% Benchmark Examples from Pierre Lim including stuff from other example files % adapted for CHRs by Thom Fruehwirth 940308 for Eclipse CHR library % the examples*math files are not yet adapted for Sicstus CHR library /* nb = not benchmarked laplace5 = laplace5(M) laplace7 = laplace7(M) %laplace12 = laplace12 fact100 = fact option1=go1 option2=go2 points = topb holzbaur5 = top5 small_sched = small_sched large_sched = bridge */ %:- nodbgcomp. %:- set_flag(prefer_rationals,on). timer(X):- T1 is cputime, once(X), T is cputime-T1,writeln(X=T),nl,fail;true. /* :- timer(laplace5(_)), timer(laplace7(_)), timer(chipfact(100,1,_)), timer(fact(100,_)), timer(solve1(_,_)), timer(solve2(_,_)), timer(topb(_,10)), timer(top5(_)), timer(small_sched), timer(laplace12(_)), timer(bridge(_)). */ /* :-['math-eager']. :- set_flag(prefer_rationals,off). laplace5([[0, 0, 0, 0, 0], [100, 57.1429, 47.3214, 57.1429, 100], [100, 81.25, 75.0, 81.25, 100], [100, 92.8571, 90.1786, 92.8571, 100], [100, 100, 100, 100, 100]]) = 0.6 laplace7([[0, 0, 0, 0, 0, 0, 0], [100, 53.1313, 37.0775, 33.0575, 37.0775, 53.1313, 100], [100, 75.4477, 62.1212, 58.075, 62.1212, 75.4478, 100], [100, 86.5385, 77.8846, 75.0, 77.8846, 86.5385, 100], [100, 92.8215, 87.8788, 86.1558, 87.8788, 92.8215, 100], [100, 96.8687, 94.6533, 93.8656, 94.6533, 96.8687, 100], [100, 100, 100, 100, 100, 100, 100]]) = 5.51667 chipfact(100, 1, 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000) = 0.1 fact(100, 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000) = 5.13333 solve1(_g944, _g1364) = 0.283333 solve2(5.7, _g704) = 0.8 topb([_g14094, _g11438, _g9074, _g7002, _g5222, _g3734, _g2538, _g1634, _g1022, _g702], 10) = 6.66667 top5([_g830, _g814, _g798, _g782, _g766, _g910, _g894, _g878, _g862, _g846, _g964, _g1020, _g1130, _g1084, _g1068, _g948, ...]) = 3.63333 small_sched = 0.583334 laplace12([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [100, 50.9134, 32.1099, 23.882, 20.0481, 18.4822, 18.4822, 20.0481, 23.882, 32.1099, 50.9134, 100], [100, 71.5439, 53.644, 43.3701, 37.8282, 35.3984, 35.3984, 37.8282, 43.3701, 53.644, 71.5439, 100], [100, 81.6182, 67.5522, 58.1261, 52.4962, 49.885, 49.8849, 52.4962, 58.1261, 67.5522, 81.6182, 100], [100, 87.3765, 76.8207, 69.0858, 64.1456, 61.7602, 61.7602, 64.1456, 69.0858, 76.8207, 87.3765, ...], [100, 91.0673, 83.2681, 77.251, 73.2401, 71.2501, 71.2501, 73.2401, 77.251, 83.2681, ...], [100, 93.6245, 87.9333, 83.41, 80.3136, 78.7499, 78.7499, 80.3136, 83.41, ...], [100, 95.4976, 91.4305, 88.1422, 85.8544, 84.6861, 84.6861, 85.8544, ...], [100, 96.9352, 94.1489, 91.8739, 90.2758, 89.4541, 89.4541, ...], [100, 98.0944, 96.356, 94.9288, 93.9207, 93.4003, ...], [100, 99.0866, 98.2518, 97.5646, 97.0778, ...], [100, 100, 100, 100, ...]]) = 423.567 bridge(_g39340) = 57.45 */ /* :-['math-eager']. :- set_flag(prefer_rationals,on). laplace5([[0, 0, 0, 0, 0], [100, 400_7, 1325_28, 400_7, 100], [100, 325_4, 75_1, 325_4, 100], [100, 650_7, 2525_28, 650_7, 100], [100, 100, 100, 100, 100]]) = 0.716667 laplace7([[0, 0, 0, 0, 0, 0, 0], [100, 5260_99, 63625_1716, 42545_1287, 63625_1716, 5260_99, 100], [100, 388405_5148, 2050_33, 149485_2574, 2050_33, 388405_5148, 100], [100, 1125_13, 2025_26, 75_1, 2025_26, 1125_13, 100], [100, 477845_5148, 2900_33, 221765_2574, 2900_33, 477845_5148, 100], [100, 9590_99, 162425_1716, 120805_1287, 162425_1716, 9590_99, 100], [100, 100, 100, 100, 100, 100, 100]]) = 7.6 chipfact(100, 1, 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000) = 0.1 fact(100, 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000) = 4.95 solve1(_g944, _g1364) = 0.3 solve2(5.7, _g704) = 0.799999 topb([_g15030, _g12174, _g9634, _g7410, _g5502, _g3910, _g2634, _g1674, _g1030, _g702], 10) = 6.66667 top5([_g830, _g814, _g798, _g782, _g766, _g910, _g894, _g878, _g862, _g846, _g964, _g1020, _g1116, _g1084, _g1068, _g948, ...]) = 3.85 small_sched = 0.6 