union(relation([{a,b}]), relation([{a,b,c}]))),
?line {'EXIT', {type_mismatch, _}} =
(catch union(from_term([{a,b}]), from_term([{c,[x]}]))),
?line {'EXIT', {type_mismatch, _}} =
(catch union(from_term([{a,b}]), from_term([{c,d}], [{d,r}]))),
?line {'EXIT', {badarg, _}} = (catch union(set([a,b,c]))),
?line eval(union(E), E),
?line eval(union(from_term([[]],[[atom]])), set([])),
?line eval(union(from_term([[{a,b},{b,c}],[{b,c}]])),
relation([{a,b},{b,c}])),
?line eval(union(from_term([[1,2,3],[2,3,4],[3,4,5]])),
set([1,2,3,4,5])),
?line eval(union(from_term([{[a],[],c}]), from_term([{[],[],q}])),
from_term([{[a],[],c},{[],[],q}])),
?line eval(union(E, E), E),
?line eval(union(set([a,b]), E), set([a,b])),
?line eval(union(E, set([a,b])), set([a,b])),
?line eval(union(from_term([[a,b]])), from_term([a,b])),
ok.
intersection_1(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line {'EXIT', {badarg, _}} = (catch intersection(from_term([a,b]))),
?line {'EXIT', {badarg, _}} = (catch intersection(E)),
?line {'EXIT', {type_mismatch, _}} =
(catch intersection(relation([{a,b}]), relation([{a,b,c}]))),
?line {'EXIT', {type_mismatch, _}} =
(catch intersection(relation([{a,b}]), from_term([{a,b}],[{d,r}]))),
?line eval(intersection(from_term([[a,b,c],[d,e,f],[g,h,i]])), set([])),
?line eval(intersection(E, E), E),
?line eval(intersection(set([a,b,c]),set([0,b,q])),
set([b])),
?line eval(intersection(set([0,b,q]),set([a,b,c])),
set([b])),
?line eval(intersection(set([a,b,c]),set([a,b,c])),
set([a,b,c])),
?line eval(intersection(set([a,b,d]),set([c,d])),
set([d])),
ok.
difference(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line {'EXIT', {type_mismatch, _}} =
(catch difference(relation([{a,b}]), relation([{a,b,c}]))),
?line eval(difference(E, E), E),
?line {'EXIT', {type_mismatch, _}} =
(catch difference(relation([{a,b}]), from_term([{a,c}],[{d,r}]))),
?line eval(difference(set([a,b,c,d,f]), set([a,d,e,g])),
set([b,c,f])),
?line eval(difference(set([a,b,c]), set([d,e,f])),
set([a,b,c])),
?line eval(difference(set([a,b,c]), set([a,b,c,d,e,f])),
set([])),
?line eval(difference(set([e,f,g]), set([a,b,c,e])),
set([f,g])),
?line eval(difference(set([a,b,d,e,f]), set([c])),
set([a,b,d,e,f])),
ok.
symdiff(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line {'EXIT', {type_mismatch, _}} =
(catch symdiff(relation([{a,b}]), relation([{a,b,c}]))),
?line {'EXIT', {type_mismatch, _}} =
(catch symdiff(relation([{a,b}]), from_term([{a,b}], [{d,r}]))),
?line eval(symdiff(E, E), E),
?line eval(symdiff(set([a,b,c,d,e,f]), set([0,1,a,c])),
union(set([b,d,e,f]), set([0,1]))),
?line eval(symdiff(set([a,b,c]), set([q,v,w,x,y])),
union(set([a,b,c]), set([q,v,w,x,y]))),
?line eval(symdiff(set([a,b,c,d,e,f]), set([a,b,c])),
set([d,e,f])),
?line eval(symdiff(set([c,e,g,h,i]), set([b,d,f])),
union(set([c,e,g,h,i]), set([b,d,f]))),
?line eval(symdiff(set([c,d,g,h,k,l]),
set([a,b,e,f,i,j,m,n])),
union(set([c,d,g,h,k,l]), set([a,b,e,f,i,j,m,n]))),
?line eval(symdiff(set([c,d,g,h,k,l]),
set([d,e,h,i,l,m,n,o,p])),
union(set([c,g,k]), set([e,i,m,n,o,p]))),
ok.
symmetric_partition(Conf) when is_list(Conf) ->
?line E = set([]),
?line S1 = set([1,2,3,4]),
?line S2 = set([3,4,5,6]),
?line S3 = set([3,4]),
?line S4 = set([1,2,3,4,5,6]),
?line T1 = set([1,2]),
?line T2 = set([3,4]),
?line T3 = set([5,6]),
?line T4 = set([1,2,5,6]),
?line {'EXIT', {type_mismatch, _}} =
(catch symmetric_partition(relation([{a,b}]), relation([{a,b,c}]))),
?line {E, E, E} = symmetric_partition(E, E),
?line {'EXIT', {type_mismatch, _}} =
(catch symmetric_partition(relation([{a,b}]),
from_term([{a,c}],[{d,r}]))),
?line {E, E, S1} = symmetric_partition(E, S1),
?line {S1, E, E} = symmetric_partition(S1, E),
?line {T1, T2, T3} = symmetric_partition(S1, S2),
?line {T3, T2, T1} = symmetric_partition(S2, S1),
?line {E, T2, T4} = symmetric_partition(S3, S4),
?line {T4, T2, E} = symmetric_partition(S4, S3),
?line S5 = set([1,3,5]),
?line S6 = set([2,4,6,7,8]),
?line {S5, E, S6} = symmetric_partition(S5, S6),
?line {S6, E, S5} = symmetric_partition(S6, S5),
?line EE = empty_set(),
?line {EE, EE, EE} = symmetric_partition(EE, EE),
ok.
is_sofs_set_1(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line true = is_sofs_set(E),
?line true = is_sofs_set(from_term([a])),
?line true = is_sofs_set(from_term({a})),
?line true = is_sofs_set(from_term(a)),
?line false = is_sofs_set(a),
ok.
is_set_1(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line true = is_set(E),
?line true = is_set(from_term([a])),
?line false = is_set(from_term({a})),
?line false = is_set(from_term(a)),
?line {'EXIT', _} = (catch is_set(a)),
?line true = is_empty_set(E),
?line false = is_empty_set(from_term([a])),
?line false = is_empty_set(from_term({a})),
?line false = is_empty_set(from_term(a)),
?line {'EXIT', _} = (catch is_empty_set(a)),
ok.
is_equal(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line true = is_equal(E, E),
?line false = is_equal(from_term([a]), E),
?line {'EXIT', {type_mismatch, _}} =
(catch is_equal(intersection(set([a]), set([b])),
intersection(from_term([{a}]), from_term([{b}])))),
?line {'EXIT', {type_mismatch, _}} =
(catch is_equal(from_term([],[{[atom],atom,[atom]}]),
from_term([],[{[atom],{atom},[atom]}]))),
?line {'EXIT', {type_mismatch, _}} =
(catch is_equal(set([a]), from_term([a],[type]))),
?line E2 = from_sets({from_term(a,atom)}),
?line true = is_equal(E2, E2),
?line true = is_equal(from_term({a}, {atom}), E2),
?line false = is_equal(from_term([{[a],[],c}]),
from_term([{[],[],q}])),
?line {'EXIT', {type_mismatch, _}} =
(catch is_equal(E, E2)),
?line {'EXIT', {type_mismatch, _}} =
(catch is_equal(E2, E)),
?line true = is_equal(from_term({[],a,[]},{[atom],atom,[atom]}),
from_term({[],a,[]},{[atom],atom,[atom]})),
?line {'EXIT', {type_mismatch, _}} =
(catch is_equal(from_term({[],a,[]},{[atom],atom,[atom]}),
from_term({[],{a},[]},{[atom],{atom},[atom]}))),
?line {'EXIT', {type_mismatch, _}} =
(catch is_equal(from_term({a}), from_term({a},{type}))),
ok.
