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Diffstat (limited to 'lib/stdlib/test/sofs_SUITE.erl')
| -rw-r--r-- | lib/stdlib/test/sofs_SUITE.erl | 2374 |
1 files changed, 2374 insertions, 0 deletions
diff --git a/lib/stdlib/test/sofs_SUITE.erl b/lib/stdlib/test/sofs_SUITE.erl new file mode 100644 index 0000000000..0849e0f59c --- /dev/null +++ b/lib/stdlib/test/sofs_SUITE.erl @@ -0,0 +1,2374 @@ +%% +%% %CopyrightBegin% +%% +%% Copyright Ericsson AB 2001-2009. 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("test_server.hrl"). +-define(format(S, A), ok). +-endif. + +-export([all/1]). + +-export([sofs/1, 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([sofs_family/1, 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, fin_per_testcase/2]). + +-compile({inline,[{eval,2}]}). + +all(suite) -> + [sofs, sofs_family]. + +init_per_testcase(_Case, Config) -> + Dog=?t:timetrap(?t:minutes(2)), + [{watchdog, Dog}|Config]. + +fin_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}]) + +sofs(suite) -> + [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]. + +from_term_1(suite) -> []; +from_term_1(doc) -> [""]; +from_term_1(Conf) when 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 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 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 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 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 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 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({sofs,union}, + 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 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({sofs,union}, + 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 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({sofs,union}, + 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 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({sofs,union}, + 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 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 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 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 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 list(Conf) -> + Fun = {external, fun(I) when 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_or_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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 eval(relative_product({relation([{a,b}])}, + from_term([],[{{atom},atom}])), + ER), + ?line eval(relative_product({relation([{a,b}]),relation([{a,1}])}, + from_term([{{b,1},{tjo,hej,sa}}])), + from_term([{a,{tjo,hej,sa}}])), + ?line eval(relative_product({relation([{a,b}]), ER}, + from_term([{{a,b},b}])), + ER), + ?line eval(relative_product({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. + +product_1(suite) -> []; +product_1(doc) -> [""]; +product_1(Conf) when 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 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 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({sofs,union}, S12a, S12b), + lpartition({sofs,union}, 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 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 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]))), + ?line {'EXIT', {badarg, [{sofs,family_to_digraph,[_,_]}|_]}} = + (catch family_to_digraph(set([a]), [foo])), + ?line {'EXIT', {badarg, [{sofs,family_to_digraph,[_,_]}|_]}} = + (catch family_to_digraph(F, [foo])), + ?line {'EXIT', {cyclic, [{sofs,family_to_digraph,[_,_]}|_]}} = + (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. + +constant_function(suite) -> []; +constant_function(doc) -> [""]; +constant_function(Conf) when 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 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)), + + %% The function external:foo/1 is undefined. + ?line {'EXIT', {undef, _}} = + (catch projection({external,foo}, 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))). + +sofs_family(suite) -> + [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]. + +family_specification(suite) -> []; +family_specification(doc) -> [""]; +family_specification(Conf) when list(Conf) -> + E = empty_set(), + %% internal + ?line eval(family_specification({sofs, is_set}, E), E), + ?line {'EXIT', {badarg, _}} = + (catch family_specification({sofs,is_set}, set([]))), + ?line F1 = from_term([{1,[1]}]), + ?line eval(family_specification({sofs,is_set}, 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({sofs,is_set}, F3), F3), + Fun2 = fun(_) -> throw(fippla) end, + ?line fippla = (catch family_specification(Fun2, family([{a,[1]}]))), + Fun3 = fun(_) -> neither_true_or_false end, + ?line {'EXIT', {badarg, _}} = + (catch family_specification(Fun3, F3)), + + %% external + IsList = {external, fun(L) when 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 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 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 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 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 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 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({sofs,union}, E), E), + ?line eval(family_projection({sofs,union}, from_term(L1, SSType)), + family(L1)), + ?line {'EXIT', {badarg, _}} = + (catch family_projection({sofs,union}, set([]))), + ?line {'EXIT', {badarg, _}} = + (catch family_projection({sofs,union}, from_term([{1,[1]}]))), + + ?line F2 = from_term([{a,[[1],[2]]},{b,[[3,4],[5]]}], SSType), + ?line eval(family_projection({sofs,union}, F2), + family_union(F2)), + + ?line F3 = from_term([{1,[{a,b},{b,c},{c,d}]},{3,[]},{5,[{3,5}]}], + SRType), + ?line eval(family_projection({sofs,domain}, F3), family_domain(F3)), + ?line eval(family_projection({sofs,range}, 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 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 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 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 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 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 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({sofs,union}, 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({sofs,union}, + 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}). + |