laplace12([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [100, 38763048600_761351911, 4395212420897975_136880414671046, 1634489974393600_68440207335523, 1372096199788400_68440207335523, 1264924397859100_68440207335523, 1264924397859100_68440207335523, 1372096199788400_68440207335523, 1634489974393600_68440207335523, 4395212420897975_136880414671046, 38763048600_761351911, 100], [100, 9792959934395825_136880414671046, 40841980350_761351911, 5936514974674025_136880414671046, 2588970426900900_68440207335523, 2422676993788900_68440207335523, 2422676993788900_68440207335523, 2588970426900900_68440207335523, 5936514974674025_136880414671046, 40841980350_761351911, 9792959934395825_136880414671046, 100], [100, 5585964267837000_68440207335523, 9246577786852575_136880414671046, 44254407000_761351911, 7185702053378575_136880414671046, 3414136156606700_68440207335523, 3414136156606700_68440207335523, 7185702053378575_136880414671046, 44254407000_761351911, 9246577786852575_136880414671046, 5585964267837000_68440207335523, 100], [100, 5980067477171500_68440207335523, 5257621757814600_68440207335523, 9456496452702825_136880414671046, 48837352350_761351911, 8453760898683825_136880414671046, 8453760898683825_136880414671046, 48837352350_761351911, 9456496452702825_136880414671046, 5257621757814600_68440207335523, 5980067477171500_68440207335523, ...], [100, 6232663149482100_68440207335523, 5698882434309200_68440207335523, 5287073624341500_68440207335523, 10025129513623175_136880414671046, 108492743075_1522703822, 108492743075_1522703822, 10025129513623175_136880414671046, 5287073624341500_68440207335523, 5698882434309200_68440207335523, ...], [100, 6407681952895400_68440207335523, 6018171205598600_68440207335523, 5708599079893800_68440207335523, 10993360422971625_136880414671046, 119912830225_1522703822, 119912830225_1522703822, 10993360422971625_136880414671046, 5708599079893800_68440207335523, ...], [100, 6535872722948600_68440207335523, 6257521355296000_68440207335523, 12064942556298575_136880414671046, 65365434300_761351911, 11591873566035175_136880414671046, 11591873566035175_136880414671046, 65365434300_761351911, ...], [100, 6634266850050700_68440207335523, 12887140428975025_136880414671046, 69948379650_761351911, 12356983338933825_136880414671046, 6122253339814900_68440207335523, 6122253339814900_68440207335523, ...], [100, 13427207458428775_136880414671046, 73360806300_761351911, 12993891210812175_136880414671046, 6427948660645400_68440207335523, 6392331566960200_68440207335523, ...], [100, 75439738050_761351911, 13448744587591225_136880414671046, 6677341108375600_68440207335523, 6644025800748400_68440207335523, ...], [100, 100, 100, 100, ...]]) = 717.767 bridge(_g43116) = 59.9833 */ /* :-['math-lazy']. :- set_flag(prefer_rationals,off). laplace5([[0, 0, 0, 0, 0], [100, 57.1428, 47.3214, 57.1429, 100], [100, 81.2497, 75.0, 81.25, 100], [100, 92.8571, 90.1786, 92.8571, 100], [100, 100, 100, 100, 100]]) = 0.466667 laplace7([[0, 0, 0, 0, 0, 0, 0], [100, 53.1315, 37.0777, 33.0576, 37.0775, 53.1313, 100], [100, 75.4484, 62.1216, 58.0751, 62.1213, 75.4478, 100], [100, 86.5385, 77.8847, 75.0, 77.8847, 86.5385, 100], [100, 92.8215, 87.8788, 86.1558, 87.8788, 92.8215, 100], [100, 96.8687, 94.6533, 93.8656, 94.6533, 96.8687, 100], [100, 100, 100, 100, 100, 100, 100]]) = 1.45 chipfact(100, 1, 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000) = 0.0999999 fact(100, 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000) = 4.78333 solve1(_g944, _g1370) = 0.25 solve2(5.7, _g704) = 0.683332 topb([_g16278, _g13132, _g10340, _g7902, _g5818, _g4088, _g2712, _g1690, _g1022, _g702], 10) = 4.4 top5([_g854, _g838, _g822, _g806, _g790, _g1096, _g1080, _g1064, _g1048, _g1032, _g1312, _g1512, _g1944, _g1718, _g1702, _g1296, ...]) = 1.7 small_sched = 0.349998 laplace12([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [100, 50.9134, 32.11, 23.8822, 