is_subset(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line true = is_subset(E, E),
?line true = is_subset(set([a,c,e]), set([a,b,c,d,e])),
?line false = is_subset(set([a,b]), E),
?line false = is_subset(set([d,e,f]), set([b,c,d,e])),
?line false = is_subset(set([a,b,c]), set([b,c])),
?line false = is_subset(set([b,c]), set([a,c])),
?line false = is_subset(set([d,e]), set([a,b])),
?line {'EXIT', {type_mismatch, _}} =
(catch is_subset(intersection(set([a]), set([b])),
intersection(from_term([{a}]), from_term([{b}])))),
?line {'EXIT', {type_mismatch, _}} =
(catch is_subset(set([a]), from_term([a,b], [at]))),
ok.
is_a_function_1(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line ER = relation([], 2),
?line {'EXIT', {badarg, _}} = (catch is_a_function(set([a,b]))),
?line true = is_a_function(E),
?line true = is_a_function(ER),
?line true = is_a_function(relation([])),
?line true = is_a_function(relation([],2)),
?line true = is_a_function(relation([{a,b},{b,c}])),
?line false = is_a_function(relation([{a,b},{b,c},{b,d},{e,f}])),
?line IS = relation([{{a,b},c},{{a,b},d}]),
?line false = is_a_function(IS),
F = 0.0, I = round(F),
?line FR = relation([{I,F},{F,1}]),
if
F == I -> % term ordering
false = is_a_function(FR);
true ->
true = is_a_function(FR)
end,
ok.
is_disjoint(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line {'EXIT', {type_mismatch, _}} =
(catch is_disjoint(relation([{a,1}]), set([a,b]))),
?line {'EXIT', {type_mismatch, _}} =
(catch is_disjoint(set([a]), from_term([a],[mota]))),
?line true = is_disjoint(E, E),
?line false = is_disjoint(set([a,b,c]),set([b,c,d])),
?line false = is_disjoint(set([b,c,d]),set([a,b,c])),
?line true = is_disjoint(set([a,c,e]),set([b,d,f])),
ok.
join(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line {'EXIT', {badarg, _}} = (catch join(relation([{a,1}]), 3, E, 5)),
?line {'EXIT', {badarg, _}} = (catch join(E, 1, relation([{a,1}]), 3)),
?line {'EXIT', {badarg, _}} = (catch join(E, 1, from_term([a]), 1)),
?line eval(join(E, 1, E, 2), E),
?line eval(join(E, 1, from_term([{{a},b}]), 2), E),
?line eval(join(from_term([{{a},b}]), 2, E, 1), E),
?line eval(join(from_term([{{a},b,e}]), 2, from_term([{c,{d}}]), 1),
from_term([], [{{atom},atom,atom,{atom}}])),
?line eval(join(relation([{a}]), 1, relation([{1,a},{2,a}]), 2),
relation([{a,1},{a,2}])),
?line eval(join(relation([{a,b,c},{b,c,d}]), 2,
relation([{1,b},{2,a},{3,c}]), 2),
relation([{a,b,c,1},{b,c,d,3}])),
?line eval(join(relation([{1,a,aa},{1,b,bb},{1,c,cc},{2,a,aa},{2,b,bb}]),
1,
relation([{1,c,cc},{1,d,dd},{1,e,ee},{2,c,cc},{2,d,dd}]),
1),
relation([{1,a,aa,c,cc},{1,a,aa,d,dd},{1,a,aa,e,ee},{1,b,bb,c,cc},
{1,b,bb,d,dd},{1,b,bb,e,ee},{1,c,cc,c,cc},{1,c,cc,d,dd},
{1,c,cc,e,ee},{2,a,aa,c,cc},{2,a,aa,d,dd},{2,b,bb,c,cc},
{2,b,bb,d,dd}])),
R1 = relation([{a,b},{b,c}]),
R2 = relation([{b,1},{a,2},{c,3},{c,4}]),
?line eval(join(R1, 1, R2, 1), from_term([{a,b,2},{b,c,1}])),
?line eval(join(R1, 2, R2, 1), from_term([{a,b,1},{b,c,3},{b,c,4}])),
?line eval(join(R1, 1, converse(R2), 2),
from_term([{a,b,2},{b,c,1}])),
?line eval(join(R1, 2, converse(R2), 2),
from_term([{a,b,1},{b,c,3},{b,c,4}])),
ok.
canonical(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line {'EXIT', {badarg, _}} =
(catch canonical_relation(set([a,b]))),
?line eval(canonical_relation(E), E),
?line eval(canonical_relation(from_term([[]])), E),
?line eval(canonical_relation(from_term([[a,b,c]])),
from_term([{a,[a,b,c]},{b,[a,b,c]},{c,[a,b,c]}])),
ok.
relation_to_family_1(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line EF = family([]),
?line eval(relation_to_family(E), E),
?line eval(relation_to_family(relation([])), EF),
?line eval(relation_to_family(relation([], 2)), EF),
?line R = relation([{b,1},{c,7},{c,9},{c,11}]),
?line F = family([{b,[1]},{c,[7,9,11]}]),
?line eval(relation_to_family(R), F),
?line eval(sofs:rel2fam(R), F),
?line {'EXIT', {badarg, _}} = (catch relation_to_family(set([a]))),
ok.
domain_1(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line ER = relation([]),
?line {'EXIT', {badarg, _}} = (catch domain(relation([],3))),
?line eval(domain(E), E),
?line eval(domain(ER), set([])),
?line eval(domain(relation([{1,a},{1,b},{2,a},{2,b}])), set([1,2])),
?line eval(domain(relation([{a,1},{b,2},{c,3}])), set([a,b,c])),
?line eval(field(relation([{a,1},{b,2},{c,3}])),
set([a,b,c,1,2,3])),
F = 0.0, I = round(F),
?line FR = relation([{I,a},{F,b}]),
if
F == I -> % term ordering
?line true = (1 =:= no_elements(domain(FR)));
true ->
?line true = (2 =:= no_elements(domain(FR)))
end,
ok.
range_1(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line ER = relation([]),
?line {'EXIT', {badarg, _}} = (catch range(relation([],3))),
?line eval(range(E), E),
?line eval(range(ER), set([])),
?line eval(range(relation([{1,a},{1,b},{2,a},{2,b}])), set([a,b])),
?line eval(range(relation([{a,1},{b,2},{c,3}])), set([1,2,3])),
ok.
inverse_1(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line ER = relation([]),
?line {'EXIT', {badarg, _}} = (catch inverse(relation([],3))),
?line {'EXIT', {bad_function, _}} =
(catch inverse(relation([{1,a},{1,b}]))),
?line {'EXIT', {bad_function, _}} =
(catch inverse(relation([{1,a},{2,a}]))),
?line eval(inverse(E), E),
?line eval(inverse(ER), ER),
?line eval(inverse(relation([{a,1},{b,2},{c,3}])),
relation([{1,a},{2,b},{3,c}])),
F = 0.0, I = round(F),
?line FR = relation([{I,a},{F,b}]),
if
F == I -> % term ordering
?line {'EXIT', {bad_function, _}} = (catch inverse(FR));
true ->
?line eval(inverse(FR), relation([{a,I},{b,F}]))
end,
ok.
