%% %% %CopyrightBegin% %% %% Copyright Ericsson AB 2001-2012. All Rights Reserved. %% %% The contents of this file are subject to the Erlang Public License, %% Version 1.1, (the "License"); you may not use this file except in %% compliance with the License. You should have received a copy of the %% Erlang Public License along with this software. If not, it can be %% retrieved online at http://www.erlang.org/. %% %% Software distributed under the License is distributed on an "AS IS" %% basis, WITHOUT WARRANTY OF ANY KIND, either express or implied. See %% the License for the specific language governing rights 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("test_server/include/test_server.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]}]. 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) -> Dog=?t:timetrap(?t:minutes(2)), [{watchdog, Dog}|Config]. end_per_testcase(_Case, Config) -> Dog=?config(watchdog, Config), test_server:timetrap_cancel(Dog), 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(suite) -> []; from_term_1(doc) -> [""]; 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(suite) -> []; set_1(doc) -> [""]; 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(suite) -> []; from_sets_1(doc) -> [""]; 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(suite) -> []; relation_1(doc) -> [""]; 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(suite) -> []; a_function_1(doc) -> [""]; 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(suite) -> []; family_1(doc) -> [""]; 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(suite) -> []; projection(doc) -> [""]; 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(suite) -> []; substitution(doc) -> [""]; 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(suite) -> []; restriction(doc) -> [""]; 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(suite) -> []; drestriction(doc) -> [""]; 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(suite) -> []; strict_relation_1(doc) -> [""]; 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(suite) -> []; extension(doc) -> [""]; 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(suite) -> []; weak_relation_1(doc) -> [""]; 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(suite) -> []; to_sets_1(doc) -> [""]; 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(suite) -> []; specification(doc) -> [""]; 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(suite) -> []; union_1(doc) -> [""]; 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(suite) -> []; intersection_1(doc) -> [""]; 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(suite) -> []; difference(doc) -> [""]; 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(suite) -> []; symdiff(doc) -> [""]; 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(suite) -> []; symmetric_partition(doc) -> [""]; 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(suite) -> []; is_sofs_set_1(doc) -> [""]; 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(suite) -> []; is_set_1(doc) -> [""]; 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(suite) -> []; is_equal(doc) -> [""]; 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(suite) -> []; is_subset(doc) -> [""]; 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(suite) -> []; is_a_function_1(doc) -> [""]; 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(suite) -> []; is_disjoint(doc) -> [""]; 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(suite) -> []; join(doc) -> [""]; 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(suite) -> []; canonical(doc) -> [""]; 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(suite) -> []; relation_to_family_1(doc) -> [""]; 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(suite) -> []; domain_1(doc) -> [""]; 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(suite) -> []; range_1(doc) -> [""]; 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(suite) -> []; inverse_1(doc) -> [""]; 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(suite) -> []; converse_1(doc) -> [""]; 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(suite) -> []; no_elements_1(doc) -> [""]; 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(suite) -> []; image(doc) -> [""]; 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(suite) -> []; inverse_image(doc) -> [""]; 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(suite) -> []; composite_1(doc) -> [""]; 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(suite) -> []; relative_product_1(doc) -> [""]; 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(suite) -> []; relative_product_2(doc) -> [""]; 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(suite) -> []; product_1(doc) -> [""]; 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(suite) -> []; partition_1(doc) -> [""]; 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(suite) -> []; partition_3(doc) -> [""]; 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(suite) -> []; multiple_relative_product(doc) -> [""]; 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(suite) -> []; digraph(doc) -> [""]; 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(suite) -> []; constant_function(doc) -> [""]; 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(suite) -> []; misc(doc) -> [""]; 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(suite) -> []; family_specification(doc) -> [""]; 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(suite) -> []; family_domain_1(doc) -> [""]; 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(suite) -> []; family_range_1(doc) -> [""]; 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(suite) -> []; family_to_relation_1(doc) -> [""]; 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(suite) -> []; union_of_family_1(doc) -> [""]; 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(suite) -> []; intersection_of_family_1(doc) -> [""]; 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(suite) -> []; family_projection(doc) -> [""]; 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(suite) -> []; family_difference(doc) -> [""]; 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(suite) -> []; family_intersection_1(doc) -> [""]; 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(suite) -> []; family_intersection_2(doc) -> [""]; 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(suite) -> []; family_union_1(doc) -> [""]; 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(suite) -> []; family_union_2(doc) -> [""]; 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(suite) -> []; partition_family(doc) -> [""]; 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}).