20.0483, 18.4824, 18.4824, 20.0482, 23.8821, 32.1099, 50.9135, 100], [100, 71.5438, 53.6443, 43.3705, 37.8287, 35.3988, 35.399, 37.8284, 43.3702, 53.6441, 71.544, 100], [100, 81.6182, 67.5524, 58.1264, 52.4965, 49.8853, 49.8854, 52.4965, 58.1263, 67.5524, 81.6182, 100], [100, 87.3766, 76.8208, 69.086, 64.1458, 61.7605, 61.7605, 64.1458, 69.086, 76.8208, 87.3766, ...], [100, 91.0673, 83.2682, 77.2511, 73.2403, 71.2503, 71.2503, 73.2402, 77.2511, 83.2681, ...], [100, 93.6246, 87.9333, 83.4101, 80.3138, 78.7501, 78.7501, 80.3137, 83.4101, ...], [100, 95.4976, 91.4305, 88.1423, 85.8545, 84.6863, 84.6862, 85.8545, ...], [100, 96.9352, 94.1489, 91.874, 90.2758, 89.4541, 89.4541, ...], [100, 98.0944, 96.356, 94.9288, 93.9207, 93.4003, ...], [100, 99.0866, 98.2518, 97.5646, 97.0778, ...], [100, 100, 100, 100, ...]]) = 21.8 bridge(_g21512) = 21.4667 */ /* :-['math-lazy']. :- set_flag(prefer_rationals,on). laplace5([[0, 0, 0, 0, 0], [100, 400_7, 1325_28, 400_7, 100], [100, 325_4, 75_1, 325_4, 100], [100, 650_7, 2525_28, 650_7, 100], [100, 100, 100, 100, 100]]) = 0.533333 laplace7([[0, 0, 0, 0, 0, 0, 0], [100, 5260_99, 63625_1716, 42545_1287, 63625_1716, 5260_99, 100], [100, 388405_5148, 2050_33, 149485_2574, 2050_33, 388405_5148, 100], [100, 1125_13, 2025_26, 75_1, 2025_26, 1125_13, 100], [100, 477845_5148, 2900_33, 221765_2574, 2900_33, 477845_5148, 100], [100, 9590_99, 162425_1716, 120805_1287, 162425_1716, 9590_99, 100], [100, 100, 100, 100, 100, 100, 100]]) = 2.16667 chipfact(100, 1, 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000) = 0.0999999 fact(100, 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000) = 4.83333 solve1(_g944, _g1370) = 0.266666 solve2(5.7, _g704) = 0.683333 topb([_g17726, _g14260, _g11188, _g8510, _g6226, _g4336, _g2840, _g1738, _g1030, _g702], 10) = 4.73333 top5([_g854, _g838, _g822, _g806, _g790, _g1096, _g1080, _g1064, _g1048, _g1032, _g1312, _g1512, _g1958, _g1718, _g1702, _g1296, ...]) = 1.98333 small_sched = 0.366667 laplace12([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [100, 38763048600_761351911, 4395212420897975_136880414671046, 1634489974393600_68440207335523, 1372096199788400_68440207335523, 1264924397859100_68440207335523, 1264924397859100_68440207335523, 1372096199788400_68440207335523, 1634489974393600_68440207335523, 4395212420897975_136880414671046, 38763048600_761351911, 100], [100, 9792959934395825_136880414671046, 40841980350_761351911, 5936514974674025_136880414671046, 2588970426900900_68440207335523, 2422676993788900_68440207335523, 2422676993788900_68440207335523, 2588970426900900_68440207335523, 5936514974674025_136880414671046, 40841980350_761351911, 9792959934395825_136880414671046, 100], [100, 5585964267837000_68440207335523, 9246577786852575_136880414671046, 44254407000_761351911, 7185702053378575_136880414671046, 3414136156606700_68440207335523, 3414136156606700_68440207335523, 7185702053378575_136880414671046, 44254407000_761351911, 9246577786852575_136880414671046, 5585964267837000_68440207335523, 100], [100, 5980067477171500_68440207335523, 5257621757814600_68440207335523, 9456496452702825_136880414671046, 48837352350_761351911, 8453760898683825_136880414671046, 8453760898683825_136880414671046, 48837352350_761351911, 9456496452702825_136880414671046, 5257621757814600_68440207335523, 5980067477171500_68440207335523, ...], [100, 6232663149482100_68440207335523, 5698882434309200_68440207335523, 5287073624341500_68440207335523, 10025129513623175_136880414671046, 108492743075_1522703822, 108492743075_1522703822, 10025129513623175_136880414671046, 5287073624341500_68440207335523, 5698882434309200_68440207335523, ...], [100, 6407681952895400_68440207335523, 6018171205598600_68440207335523, 5708599079893800_68440207335523, 10993360422971625_136880414671046, 119912830225_1522703822, 119912830225_1522703822, 10993360422971625_136880414671046, 5708599079893800_68440207335523, ...], [100, 