converse_1(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line ER = relation([]),
?line {'EXIT', {badarg, _}} = (catch converse(relation([],3))),
?line eval(converse(ER), ER),
?line eval(converse(E), E),
?line eval(converse(relation([{a,1},{b,2},{c,3}])),
relation([{1,a},{2,b},{3,c}])),
?line eval(converse(relation([{1,a},{1,b}])),
relation([{a,1},{b,1}])),
?line eval(converse(relation([{1,a},{2,a}])),
relation([{a,1},{a,2}])),
ok.
no_elements_1(Conf) when is_list(Conf) ->
?line 0 = no_elements(empty_set()),
?line 0 = no_elements(set([])),
?line 1 = no_elements(from_term([a])),
?line 10 = no_elements(from_term(lists:seq(1,10))),
?line 3 = no_elements(from_term({a,b,c},{atom,atom,atom})),
?line {'EXIT', {badarg, _}} = (catch no_elements(from_term(a))),
?line {'EXIT', {function_clause, _}} = (catch no_elements(a)),
ok.
image(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line ER = relation([]),
?line eval(image(E, E), E),
?line eval(image(ER, E), set([])),
?line eval(image(relation([{a,1},{b,2},{c,3},{f,6}]), set([a,b,c,d,f])),
set([1,2,3,6])),
?line eval(image(relation([{a,1},{b,2},{c,3},{d,4},{r,17}]),
set([b,c,q,r])),
set([2,3,17])),
?line eval(image(from_term([{[a],{1}},{[b],{2}}]), from_term([[a]])),
from_term([{1}])),
?line eval(image(relation([{1,a},{2,a},{3,a},{4,b},{2,b}]), set([1,2,4])),
set([a,b])),
?line {'EXIT', {badarg, _}} =
(catch image(from_term([a,b]), E)),
?line {'EXIT', {type_mismatch, _}} =
(catch image(from_term([{[a],1}]), set([[a]]))),
ok.
inverse_image(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line ER = relation([]),
?line eval(inverse_image(E, E), E),
?line eval(inverse_image(ER, E), set([])),
?line eval(inverse_image(converse(relation([{a,1},{b,2},{c,3},{f,6}])),
set([a,b,c,d,f])),
set([1,2,3,6])),
?line eval(inverse_image(converse(relation([{a,1},{b,2},{c,3},
{d,4},{r,17}])),
set([b,c,q,r])),
set([2,3,17])),
?line eval(inverse_image(converse(from_term([{[a],{1}},{[b],{2}}])),
from_term([[a]])),
from_term([{1}])),
?line eval(inverse_image(converse(relation([{1,a},{2,a},
{3,a},{4,b},{2,b}])),
set([1,2,4])),
set([a,b])),
?line {'EXIT', {badarg, _}} =
(catch inverse_image(from_term([a,b]), E)),
?line {'EXIT', {type_mismatch, _}} =
(catch inverse_image(converse(from_term([{[a],1}])), set([[a]]))),
ok.
composite_1(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line EF = a_function([]),
?line eval(composite(E, E), E),
?line eval(composite(E, a_function([{a,b}])), E),
?line eval(composite(relation([{a,b}]), E), E),
?line {'EXIT', {bad_function, _}} =
(catch composite(EF, relation([{a,b},{a,c}]))),
?line {'EXIT', {bad_function, _}} =
(catch composite(a_function([{b,a}]), EF)),
?line {'EXIT', {bad_function, _}} =
(catch composite(relation([{1,a},{2,b},{2,a}]),
a_function([{a,1},{b,3}]))),
?line {'EXIT', {bad_function, _}} =
(catch composite(a_function([{1,a},{2,b}]), a_function([{b,3}]))),
?line eval(composite(EF, EF), EF),
?line eval(composite(a_function([{b,a}]), from_term([{a,{b,c}}])),
from_term([{b,{b,c}}])),
?line eval(composite(a_function([{q,1},{z,2}]),
a_function([{1,a},{2,a}])),
a_function([{q,a},{z,a}])),
?line eval(composite(a_function([{a,0},{b,0},{c,1},{d,1},{e,2},{f,3}]),
a_function([{0,p},{1,q},{2,r},{3,w},{4,aa}])),
a_function([{c,q},{d,q},{f,w},{e,r},{a,p},{b,p}])),
?line eval(composite(a_function([{1,c}]),
a_function([{a,1},{b,3},{c,4}])),
a_function([{1,4}])),
?line {'EXIT', {bad_function, _}} =
(catch composite(a_function([{1,a},{2,b}]),
a_function([{a,1},{c,3}]))),
?line {'EXIT', {badarg, _}} =
(catch composite(from_term([a,b]), E)),
?line {'EXIT', {badarg, _}} =
(catch composite(E, from_term([a,b]))),
?line {'EXIT', {type_mismatch, _}} =
(catch composite(from_term([{a,b}]), from_term([{{a},b}]))),
?line {'EXIT', {type_mismatch, _}} =
(catch composite(from_term([{a,b}]),
from_term([{b,c}], [{d,r}]))),
F = 0.0, I = round(F),
?line FR1 = relation([{1,c}]),
?line FR2 = relation([{I,1},{F,3},{c,4}]),
if
F == I -> % term ordering
?line {'EXIT', {bad_function, _}} = (catch composite(FR1, FR2));
true ->
?line eval(composite(FR1, FR2), a_function([{1,4}]))
end,
ok.
relative_product_1(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line ER = relation([]),
?line eval(relative_product1(E, E), E),
?line eval(relative_product1(E, relation([{a,b}])), E),
?line eval(relative_product1(relation([{a,b}]), E), E),
?line eval(relative_product1(relation([{a,b}]), from_term([{a,{b,c}}])),
from_term([{b,{b,c}}])),
?line eval(relative_product1(relation([{1,z},{1,q},{2,z}]),
relation([{1,a},{1,b},{2,a}])),
relation([{q,a},{q,b},{z,a},{z,b}])),
?line eval(relative_product1(relation([{0,a},{0,b},{1,c},
{1,d},{2,e},{3,f}]),
relation([{1,q},{3,w}])),
relation([{c,q},{d,q},{f,w}])),
?line {'EXIT', {badarg, _}} =
(catch relative_product1(from_term([a,b]), ER)),
?line {'EXIT', {badarg, _}} =
(catch relative_product1(ER, from_term([a,b]))),
?line {'EXIT', {type_mismatch, _}} =
(catch relative_product1(from_term([{a,b}]), from_term([{{a},b}]))),
?line {'EXIT', {type_mismatch, _}} =
(catch relative_product1(from_term([{a,b}]),
from_term([{b,c}], [{d,r}]))),
ok.