6535872722948600_68440207335523, 6257521355296000_68440207335523, 12064942556298575_136880414671046, 65365434300_761351911, 11591873566035175_136880414671046, 11591873566035175_136880414671046, 65365434300_761351911, ...], [100, 6634266850050700_68440207335523, 12887140428975025_136880414671046, 69948379650_761351911, 12356983338933825_136880414671046, 6122253339814900_68440207335523, 6122253339814900_68440207335523, ...], [100, 13427207458428775_136880414671046, 73360806300_761351911, 12993891210812175_136880414671046, 6427948660645400_68440207335523, 6392331566960200_68440207335523, ...], [100, 75439738050_761351911, 13448744587591225_136880414671046, 6677341108375600_68440207335523, 6644025800748400_68440207335523, ...], [100, 100, 100, 100, ...]]) = 61.05 bridge(_g25632) = 24.8167 */ /* :-['math-gauss']. :- set_flag(prefer_rationals,off). laplace5([[0, 0, 0, 0, 0], [100, _g1269, _g1301, _g2123, 100], [100, _g1333, _g2165, _g3283, 100], [100, _g4839, _g6857, _g9467, 100], [100, 100, 100, 100, 100]]) = 1.11667 laplace7([[0, 0, 0, 0, 0, 0, 0], [100, _g910, _g926, _g958, _g990, _g1022, 100], [100, _g942, _g974, _g1006, _g1038, _g1054, 100], [100, _g1084, _g1114, _g1144, _g1174, _g1204, 100], [100, _g1234, _g1264, _g1294, _g1324, _g1354, 100], [100, _g1384, _g1414, _g1444, _g1474, _g1534, 100], [100, 100, 100, 100, 100, 100, 100]]) = 20.0333 calling an undefined procedure _g1770 =:= _g776 * _g1030 in module eclipse .... topb([_g2601, _g2241, _g1917, _g1629, _g1377, _g1161, _g981, _g837, _g729, _g657], 10) = 0.0166664 .... % no computation done with inequalities... */ /* %:- nodbgcomp. % get spurious interupt error if nodbgcomp compiled !!! :-['math-fourier']. :- set_flag(prefer_rationals,off). laplace5([[0, 0, 0, 0, 0], [100, 57.1429, 47.3214, 57.1429, 100], [100, 81.2499, 75.0, 81.25, 100], [100, 92.8571, 90.1786, 92.8571, 100], [100, 100, 100, 100, 100]]) = 0.65 laplace7([[0, 0, 0, 0, 0, 0, 0], [100, 53.1311, 37.0772, 33.0574, 37.0775, 53.1313, 100], [100, 75.4463, 62.1207, 58.0749, 62.1212, 75.4477, 100], [100, 86.538, 77.8843, 74.9999, 77.8846, 86.5384, 100], [100, 92.8213, 87.8786, 86.1557, 87.8787, 92.8215, 100], [100, 96.8686, 94.6532, 93.8655, 94.6532, 96.8687, 100], [100, 100, 100, 100, 100, 100, 100]]) = 8.2 chipfact(100, 1, 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000) = 0.166667 fact(100, 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000) = 7.66667 solve1(_g1016, _g1446) = 0.466665 solve2(5.7, _g754) = 1.5 topb([P, P, P, _g3934, P, _g6800, _g3274, _g1968, _g5166, P], 10) = 4.21667 top5 seems to loop or take very long small_sched = 3.05 laplace12 seems to loop or take very long bridge seems to loop or take very long */ %============================================================================ % ************************************* % CLP(R) Version 1.1 - Example Programs % ************************************* % % Algebraic combinations of options transactions % heaviside function h(X, Y, Z) :- {Y < X, Z =:= 0}. h(X, Y, Z) :- {Y >= X, Z =:= 1}. % ramp function r(X, Y, Z) :- {Y < X , Z =:= 0}. r(X, Y, Z) :- {Y >= X, Z =:= Y - X}. % option valuation value(Type,Buy_or_Sell,S,C,P,I,X,B,Value) :- check_param(S,C,P,I,X,B), get_sign(Buy_or_Sell,Sign), lookup_option(Type,S,C,P,I,X,B, B1,B2,H1,H2,R1,R2), h(B1,S,T1),h(B2,S,T2),r(B1,S,T3),r(B2,S,T4), {Value =:= Sign*(H1*T1 + H2*T2 + R1*T3 + R2*T4)}. % safety check check_param(S,C,P,I,X,B) :- { S >= 0, C >= 0, P >= 0, I >= 0, X >= 0, B >= 0 }. % Buy or sell are just opposite get_sign(buy,S) :- {S =:= -1}. get_sign(sell,S) :- {S =:= 1}. % lookup option vector lookup_option(Type,S,C,P,I,X,B,B1,B2,H1,H2,R1,R2) :- table(Type,S,C,P,I,X,B,B1,B2,H1,H2,R1,R2). % Table of values for B1,B2,H1,H2,R1,R2 % generic format - lookup_table(Type,Pos_neg,S,C,P,I,X,B,B1,B2,H1,H2,R1,R2). % where K to R21 are obtained from the table % M is a multiplier which is -1 or 1 depending