relative_product_2(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line ER = relation([]),
?line {'EXIT', {badarg, _}} = (catch relative_product({from_term([a,b])})),
?line {'EXIT', {type_mismatch, _}} =
(catch relative_product({from_term([{a,b}]), from_term([{{a},b}])})),
?line {'EXIT', {badarg, _}} = (catch relative_product({})),
?line true = is_equal(relative_product({ER}),
from_term([], [{atom,{atom}}])),
?line eval(relative_product({relation([{a,b},{c,a}]),
relation([{a,1},{a,2}]),
relation([{a,aa},{c,1}])}),
from_term([{a,{b,1,aa}},{a,{b,2,aa}}])),
?line eval(relative_product({relation([{a,b}])}, E), E),
?line eval(relative_product({E}, relation([{a,b}])), E),
?line eval(relative_product({E,from_term([], [{{atom,atom,atom},atom}])}),
E),
?line {'EXIT', {badarg, _}} =
(catch relative_product({from_term([a,b])}, E)),
?line {'EXIT', {badarg, _}} =
(catch relative_product({relation([])}, set([]))),
?line {'EXIT', {type_mismatch, _}} =
(catch relative_product({from_term([{a,b}]),
from_term([{{a},b}])}, ER)),
?line {'EXIT', {badarg, _}} = (catch relative_product({}, ER)),
?line relprod2({relation([{a,b}])}, from_term([],[{{atom},atom}]), ER),
?line relprod2({relation([{a,b}]),relation([{a,1}])},
from_term([{{b,1},{tjo,hej,sa}}]),
from_term([{a,{tjo,hej,sa}}])),
?line relprod2({relation([{a,b}]), ER}, from_term([{{a,b},b}]), ER),
?line relprod2({relation([{a,b},{c,a}]),
relation([{a,1},{a,2}])},
from_term([{{b,1},b1},{{b,2},b2}]),
relation([{a,b1},{a,b2}])),
?line eval(relative_product({relation([{a,b}]), ER}),
from_term([],[{atom,{atom,atom}}])),
?line eval(relative_product({from_term([{{a,[a,b]},[a]}]),
from_term([{{a,[a,b]},[[a,b]]}])}),
from_term([{{a,[a,b]},{[a],[[a,b]]}}])),
ok.
relprod2(A1T, A2, R) ->
%% A tuple as first argument is the old interface:
eval(relative_product(A1T, A2), R),
eval(relative_product(tuple_to_list(A1T), A2), R).
product_1(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line eval(product(E, E), E),
?line eval(product(relation([]), E), E),
?line eval(product(E, relation([])), E),
?line eval(product(relation([{a,b}]),relation([{c,d}])),
from_term([{{a,b},{c,d}}],[{{atom,atom},{atom,atom}}])),
?line eval(product({E, set([a,b,c])}), E),
?line eval(product({set([a,b,c]), E}), E),
?line eval(product({set([a,b,c]), E, E}), E),
?line eval(product({E,E}), E),
?line eval(product({set([a,b]),set([1,2])}),
relation([{a,1},{a,2},{b,1},{b,2}])),
?line eval(product({from_term([a,b]), from_term([{a,b},{c,d}]),
from_term([1])}),
from_term([{a,{a,b},1},{a,{c,d},1},{b,{a,b},1},{b,{c,d},1}])),
?line {'EXIT', {badarg, _}} = (catch product({})),
?line {'EXIT', {badarg, _}} = (catch product({foo})),
?line eval(product({E}), E),
?line eval(product({E, E}), E),
?line eval(product(set([a,b]), set([1,2])),
relation([{a,1},{a,2},{b,1},{b,2}])),
?line eval(product({relation([]), E}), E),
ok.
partition_1(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line ER = relation([]),
?line Id = fun(A) -> A end,
?line S1 = relation([{a,1},{b,2},{b,22},{c,0}]),
?line eval(partition(1, E), E),
?line eval(partition(2, E), E),
?line eval(partition(1, ER), from_term([], [type(ER)])),
?line eval(partition(2, ER), from_term([], [type(ER)])),
?line eval(partition(1, relation([{1,a},{1,b},{2,c},{2,d}])),
from_term([[{1,a},{1,b}],[{2,c},{2,d}]])),
?line eval(partition(2, relation([{1,a},{1,b},{2,a},{2,b},{3,c}])),
from_term([[{1,a},{2,a}],[{1,b},{2,b}],[{3,c}]])),
?line eval(partition(2, relation([{1,a}])), from_term([[{1,a}]])),
?line eval(partition(2, relation([{1,a},{2,b}])),
from_term([[{1,a}],[{2,b}]])),
?line eval(partition(2, relation([{1,a},{2,a},{3,a}])),
from_term([[{1,a},{2,a},{3,a}]])),
?line eval(partition(2, relation([{1,b},{2,a}])), % OTP-4516
from_term([[{1,b}],[{2,a}]])),
?line eval(union(partition(Id, S1)), S1),
?line eval(partition({external, fun({A,{B,_}}) -> {A,B} end},
from_term([{a,{b,c}},{b,{c,d}},{a,{b,f}}])),
from_term([[{a,{b,c}},{a,{b,f}}],[{b,{c,d}}]])),
F = 0.0, I = round(F),
?line FR = relation([{I,a},{F,b}]),
if
F == I -> % term ordering
?line eval(partition(1, FR), from_term([[{I,a},{F,b}]]));
true ->
?line eval(partition(1, FR), from_term([[{I,a}],[{F,b}]]))
end,
?line {'EXIT', {badarg, _}} = (catch partition(2, set([a]))),
?line {'EXIT', {badarg, _}} = (catch partition(1, set([a]))),
?line eval(partition(Id, set([a])), from_term([[a]])),
?line eval(partition(E), E),
?line P1 = from_term([[a,b,c],[d,e,f],[g,h]]),
?line P2 = from_term([[a,d],[b,c,e,f,q,v]]),
?line eval(partition(union(P1, P2)),
from_term([[a],[b,c],[d],[e,f],[g,h],[q,v]])),
?line {'EXIT', {badarg, _}} = (catch partition(from_term([a]))),
ok.
partition_3(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line ER = relation([]),
%% set of ordered sets
?line S1 = relation([{a,1},{b,2},{b,22},{c,0}]),
?line eval(partition(1, S1, set([0,1,d,e])),
lpartition(1, S1, set([0,1,d,e]))),
?line eval(partition(1, S1, E), lpartition(1, S1, E)),
?line eval(partition(2, ER, set([a,b])), lpartition(2, ER, set([a,b]))),
XFun1 = {external, fun({_A,B,C}) -> {B,C} end},
R1a = relation([{a,aa,1},{b,bb,2},{c,cc,3}]),
R1b = relation([{bb,2},{cc,3}]),
?line eval(partition(XFun1, R1a, R1b), lpartition(XFun1, R1a, R1b)),
Id = fun(X) -> X end,
XId = {external, Id},
R2 = relation([{a,b}]),
?line eval(partition(XId, R2, E), lpartition(XId, R2, E)),
R3 = relation([{b,d}]),
?line eval(partition(XId, E, R3), lpartition(XId, E, R3)),
Fun1 = fun(S) -> {_A,B,C} = to_external(S), from_term({B,C}) end,
R4a = relation([{a,aa,1},{b,bb,2},{c,cc,3}]),
R4b = relation([{bb,2},{cc,3}]),
?line eval(partition(Fun1,R4a,R4b), lpartition(Fun1,R4a,R4b)),
XFun2 = {external, fun({_,{A},B}) -> {A,B} end},
R5a = from_term([{a,{aa},1},{b,{bb},2},{c,{cc},3}]),
R5b = from_term([{bb,2},{cc,3}]),
?line eval(partition(XFun2,R5a, R5b), lpartition(XFun2,R5a, R5b)),
R6 = relation([{a,b}]),
?line eval(partition(2, R6, E), lpartition(2, R6, E)),
R7 = relation([{b,d}]),
?line eval(partition(2, E, R7), lpartition(2, E, R7)),
S2 = set([a]),
?line eval(partition(XId, E, S2), lpartition(XId, E, S2)),
?line eval(partition(XId, S1, E), lpartition(XId, S1, E)),
?line {'EXIT', {badarg, _}} =
(catch partition(3, relation([{a,b}]), E)),
?line {'EXIT', {badarg, _}} =
(catch partition(3, relation([{a,b}]), relation([{b,d}]))),
?line {'EXIT', {badarg, _}} =
(catch partition(3, relation([{a,b}]), set([{b,d}]))),
?line {'EXIT', {type_mismatch, _}} =
(catch partition(2, relation([{a,b}]), relation([{b,d}]))),
?line {'EXIT', {type_mismatch, _}} =
(catch partition({external, fun({A,_B}) -> A end},
relation([{a,b}]), relation([{b,d}]))),
?line {'EXIT', {badarg, _}} =
(catch partition({external, fun({A,_}) -> {A,0} end},
from_term([{1,a}]),
from_term([{1,0}]))),
S18a = relation([{1,e},{2,b},{3,c},{4,b},{5,a},{6,0}]),
S18b = set([b,d,f]),
?line eval(partition({external,fun({_,X}) -> X end}, S18a, S18b),
lpartition({external,fun({_,X}) -> X end}, S18a, S18b)),
S19a = sofs:relation([{3,a},{8,b}]),
S19b = set([2,6,7]),
?line eval(partition({external,fun({X,_}) -> X end}, S19a, S19b),
lpartition({external,fun({X,_}) -> X end}, S19a, S19b)),
R8a = relation([{a,d},{b,e},{c,b},{d,c}]),
S8 = set([b,d]),
?line eval(partition(2, R8a, S8), lpartition(2, R8a, S8)),
S16a = relation([{1,e},{2,b},{3,c},{4,b},{5,a},{6,0}]),
S16b = set([b,c,d]),
?line eval(partition(2, S16a, S16b), lpartition(2, S16a, S16b)),
S17a = relation([{e,1},{b,2},{c,3},{b,4},{a,5},{0,6}]),
S17b = set([b,c,d]),
?line eval(partition(1, S17a, S17b), lpartition(1, S17a, S17b)),
?line {'EXIT', {function_clause, _}} =
(catch partition({external, fun({A,_B}) -> A end}, set([]), E)),
Fun3 = fun(S) -> from_term({to_external(S),0}, {type(S),atom}) end,
S9a = set([1,2]),
S9b = from_term([{1,0}]),
?line eval(partition(Fun3, S9a, S9b), lpartition(Fun3, S9a, S9b)),
S14a = relation([{1,a},{2,b},{3,c},{0,0}]),
S14b = set([b,c]),
?line eval(partition(2, S14a, S14b), lpartition(2, S14a, S14b)),
S15a = relation([{a,1},{b,2},{c,3},{0,0}]),
S15b = set([b,c]),
?line eval(partition(1, S15a, S15b), lpartition(1, S15a, S15b)),
%% set of sets
?line {'EXIT', {badarg, _}} =
(catch partition({external, fun(X) -> X end},
from_term([], [[atom]]), set([a]))),
S10 = from_term([], [[atom]]),
?line eval(partition(Id, S10, E), lpartition(Id, S10, E)),
S10e = from_term([[a],[b]], [[atom]]),
?line eval(partition(Id, S10e, E), lpartition(Id, S10e, E)),
S11a = from_term([], [[atom]]),
S11b = set([a]),
?line eval(partition(Id, S11a, S11b), lpartition(Id, S11a, S11b)),
S12a = from_term([[[a],[b]], [[b],[c]], [[], [a,b]], [[1],[2]]]),
S12b = from_term([[a,b],[1,2,3],[b,c]]),
?line eval(partition(fun sofs:union/1, S12a, S12b),
lpartition(fun sofs:union/1, S12a, S12b)),
Fun13 = fun(_) -> from_term([a]) end,
S13a = from_term([], [[atom]]),
S13b = from_term([], [[a]]),
?line eval(partition(Fun13, S13a, S13b), lpartition(Fun13, S13a, S13b)),
?line {'EXIT', {type_mismatch, _}} =
(catch partition(fun(_) -> from_term([a]) end,
from_term([[1,2],[3,4]]),
from_term([], [atom]))),
Fun10 = fun(S) ->
%% Cheating a lot...
case to_external(S) of
[1] -> from_term({1,1});
_ -> S
end
end,
?line {'EXIT', {type_mismatch, _}} =
(catch partition(Fun10, from_term([[1]]), from_term([], [[atom]]))),
?line {'EXIT', {type_mismatch, _}} =
(catch partition(fun(_) -> from_term({a}) end,
from_term([[a]]),
from_term([], [atom]))),
?line {'EXIT', {badarg, _}} =
(catch partition(fun(_) -> {a} end,
from_term([[a]]),
from_term([], [atom]))),
ok.
lpartition(F, S1, S2) ->
{restriction(F, S1, S2), drestriction(F, S1, S2)}.
multiple_relative_product(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line ER = relation([]),
?line T = relation([{a,1},{a,11},{b,2},{c,3},{c,33},{d,4}]),
?line {'EXIT', {badarg, _}} =
(catch multiple_relative_product({}, ER)),
?line {'EXIT', {badarg, _}} =
(catch multiple_relative_product({}, relation([{a,b}]))),
?line eval(multiple_relative_product({E,T,T}, relation([], 3)), E),
?line eval(multiple_relative_product({T,T,T}, E), E),
?line eval(multiple_relative_product({T,T,T}, relation([],3)),
from_term([],[{{atom,atom,atom},{atom,atom,atom}}])),
?line eval(multiple_relative_product({T,T,T},
relation([{a,b,c},{c,d,a}])),
from_term([{{a,b,c},{1,2,3}}, {{a,b,c},{1,2,33}},
{{a,b,c},{11,2,3}}, {{a,b,c},{11,2,33}},
{{c,d,a},{3,4,1}}, {{c,d,a},{3,4,11}},
{{c,d,a},{33,4,1}}, {{c,d,a},{33,4,11}}])),
?line {'EXIT', {type_mismatch, _}} =
(catch multiple_relative_product({T}, from_term([{{a}}]))),
ok.
digraph(Conf) when is_list(Conf) ->
?line T0 = ets:all(),
?line E = empty_set(),
?line R = relation([{a,b},{b,c},{c,d},{d,a}]),
?line F = relation_to_family(R),
Type = type(F),
?line {'EXIT', {badarg, _}} =
(catch family_to_digraph(set([a]))),
digraph_fail(badarg, catch family_to_digraph(set([a]), [foo])),
digraph_fail(badarg, catch family_to_digraph(F, [foo])),
digraph_fail(cyclic, catch family_to_digraph(family([{a,[a]}]),[acyclic])),
?line G1 = family_to_digraph(E),
?line {'EXIT', {badarg, _}} = (catch digraph_to_family(G1, foo)),
?line {'EXIT', {badarg, _}} = (catch digraph_to_family(G1, atom)),
?line true = [] == to_external(digraph_to_family(G1)),
?line true = [] == to_external(digraph_to_family(G1, Type)),
?line true = digraph:delete(G1),
?line G1a = family_to_digraph(E, [protected]),
?line true = [] == to_external(digraph_to_family(G1a)),
?line true = [] == to_external(digraph_to_family(G1a, Type)),
?line true = digraph:delete(G1a),
?line G2 = family_to_digraph(F),
?line true = F == digraph_to_family(G2),
?line true = F == digraph_to_family(G2, type(F)),
?line true = digraph:delete(G2),
?line R2 = from_term([{{a},b},{{c},d}]),
?line F2 = relation_to_family(R2),
?line Type2 = type(F2),
?line G3 = family_to_digraph(F2, [protected]),
?line true = is_subset(F2, digraph_to_family(G3, Type2)),
?line true = digraph:delete(G3),
Fl = 0.0, I = round(Fl),
if
Fl == I -> % term ordering
?line G4 = digraph:new(),
digraph:add_vertex(G4, Fl),
digraph:add_vertex(G4, I),
?line {'EXIT', {badarg, _}} =
(catch digraph_to_family(G4, Type)),
?line {'EXIT', {badarg, _}} =
(catch digraph_to_family(G4)),
?line true = digraph:delete(G4);
true -> ok
end,
?line true = T0 == ets:all(),
ok.
digraph_fail(ExitReason, Fail) ->
{'EXIT', {ExitReason, [{sofs,family_to_digraph,A,_}|_]}} = Fail,
case {test_server:is_native(sofs),A} of
{false,[_,_]} -> ok;
{true,2} -> ok
end.
constant_function(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line C = from_term(3),
?line eval(constant_function(E, C), E),
?line eval(constant_function(set([a,b]), E), from_term([{a,[]},{b,[]}])),
?line eval(constant_function(set([a,b]), C), from_term([{a,3},{b,3}])),
?line {'EXIT', {badarg, _}} = (catch constant_function(C, C)),
?line {'EXIT', {badarg, _}} = (catch constant_function(set([]), foo)),
ok.
misc(Conf) when is_list(Conf) ->
%% find "relational" part of relation:
?line S = relation([{a,b},{b,c},{b,d},{c,d}]),
Id = fun(A) -> A end,
?line RR = relational_restriction(S),
?line eval(union(difference(partition(Id,S), partition(1,S))), RR),
?line eval(union(difference(partition(1,S), partition(Id,S))), RR),
%% the "functional" part:
?line eval(union(intersection(partition(1,S), partition(Id,S))),
difference(S, RR)),
?line {'EXIT', {undef, _}} =
(catch projection(fun external:foo/1, set([a,b,c]))),
ok.
relational_restriction(R) ->
Fun = fun(S) -> no_elements(S) > 1 end,
family_to_relation(family_specification(Fun, relation_to_family(R))).
family_specification(Conf) when is_list(Conf) ->
E = empty_set(),
%% internal
?line eval(family_specification(fun sofs:is_set/1, E), E),
?line {'EXIT', {badarg, _}} =
(catch family_specification(fun sofs:is_set/1, set([]))),
?line F1 = from_term([{1,[1]}]),
?line eval(family_specification(fun sofs:is_set/1, F1), F1),
Fun = fun(S) -> is_subset(S, set([0,1,2,3,4])) end,
?line F2 = family([{a,[1,2]},{b,[3,4,5]}]),
?line eval(family_specification(Fun, F2), family([{a,[1,2]}])),
?line F3 = from_term([{a,[]},{b,[]}]),
?line eval(family_specification(fun sofs:is_set/1, F3), F3),
Fun2 = fun(_) -> throw(fippla) end,
?line fippla = (catch family_specification(Fun2, family([{a,[1]}]))),
Fun3 = fun(_) -> neither_true_nor_false end,
?line {'EXIT', {badarg, _}} =
(catch family_specification(Fun3, F3)),
%% external
IsList = {external, fun(L) when is_list(L) -> true; (_) -> false end},
?line eval(family_specification(IsList, E), E),
?line eval(family_specification(IsList, F1), F1),
MF = {external, fun(L) -> lists:member(3, L) end},
?line eval(family_specification(MF, F2), family([{b,[3,4,5]}])),
?line fippla = (catch family_specification(Fun2, family([{a,[1]}]))),
?line {'EXIT', {badarg, _}} =
(catch family_specification({external, Fun3}, F3)),
ok.
family_domain_1(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line ER = from_term([{a,[]},{b,[]}],[{atom,[{atom,atom}]}]),
?line EF = from_term([{a,[]},{b,[]}],[{atom,[atom]}]),
?line eval(family_domain(E), E),
?line eval(family_domain(ER), EF),
?line FR = from_term([{a,[{1,a},{2,b},{3,c}]},{b,[]},{c,[{4,d},{5,e}]}]),
?line eval(family_domain(FR), from_term([{a,[1,2,3]},{b,[]},{c,[4,5]}])),
?line eval(family_field(E), E),
?line eval(family_field(FR),
from_term([{a,[a,b,c,1,2,3]},{b,[]},{c,[d,e,4,5]}])),
?line eval(family_domain(from_term([{{a},[{{1,[]},c}]}])),
from_term([{{a},[{1,[]}]}])),
?line eval(family_domain(from_term([{{a},[{{1,[a]},c}]}])),
from_term([{{a},[{1,[a]}]}])),
?line eval(family_domain(from_term([{{a},[]}])),
from_term([{{a},[]}])),
?line eval(family_domain(from_term([], type(FR))),
from_term([], [{atom,[atom]}])),
?line {'EXIT', {badarg, _}} = (catch family_domain(set([a]))),
?line {'EXIT', {badarg, _}} = (catch family_field(set([a]))),
?line {'EXIT', {badarg, _}} = (catch family_domain(set([{a,[b]}]))),
ok.
family_range_1(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line ER = from_term([{a,[]},{b,[]}],[{atom,[{atom,atom}]}]),
?line EF = from_term([{a,[]},{b,[]}],[{atom,[atom]}]),
?line eval(family_range(E), E),
?line eval(family_range(ER), EF),
?line FR = from_term([{a,[{1,a},{2,b},{3,c}]},{b,[]},{c,[{4,d},{5,e}]}]),
?line eval(family_range(FR), from_term([{a,[a,b,c]},{b,[]},{c,[d,e]}])),
?line eval(family_range(from_term([{{a},[{c,{1,[a]}}]}])),
from_term([{{a},[{1,[a]}]}])),
?line eval(family_range(from_term([{{a},[{c,{1,[]}}]}])),
from_term([{{a},[{1,[]}]}])),
?line eval(family_range(from_term([{{a},[]}])),
from_term([{{a},[]}])),
?line eval(family_range(from_term([], type(FR))),
from_term([], [{atom,[atom]}])),
?line {'EXIT', {badarg, _}} = (catch family_range(set([a]))),
?line {'EXIT', {badarg, _}} = (catch family_range(set([{a,[b]}]))),
ok.
family_to_relation_1(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line ER = relation([]),
?line EF = family([]),
?line eval(family_to_relation(E), E),
?line eval(family_to_relation(EF), ER),
?line eval(sofs:fam2rel(EF), ER),
?line F = family([{a,[]},{b,[1]},{c,[7,9,11]}]),
?line eval(family_to_relation(F), relation([{b,1},{c,7},{c,9},{c,11}])),
?line {'EXIT', {badarg, _}} = (catch family_to_relation(set([a]))),
ok.
union_of_family_1(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line EF = from_term([{a,[]},{b,[]}],[{atom,[atom]}]),
?line eval(union_of_family(E), E),
?line eval(union_of_family(EF), set([])),
?line eval(union_of_family(family([])), set([])),
?line FR = from_term([{a,[1,2,3]},{b,[]},{c,[4,5]}]),
?line eval(union_of_family(FR), set([1,2,3,4,5])),
?line eval(union_of_family(sofs:family([{a,[1,2]},{b,[1,2]}])),
set([1,2])),
?line {'EXIT', {badarg, _}} = (catch union_of_family(set([a]))),
ok.
intersection_of_family_1(Conf) when is_list(Conf) ->
?line EF = from_term([{a,[]},{b,[]}],[{atom,[atom]}]),
?line eval(intersection_of_family(EF), set([])),
?line FR = from_term([{a,[1,2,3]},{b,[2,3]},{c,[3,4,5]}]),
?line eval(intersection_of_family(FR), set([3])),
?line {'EXIT', {badarg, _}} =
(catch intersection_of_family(family([]))),
?line EE = from_term([], [[atom]]),
?line {'EXIT', {badarg, _}} = (catch intersection_of_family(EE)),
?line {'EXIT', {badarg, _}} = (catch intersection_of_family(set([a]))),
ok.
family_projection(Conf) when is_list(Conf) ->
SSType = [{atom,[[atom]]}],
SRType = [{atom,[{atom,atom}]}],
?line E = empty_set(),
?line eval(family_projection(fun(X) -> X end, family([])), E),
?line L1 = [{a,[]}],
?line eval(family_projection(fun sofs:union/1, E), E),
?line eval(family_projection(fun sofs:union/1, from_term(L1, SSType)),
family(L1)),
?line {'EXIT', {badarg, _}} =
(catch family_projection(fun sofs:union/1, set([]))),
?line {'EXIT', {badarg, _}} =
(catch family_projection(fun sofs:union/1, from_term([{1,[1]}]))),
?line F2 = from_term([{a,[[1],[2]]},{b,[[3,4],[5]]}], SSType),
?line eval(family_projection(fun sofs:union/1, F2),
family_union(F2)),
?line F3 = from_term([{1,[{a,b},{b,c},{c,d}]},{3,[]},{5,[{3,5}]}],
SRType),
?line eval(family_projection(fun sofs:domain/1, F3), family_domain(F3)),
?line eval(family_projection(fun sofs:range/1, F3), family_range(F3)),
?line eval(family_projection(fun(_) -> E end, family([{a,[b,c]}])),
from_term([{a,[]}])),
Fun1 = fun(S) ->
case to_external(S) of
[1] -> from_term({1,1});
_ -> S
end
end,
?line eval(family_projection(Fun1, family([{a,[1]}])),
from_term([{a,{1,1}}])),
Fun2 = fun(_) -> throw(fippla) end,
?line fippla =
(catch family_projection(Fun2, family([{a,[1]}]))),
?line {'EXIT', {type_mismatch, _}} =
(catch family_projection(Fun1, from_term([{1,[1]},{2,[2]}]))),
?line {'EXIT', {type_mismatch, _}} =
(catch family_projection(Fun1, from_term([{1,[1]},{0,[0]}]))),
?line eval(family_projection(fun(_) -> E end, from_term([{a,[]}])),
from_term([{a,[]}])),
F4 = from_term([{a,[{1,2,3}]},{b,[{4,5,6}]},{c,[]},{m3,[]}]),
Z = from_term(0),
?line eval(family_projection(fun(S) -> local_adjoin(S, Z) end, F4),
from_term([{a,[{{1,2,3},0}]},{b,[{{4,5,6},0}]},{c,[]},{m3,[]}])),
?line {'EXIT', {badarg, _}} =
(catch family_projection({external, fun(X) -> X end},
from_term([{1,[1]}]))),
%% ordered set element
?line eval(family_projection(fun(_) -> from_term(a, atom) end,
from_term([{1,[a]}])),
from_term([{1,a}])),
ok.
family_difference(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line EF = family([]),
?line F9 = from_term([{b,[b,c]}]),
?line F10 = from_term([{a,[b,c]}]),
?line eval(family_difference(E, E), E),
?line eval(family_difference(E, F10), from_term([], type(F10))),
?line eval(family_difference(F10, E), F10),
?line eval(family_difference(F9, F10), F9),
?line eval(family_difference(F10, F10), family([{a,[]}])),
?line F20 = from_term([{a,[1,2,3]},{b,[1,2,3]},{c,[1,2,3]}]),
?line F21 = from_term([{b,[1,2,3]},{c,[1,2,3]}]),
?line eval(family_difference(F20, from_term([{a,[2]}])),
from_term([{a,[1,3]},{b,[1,2,3]},{c,[1,2,3]}])),
?line eval(family_difference(F20, from_term([{0,[2]},{q,[1,2]}])), F20),
?line eval(family_difference(F20, F21),
from_term([{a,[1,2,3]},{b,[]},{c,[]}])),
?line eval(family_difference(from_term([{e,[f,g]}]), family([])),
from_term([{e,[f,g]}])),
?line eval(family_difference(from_term([{e,[f,g]}]), EF),
from_term([{e,[f,g]}])),
?line eval(family_difference(from_term([{a,[a,b,c,d]},{c,[b,c]}]),
from_term([{a,[b,c]},{b,[d]},{d,[e,f]}])),
from_term([{a,[a,d]},{c,[b,c]}])),
?line {'EXIT', {badarg, _}} =
(catch family_difference(set([]), set([]))),
?line {'EXIT', {type_mismatch, _}} =
(catch family_difference(from_term([{a,[b,c]}]),
from_term([{e,[{f}]}]))),
?line {'EXIT', {type_mismatch, _}} =
(catch family_difference(from_term([{a,[b]}]),
from_term([{c,[d]}], [{i,[s]}]))),
ok.
family_intersection_1(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line EF = family([]),
?line ES = from_term([], [{atom,[[atom]]}]),
?line eval(family_intersection(E), E),
?line {'EXIT', {badarg, _}} = (catch family_intersection(EF)),
?line eval(family_intersection(ES), EF),
?line {'EXIT', {badarg, _}} = (catch family_intersection(set([]))),
?line {'EXIT', {badarg, _}} =
(catch family_intersection(from_term([{a,[1,2]}]))),
?line F1 = from_term([{a,[[1],[2],[2,3]]},{b,[]},{c,[[4]]}]),
?line {'EXIT', {badarg, _}} = (catch family_intersection(F1)),
?line F2 = from_term([{b,[[1],[2],[2,3]]},{a,[]},{c,[[4]]}]),
?line {'EXIT', {badarg, _}} = (catch family_intersection(F2)),
?line F3 = from_term([{a,[[1,2,3],[2],[2,3]]},{c,[[4,5,6],[5,6,7]]}]),
?line eval(family_intersection(F3), family([{a,[2]},{c,[5,6]}])),
ok.
family_intersection_2(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line EF = family([]),
?line F1 = from_term([{a,[1,2]},{b,[4,5]},{c,[7,8]},{d,[10,11]}]),
?line F2 = from_term([{c,[6,7]},{d,[9,10,11]},{q,[1]}]),
?line F3 = from_term([{a,[1,2]},{b,[4,5]},{c,[6,7,8]},{d,[9,10,11]},
{q,[1]}]),
?line eval(family_intersection(E, E), E),
?line eval(family_intersection(EF, EF), EF),
?line eval(family_intersection(F1, F2),
from_term([{c,[7]},{d,[10,11]}])),
?line eval(family_intersection(F1, F3), F1),
?line eval(family_intersection(F2, F3), F2),
?line eval(family_intersection(EF, from_term([{e,[f,g]}])), EF),
?line eval(family_intersection(E, from_term([{e,[f,g]}])), EF),
?line eval(family_intersection(from_term([{e,[f,g]}]), EF), EF),
?line eval(family_intersection(from_term([{e,[f,g]}]), E), EF),
?line {'EXIT', {type_mismatch, _}} =
(catch family_intersection(from_term([{a,[b,c]}]),
from_term([{e,[{f}]}]))),
?line F11 = family([{a,[1,2,3]},{b,[0,2,4]},{c,[0,3,6,9]}]),
?line eval(union_of_family(F11), set([0,1,2,3,4,6,9])),
?line F12 = from_term([{a,[1,2,3,4]},{b,[0,2,4]},{c,[2,3,4,5]}]),
?line eval(intersection_of_family(F12), set([2,4])),
ok.
family_union_1(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line EF = family([]),
?line ES = from_term([], [{atom,[[atom]]}]),
?line eval(family_union(E), E),
?line eval(family_union(ES), EF),
?line {'EXIT', {badarg, _}} = (catch family_union(set([]))),
?line {'EXIT', {badarg, _}} =
(catch family_union(from_term([{a,[1,2]}]))),
?line eval(family_union(from_term([{a,[[1],[2],[2,3]]},{b,[]},{c,[[4]]}])),
family([{a,[1,2,3]},{b,[]},{c,[4]}])),
ok.
family_union_2(Conf) when is_list(Conf) ->
?line E = empty_set(),
?line EF = family([]),
?line F1 = from_term([{a,[1,2]},{b,[4,5]},{c,[7,8]},{d,[10,11]}]),
?line F2 = from_term([{c,[6,7]},{d,[9,10,11]},{q,[1]}]),
?line F3 = from_term([{a,[1,2]},{b,[4,5]},{c,[6,7,8]},{d,[9,10,11]},
{q,[1]}]),
?line eval(family_union(E, E), E),
?line eval(family_union(F1, E), F1),
?line eval(family_union(E, F2), F2),
?line eval(family_union(F1, F2), F3),
?line eval(family_union(F2, F1), F3),
?line eval(family_union(E, from_term([{e,[f,g]}])),
from_term([{e,[f,g]}])),
?line eval(family_union(EF, from_term([{e,[f,g]}])),
from_term([{e,[f,g]}])),
?line eval(family_union(from_term([{e,[f,g]}]), E),
from_term([{e,[f,g]}])),
?line {'EXIT', {badarg, _}} =
(catch family_union(set([]),set([]))),
?line {'EXIT', {type_mismatch, _}} =
(catch family_union(from_term([{a,[b,c]}]),
from_term([{e,[{f}]}]))),
ok.
partition_family(Conf) when is_list(Conf) ->
?line E = empty_set(),
%% set of ordered sets
?line ER = relation([]),
?line EF = from_term([], [{atom,[{atom,atom}]}]),
?line eval(partition_family(1, E), E),
?line eval(partition_family(2, E), E),
?line eval(partition_family(fun sofs:union/1, E), E),
?line eval(partition_family(1, ER), EF),
?line eval(partition_family(2, ER), EF),
?line {'EXIT', {badarg, _}} = (catch partition_family(1, set([]))),
?line {'EXIT', {badarg, _}} = (catch partition_family(2, set([]))),
?line {'EXIT', {function_clause, _}} =
(catch partition_family(fun({_A,B}) -> {B} end, from_term([{1}]))),
?line eval(partition_family(1, relation([{1,a},{1,b},{2,c},{2,d}])),
from_term([{1,[{1,a},{1,b}]},{2,[{2,c},{2,d}]}])),
?line eval(partition_family(1, relation([{1,a},{2,b}])),
from_term([{1,[{1,a}]},{2,[{2,b}]}])),
?line eval(partition_family(2, relation([{1,a},{1,b},{2,a},{2,b},{3,c}])),
from_term([{a,[{1,a},{2,a}]},{b,[{1,b},{2,b}]},{c,[{3,c}]}])),
?line eval(partition_family(2, relation([{1,a}])),
from_term([{a,[{1,a}]}])),
?line eval(partition_family(2, relation([{1,a},{2,a},{3,a}])),
from_term([{a,[{1,a},{2,a},{3,a}]}])),
?line eval(partition_family(2, relation([{1,a},{2,b}])),
from_term([{a,[{1,a}]},{b,[{2,b}]}])),
?line F13 = from_term([{a,b,c},{a,b,d},{b,b,c},{a,c,c},{a,c,d},{b,c,c}]),
?line eval(partition_family(2, F13),
from_term([{b,[{a,b,c},{a,b,d},{b,b,c}]},
{c,[{a,c,c},{a,c,d},{b,c,c}]}])),
Fun1 = {external, fun({A,_B}) -> {A} end},
?line eval(partition_family(Fun1, relation([{a,1},{a,2},{b,3}])),
from_term([{{a},[{a,1},{a,2}]},{{b},[{b,3}]}])),
Fun2 = fun(S) -> {A,_B} = to_external(S), from_term({A}) end,
?line eval(partition_family(Fun2, relation([{a,1},{a,2},{b,3}])),
from_term([{{a},[{a,1},{a,2}]},{{b},[{b,3}]}])),
?line {'EXIT', {badarg, _}} =
(catch partition_family({external, fun({A,_}) -> {A,0} end},
from_term([{1,a}]))),
?line [{{atom,atom},[{atom,atom,atom,atom}]}] =
type(partition_family({external, fun({A,_B,C,_D}) -> {C,A} end},
relation([],4))),
Fun3 = fun(S) -> from_term({to_external(S),0}, {type(S),atom}) end,
?line eval(partition_family(Fun3, E), E),
?line eval(partition_family(Fun3, set([a,b])),
from_term([{{a,0},[a]}, {{b,0},[b]}])),
?line eval(partition_family(Fun3, relation([{a,1},{b,2}])),
from_term([{{{a,1},0},[{a,1}]},{{{b,2},0},[{b,2}]}])),
?line eval(partition_family(Fun3, from_term([[a],[b]])),
from_term([{{[a],0},[[a]]}, {{[b],0},[[b]]}])),
?line partition_family({external, fun(X) -> X end}, E),
F = 0.0, I = round(F),
?line FR = relation([{I,a},{F,b}]),
if
F == I -> % term ordering
?line true = (1 =:= no_elements(partition_family(1, FR)));
true ->
?line eval(partition_family(1, FR),
from_term([{I,[{I,a}]},{F,[{F,b}]}]))
end,
%% set of sets
?line {'EXIT', {badarg, _}} =
(catch partition_family({external, fun(X) -> X end},
from_term([], [[atom]]))),
?line {'EXIT', {badarg, _}} =
(catch partition_family({external, fun(X) -> X end},
from_term([[a]]))),
?line eval(partition_family(fun sofs:union/1,
from_term([[[1],[1,2]], [[1,2]]])),
from_term([{[1,2], [[[1],[1,2]],[[1,2]]]}])),
?line eval(partition_family(fun(X) -> X end,
from_term([[1],[1,2],[1,2,3]])),
from_term([{[1],[[1]]},{[1,2],[[1,2]]},{[1,2,3],[[1,2,3]]}])),
?line eval(partition_family(fun(_) -> from_term([a]) end,
from_term([], [[atom]])),
E),
Fun10 = fun(S) ->
%% Cheating a lot...
case to_external(S) of
[1] -> from_term({1,1});
_ -> S
end
end,
?line eval(partition_family(Fun10, from_term([[1]])),
from_term([{{1,1},[[1]]}])),
?line eval(partition_family(fun(_) -> from_term({a}) end,
from_term([[a]])),
from_term([{{a},[[a]]}])),
?line {'EXIT', {badarg, _}} =
(catch partition_family(fun(_) -> {a} end, from_term([[a]]))),
ok.
%% Not meant to be efficient...
local_adjoin(S, C) ->
X = to_external(C),
T = type(C),
F = fun(Y) -> from_term({to_external(Y),X}, {type(Y),T}) end,
projection(F, S).
eval(R, E) when R == E ->
R;
eval(R, E) ->
io:format("expected ~p~n got ~p~n", [E, R]),
exit({R,E}).