on whether one % is buying or selling the option table( stock, S, C, P, I, X, B, 0, 0, S*(1+I), 0, -1, 0). table( call, S, C, P, I, X, B, 0, X, C*(1+I), 0, 0, -1). table( put, S, C, P, I, X, B, 0, X, P*(1+I)-X, 0, 1, -1). table( bond, S, C, P, I, X, B, 0, 0, B*(1+I), 0, 0, 0). solve1(Wealth, Stockprice) :- { Wealth =:= Wealth1 + Wealth2, X =:= 99, P =:= 10, C =:= 10, I =:= 0 }, value(put, buy, Stockprice, _, P, I, X, _, Wealth1), value(call, buy, Stockprice, C, _, I, X, _, Wealth2). % dump([Stockprice, Wealth]). solve2(Wealth, Stockprice) :- {I =:= 0.1, P1 =:= 10, X1 =:= 20}, value(put, sell, Stockprice, _, P1, I, X1, _, Wealth1), {P2 =:= 18, X2 =:= 40}, value(put, buy, Stockprice, _, P2, I, X2, _, Wealth2), {C3 =:= 15, X3 =:= 60}, value(call, buy, Stockprice, C3, _, I, X3, _, Wealth3), {C4 =:= 10, X4 =:= 80}, value(call, sell, Stockprice, C4, _, I, X4, _, Wealth4), {Wealth =:= Wealth1 + Wealth2 + Wealth3 + Wealth4}. % dump([Stockprice, Wealth]). /* go1 :- solve1(Wealth, Stockprice), fail. go1. go2 :- solve2(Wealth, Stockprice), fail. go2. %?- printf("\n>>> Sample goals: go1/0, go2/0\n", []). */ %============================================================================== %From lim@scorpio Thu Jun 17 14:09:36 1993 % thom fruehwirth 930617 % checked with eager.chr: rpoblem in last big equation (top5/n) % fourier very slow, maybe loops with beale/1, opt1/1 for sure (opt2/1 works) rmin(E):- {M=:=E}. % thom: no optimisation rmax(E):- {(-M)=:=E}. % thom: no optimisation %! nb beale([X1,X2,X3,X4,X5,X6,X7]) :- { X1 + 1/4 * X4 - 8 * X5 - X6 + 9 * X7 =:= 0, X2 + 1/2 * X4 - 12 * X5 - 1/2 * X6 + 3 * X7 =:= 0, X3 + X6 =:= 1, X1 >= 0, X2 >= 0, X3 >= 0, X4 >= 0, X5 >= 0, X6 >= 0, X7 >= 0 }, rmin( - 3/4 * X4 + 20 * X5 - 1/2 * X6 + 6* X7). %! topb(L,N) :- topb1([],L,0,N). topb1(Li,Li,I,I) :- !. topb1(Li,Lo,I,N) :- insertb(P,Li,Lt), J is I+1, putcons(Lt,1,J), topb1(Lt,Lo,J,N). insertb(P,[],[P]). insertb(P,[A|B],[P,A|B]). insertb(P,[A|B],[A|C]) :- insertb(P,B,C). putcons(_,M,N) :- M > N, !. putcons([P|R],M,N) :- M0 is M - 1, % bwriteln(P > M0/N), % bwriteln(P < M/N), { P > M0/N, P < M/N }, M1 is M + 1, putcons(R,M1,N). bwriteln(X) :- writeln(X). bwriteln(X) :- writeln(delete(X)). %! fib(X,Y) :- {X =:= 0, Y =:= 1}. fib(X,Y) :- {X =:= 1, Y =:= 1}. fib(N,Z) :- {N > 1, Z =:= X1 + X2}, fib(N-1,X1), fib(N-2,X2). laplace([_, _]) :- !. laplace([H1, H2, H3|T]):- laplace_vec(H1, H2, H3), laplace([H2, H3|T]). laplace_vec([_, _], [_, _], [_, _]) :- !. laplace_vec([_TL, T, TR|T1], [ML, M, MR|T2], [_BL, B, BR|T3]):- { B + T + ML + MR - 4 * M =:= 0 }, laplace_vec([T, TR|T1], [M, MR|T2], [B, BR|T3]). %! laplace5(M) :- M = [ [0,0,0,0,0], [100,R,S,T,100], [100,U,V,W,100], [100,X,Y,Z,100], [100,100,100,100,100] ], laplace(M). % [chipc]: laplace7(X). % % X = [[0, 0, 0, 0, 0, 0, 0], [100, (5260/99), (63625/1716), (42545/1287), (63625/1716), (5260/99), 100], [100, (388405/5148), (2050/33), (149485/2574), (2050/33), (388405/5148), 100], [100, (1125/13), (2025/26), (75), (2025/26), (1125/13), 100], [100, (477845/5148), (2900/33), (221765/2574), (2900/33), (477845/5148), 100], [100, (9590/99), (162425/1716), (120805/1287), (162425/1716), (9590/99), 100], [100, 100, 100, 100, 100, 100, 100]] %! laplace7(M) :- M = [ [0,0,0,0,0,0,0], [100,R11,R12,R13,R14,R15,100], [100,R21,R22,R23,R24,R25,100], [100,R31,R32,R33,R34,R35,100], [100,R41,R42,R43,R44,R45,100], [100,R51,R52,R53,R54,R55,100], [100,100,100,100,100,100,100] ], laplace(M). laplace12(M) :- M = [ [0, 0,0,0,0,0,0,0,0,0,0,0], [100,_,_,_,_,_,_,_,_,_,_,100], [100,_,_,_,_,_,_,_,_,_,_,100], [100,_,_,_,_,_,_,_,_,_,_,100], [100,_,_,_,_,_,_,_,_,_,_,100], [100,_,_,_,_,_,_,_,_,_,_,100], [100,_,_,_,_,_,_,_,_,_,_,100], [100,_,_,_,_,_,_,_,_,_,_,100], [100,_,_,_,_,_,_,_,_,_,_,100], [100,_,_,_,_,_,_,_,_,_,_,100], [100,_,_,_,_,_,_,_,_,_,_,100], [100,100,100,100,100,100,100,100,100,100,100,100] ], laplace(M). % [chipc]: chipOpt(X,Y,Z). % % X = (8/5) % Y = (6/5) % Z = (14/5) %! chipOpt(X1,X2,X3) :- {X1 + 2 * X2 =< 4, 3 * X1 + X2 =< 6, X3 =:= X1 + X2}, rmax(X3). %! chipfact(n,1,N) chipfact(X,Y,M) :- {X =:= 0}, !, {Y =:= M}. chipfact(X,Y,M) :- {X1 =:= X - 1, M1 =:= X * Y}, chipfact(X1,M1,M). %! order of magnitude slower than chipfact fact(X,Y) :- {X =:= 0, Y =:= 1}. fact(X,Y) :- {X =:= 1, Y =:= 1}. fact(N,R) :- {1 < N, N =< R, M =:= N-1}, fact(M,T), {R =:= N * T}. mg(P,T,I,B,MP):- {T > 0, T =< 1, B + MP =:= P * (1 + I/100) }. mg(P,T,I,B,MP):- {T > 1, I1 =:= I / 100, T1 =:= T -1, P2 =:= P * (1 + I1) - MP }, mg(P2, T1, I, B, MP). mg1(X,Y,Z) :- { 2 =:= T, 1 =:= I, T > 1, I1 =:= I / 100, T1 =:= T -1, P2 =:= P * (1 + I1) - MP, T1 > 0, T1 =< 1, B + MP =:= P2 * (1 + I/100) }. % [chipc]: top0(X,Y,Z). % % X = _r94 % Y = (-9462212541120451001/1000000000000000000) * _r94 + (10462212541120451001/1000000000000000000) * _r90 % Z = (101/100) * _r94 + (-1) * _r90 More? (;) % % --------------------------------------------------------- % [chipc]: top1(X,Y,Z). % % X = _r94 % Y = (-101/100) * _r94 + (201/100) * _r90 % Z = (101/100) * _r94 + (-1) * _r90 More? (;) % --------------------------------------------------------- % [chipc]: top(X,Y,Z). % % X = _r94 % Y = (-2101900399479668244827490915525641902001/100000000000000000000000000000000000000) * _r94 + (2201900399479668244827490915525641902001/100000000000000000000000000000000000000) * _r90 % Z = (101/100) * _r94 + (-1) * _r90 More? (;) % %! top0(P, B, MP) :- mg(P,10,1,B,MP). top1(P, B, MP) :- mg(P,2,1,B,MP). top(P, B, MP) :- mg(P,20,1,B,MP). % Detection of Implied Equalities %! top4([A,B,C,D]) :- { A==D }. % B = A, % C = A, % D = A /* L = [A_m108, B_m128, C_m336, D_m660] Constraints: eq0([B_m128 * 1, D_m660 * -1], 0) eq0([C_m336 * 1, D_m660 * -1], 0) eq0([A_m108 * -1, D_m660 * 1], 0) */ % % X = [(1/3), (0), (13/3)] % %! nb opt1([X1,X2,X3]) :- { X1 + X2 + 2 * X3 =< 9, X1 + X2 - X3 =< 2, -X1 + X2 + X3 =< 4, X1 >= 0, X2 >= 0, X3 >= 0 }, rmin(X1 + X2 - 4 * X3). % % X = [(0), (0)] % %! nb opt2([X1,X2]) :- { X1 + 2 * X2 =< 4, X2 =< 1, X1 >= 0, X2 >= 0 }, rmin(X1 + X2). % resistor example nb available_res(10). available_res(14). available_res(27). available_res(60). available_res(100). available_cell(10). available_cell(20). ohm(V,I,R) :- % bwriteln(V =:= I * R), {V =:= I * R}. sum([],Z) :- % bwriteln(Z =:= 0), {Z =:= 0}. sum([H|T],N) :- % bwriteln(N =:= H + M), {N =:= H + M}, sum(T,M). kirchoff(L) :- sum(L,0). % X = [(200/37), (540/37)] More? (;) % % X = [(140/37), (600/37)] More? (;) % % X = [(540/127), (2000/127)] More? (;) %! ohm_example([V1,V2]) :- {29/2 < V2, V2 < 65/4}, available_res(R1), available_res(R2), available_cell(V), ohm(V1,I1,R1), ohm(V2,I2,R2), kirchoff([I1,-I2]), kirchoff([-V,V1,V2]). % X = [10, 27, 20] More? (;) % % X = [14, 60, 20] More? (;) % % X = [27, 100, 20] More? (;) %! ohm_example1([R1,R2,V]) :- {29/2 < V2, V2 < 65/4}, available_res(R1), available_res(R2), available_cell(V), ohm(V1,I1,R1), ohm(V2,I2,R2), kirchoff([I1,-I2]), kirchoff([-V,V1,V2]). % % X = [(14), (60), (20)] % %! ohm1([A,B,C]) :- { A =:= 14, B =:= 60, C =:= 20, 29/2 < V2, V2 < 65/4, V1/A - V2/B =:= 0, V1 + V2 =:= C }. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %! example( [X0,X1,X2,X3,X4]) :- { 87*X0 +52*X1 +27*X2 -54*X3 +56*X4 =< -93, 33*X0 -10*X1 +61*X2 -28*X3 -29*X4 =< 63, -68*X0 +8*X1 +35*X2 +68*X3 +35*X4 =< -85, 90*X0 +60*X1 -76*X2 -53*X3 +24*X4 =< -68, -95*X0 -10*X1 +64*X2 +76*X3 -24*X4 =< 33, 43*X0 -22*X1 +67*X2 -68*X3 -92*X4 =< -97, 39*X0 +7*X1 +62*X2 +54*X3 -26*X4 =< -27, 48*X0 -13*X1 +7*X2 -61*X3 -59*X4 =< -2, 49*X0 -23*X1 -31*X2 -76*X3 +27*X4 =< 3, -50*X0 +58*X1 -1*X2 +57*X3 +20*X4 =< 6, -13*X0 -63*X1 +81*X2 -3*X3 +70*X4 =< 64, 20*X0 +67*X1 -23*X2 -41*X3 -66*X4 =< 52, -81*X0 -44*X1 +19*X2 -22*X3 -73*X4 =< -17, -43*X0 -9*X1 +14*X2 +27*X3 +40*X4 =< 39, 16*X0 +83*X1 +89*X2 +25*X3 +55*X4 =< 36, +2*X0 +40*X1 +65*X2 +59*X3 -32*X4 =< 13, -65*X0 -11*X1 +10*X2 -13*X3 +91*X4 =< 49, 93*X0 -73*X1 +91*X2 -1*X3 +23*X4 =< -87 }. top2 :- example( [X0,X1,X2,X3,X4]). % X3<=-5/4-35/68*X2-2/17*X1+X0-35/68*X4, % X3<=68/53-76/53*X2+60/53*X1+90/53*X0+24/53*X4, % X3<=-1/2-31/27*X2-7/54*X1-13/18*X0+13/27*X4, % X3<=17/22+19/22*X2-2*X1-81/22*X0-73/22*X4, % X3<=33/76-16/19*X2+5/38*X1+5/4*X0+6/19*X4, % X3>=87+91*X2-73*X1+93*X0+23*X4, % X3>=-3/76-31/76*X2-23/76*X1+49/76*X0+27/76*X4, % X3<=13/9-14/27*X2+1/3*X1+43/27*X0-40/27*X4, % X3<=2/19+1/57*X2-58/57*X1+50/57*X0-20/57*X4 top3 :- example( [X0,_,_,_,X4]). % X0>=477804/40409+6973307/969816*X4, % X0>=7357764/4517605-5006476/13552815*X4, % X0>=58416/36205-4659804/12418315*X4, % X0>=3139326/1972045-745308/1972045*X4, % X0>=67158/43105-16394/43105*X4, % X0>=1327097/6210451-2619277/6210451*X4, % X0<=-688135/1217232-2174029/811488*X4 % [chipc]: top5(X). % % X = [(0), (0), (0), (1000), (0), (0), (50), (200/9) + (-1/9) * _rp522 , (1000/3), (5350/9) + (1/9) * _rp522 , (4000), (0), (7450/3), (0), (0), (5000), (250), (600), (1000/9) + (-5/9) * _rp522 , (0)] % yes. top5([X11,X12,X13,X14,X15,X21,X22,X23,X24,X25,Y21,Y22,Y23,Y24,Y25,Z21,Z22,Z23,Z24,Z25]) :- { X11 + X12 + X13 + X14 + X15 =:= 1000, X21 + X22 + X23 + X24 + X25 =:= 1000, 4*X11 + 5*X21 - Y21 - Z21 =< 0, -4*X12 - 5*X22 + Y22 + Z22 =:= 0, -4*X13 - 5*X23 + Y24 - Y25 + Z24 - Z25 =:= 0, -4*X14 - 5*X24 + Y21 - Y22 - Y23 + Y25 + Z21 - Z22 - Z23 + Z25 =:= 0, -4*X15 - 5*X25 + Y23 - Y24 + Z23 - Z24 =:= 0, 7*X11 + 9*X21 >= 0, 7*X12 + 9*X22 =< 3000, 7*X13 + 9*X23 =< 200, 7*X14 + 9*X24 =< 10000, 7*X15 + 9*X25 =< 7000, Z21 =< 5000, Z22 =< 250, Z23 =< 600, Z24 =< 7000, Z25 =< 4000, X11 >= 0, X12 >= 0, X13 >= 0, X14 >= 0, X15 >= 0, X21 >= 0, X22 >= 0, X23 >= 0, X24 >= 0, X25 >= 0, Y21 >= 0, Y22 >= 0, Y23 >= 0, Y24 >= 0, Y25 >= 0, Z21 >= 0, Z22 >= 0, Z23 >= 0, Z24 >= 0, Z25 >= 0, M =:= 99999, - Min =:= 99999 * X11 + 99999 * X21 + 4 * Y21 + 7 * Y22 + 3 * Y23 + 8*Y24 + 5*Y25 }, rmax(Min). %! top5a(List) :- List = [X11,X12,X13,X14,X15,X21,X22,X23,X24,X25,Y21,Y22,Y23,Y24,Y25,Z21,Z22,Z23,Z24,Z25], { X11 + X12 + X13 + X14 + X15 =:= 1000, X21 + X22 + X23 + X24 + X25 =:= 1000, 4*X11 + 5*X21 - Y21 - Z21 =< 0, -4*X12 - 5*X22 + Y22 + Z22 =:= 0, -4*X13 - 5*X23 + Y24 - Y25 + Z24 - Z25 =:= 0, -4*X14 - 5*X24 + Y21 - Y22 - Y23 + Y25 + Z21 - Z22 - Z23 + Z25 =:= 0, -4*X15 - 5*X25 + Y23 - Y24 + Z23 - Z24 =:= 0, 7*X11 + 9*X21 >= 0, 7*X12 + 9*X22 =< 3000, 7*X13 + 9*X23 =< 200, 7*X14 + 9*X24 =< 10000, 7*X15 + 9*X25 =< 7000, Z21 =< 5000, Z22 =< 250, Z23 =< 600, Z24 =< 7000, Z25 =< 4000, X11 >= 0, X12 >= 0, X13 >= 0, X14 >= 0, X15 >= 0, X21 >= 0, X22 >= 0, X23 >= 0, X24 >= 0, X25 >= 0, Y21 >= 0, Y22 >= 0, Y23 >= 0, Y24 >= 0, Y25 >= 0, Z21 >= 0, Z22 >= 0, Z23 >= 0, Z24 >= 0, Z25 >= 0, M =:= 99999, Min = 23450, - Min =:= 99999 * X11 + 99999 * X21 + 4 * Y21 + 7 * Y22 + 3 * Y23 + 8*Y24 + 5*Y25 }. % M = 99999, % Min = 23450, % X11 = 0, % X12 = 0, % X13 = 0, % X14 = 1000, % X15 = 0, % X21 = 0, % X22 = 50, % X23 = 1850/3-X25, % X24 = 1000/3, % Y21 = 4000, % Y22 = 0, % Y23 = 7450/3, % Y24 = 0, % Y25 = 0, % Z21 = 5000, % Z22 = 250, % Z23 = 600, % Z24 = 9250/3-5*X25, % Z25 = 0, % X25>=5350/9, % X25<=1850/3 %============================================================================= %From lim@scorpio Thu Jun 17 14:09:28 1993 % thom fruehwirth 930617 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Rational Constraint Solver Source Module % % sccsid("@(#)data 1.00 92/06/29"). % sccscr("@(#) Copyright 1992 ECRC GmbH "). % % IDENTIFICATION: examples % % AUTHOR: Pierre Lim % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % X + Y =:= 4 % X - Y =:= 0 % Answer: % % X =:= 2, Y =:= 2 % test40:- {X + Y =:= 4, X - Y =:= 0}. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %-8x + 5y + -1z =:= 18, %x + -11z + -5y =:= 6, %-1x + 5y + 5z =:= 0. % Answer: % % x =:= -12/7, y =:= 23/35, z =:= -1 test8518:- {-8 * X + 5 * Y - Z =:= 18, X - 11 * Z - 5 * Y =:= 6, -X + 5 * Y + 5 * Z =:= 0}. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %-11z + -5y + x =:= -6, %5z + -1x + 5y =:= 0. % % Answer: % % z =:= 1, x =:= 5 * Y + 5, y =:= (unconstrained) % % Notes: % CLP(R) compiler % % Y =:= 0.2*X - 1 % Z =:= 1 % % CHIP compiler % Z =:= (1) % X =:= (5) + (5) * _r80 % Y =:= _r80 % % My rational constraint solver produces % Z =:= 1 % X =:= 5 * _m277 + 5 % Y =:= 1 * _m277 % % test1156:- {-11*Z - 5*Y + X =:= -6, 5*Z - X + 5*Y =:= 0}. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % X + -5*Y + -11 * Z =:= -6, % -X + 5* Z + 5* Y =:= 0, % X + 2* Z + -3* Y =:= 7, % 8*X + Z + -5*Y + P =:= 18. % % Answer: z =:= 1.0, x =:= 5.0, y =:= 0.0, p =:= -23 % test5116:- {X - 5*Y - 11 * Z =:= -6, -X + 5* Z + 5* Y =:= 0, X + 2* Z - 3* Y =:= 7, 8*X + Z - 5*Y + P =:= 18}. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %-8x + -1z + 5y =:= -18, %x + -5y + -11z =:= -6, %-x + 5z + y =:= 0, %x + 2z + -3y =:= 7. % % Answer inconsistent % test815:- {-8*X + -1*Z + 5*Y =:= -18, X + -5*Y + -11*Z =:= -6, -X + 5*Z + Y =:= 0, X + 2*Z + -3*Y =:= 7}. % % 0 =< X, X =< 10. % test01011:- {0 =< X, X =< 10, X =:= 11}. % inconsistent test0101:- {0 =< X, X =< 10, X =:= 1}. % X =:= 1 test1212:- {X =:= (1/2)/(1/2)}. % X =:= 1 % % Inequality example 1 /* X1 + X2 >= 2, -X1 + X2 >= 1, X2 =< 3, X1 >= 0, X2 >= 0. */ % % % CHIP compiler % % X1 =:= (1/2) + (-1/2) * _rp105 + (1/2) * _rp78 % X2 =:= (3/2) + (1/2) * _rp105 + (1/2) * _rp78 % % test112:- {X1 + X2 >= 2, -X1 + X2 >= 1, X2 =< 3, X1 >= 0, X2 >= 0}. % print_store. % % % Answer: X =:= 5 % test55:- {X >= 5, X =< 5}. % % x1 + x2 =< 4, % 2x1 + 3x2 >= 18, % x1 >= 0, % x2 >= 0. % % Answer: inconsistent test114:- {X1 + X2 =< 4, 2 * X1 + 3 * X2 >= 18, X1 >= 0, X2 >= 0}. % % /* X1 =< 50, X2 =< 200, X1 + 0.2 * X2 =< 72, 150 * X1 + 25 * X2 =< 10000, Z =:= 250 * X1 + 45 * X2. */ % % % Answer: CLP(R) compiler % % X1 =:= 0.004*Z - 0.18*X2 % Z =< 3.33333*X2 + 16666.7 % Z + 5*X2 =< 18000 % X2 =< 200 % Z =< 45*X2 + 12500 % % Answer: CHIP compiler % % Z =:= (17000) + (-9/5) * _rp161 + (20) * _rp101 % X1 =:= (50) + (-1) * _rp101 % X2 =:= (100) + (-1/25) * _rp161 + (6) * _rp101 % % First 3 constraints % X1 =:= (50) + (-1) * _rp67 % X2 =:= (110) + (-5) * _rp105 + (5) * _rp67 % test50200:- {X1 =< 50, X2 =< 200, X1 + 2/10 * X2 =< 72, 150 * X1 + 25 * X2 =< 10000, Z =:= 250 * X1 + 45 * X2}. %,output. /* Eclipse input: X1 =< 50, X2 =< 200, X1 + 2/10 * X2 =< 72, 150 * X1 + 25 * X2 =< 10000, Z =:= 250 * X1 + 45 * X2. */ % % % X4 =< 1 + 3 * X3, % X4 =< 4/13+18/13*X3, % X4 >= -1/8+9/8*X3, % X4 >= -2+6*X3, % X4 >= -1/11+9/11*X3 /* X4 - 3 * X3 =< 1, X4 - 1.38462 * X3 =< 0.307692, X4 - 1.125 * X3 >= -0.125, X4 - 6 * X3 >= -2, X4 - 0.818182 * X3 >= -0.0909091. X4 - 3 * X3 =< 1, X4 - 18/13 * X3 =< 4/13, X4 - 9/8 * X3 >= -1/8, X4 - 6 * X3 >= -2, X4 - 9/11 * X3 >= -1/11. */ % % CHIP Compiler % X4 =:= (-2/7) + (-13/7) * _rp145 + (6/7) * _rp118 % X3 =:= (-3/7) + (-13/21) * _rp145 + (13/21) * _rp118 % % CLP(R) Compiler % % 0.818182*X3 =< X4 + 0.0909091 % 6*X3 =< X4 + 2 % 1.125*X3 =< X4 + 0.125 % X4 =< 1.38462*X3 + 0.307692 % X4 =< 3*X3 + 1 % % test13:- {X4 =< 1+3*X3, X4 =< 4/13+18/13*X3, X4 >= -1/8+9/8*X3, X4 >= -2+6*X3, X4 >= -1/11+9/11*X3}. % % % % CHIP Compiler % % X3 =:= (1/9) * _rp256 + (5/6) * _rp229 + (-4/9) * _rp202 + (-1/2) * _rp159 % X4 =:= (2/3) * _rp229 + (-1/3) * _rp202 % X1 =:= (1/9) * _rp256 + (1/3) * _rp229 + (-1/9) * _rp202 + (-1/3) * _rp159 % X2 =:= (1) + (-1) * _rp256 + (-13/6) * _rp229 + (1/3) * _rp202 + % (3/2) * _rp159 % % test12131:- { 12*X1 + X2 - 3*X3 + X4 =< 1, -36*X1 - 2*X2 + 18*X3 - 11*X4 =< -2, -18*X1 - X2 + 9*X3 - 7*X4 =< -1, 45*X1 + 4*X2 - 18*X3 + 13*X4 =< 4, X1 >= 0, X2 >= 0}. % % % Small Scheduling Problem % CHIP Compiler % % SA =:= (-7) + (1) * _r218 + (-1) * _rp211 % SB =:= _r218 % SD =:= (1) * _r218 + (1) * _rp238 + (-1) * _rp211 % SC =:= (3) + (1) * _r218 + (1) * _rp264 % SF =:= (8) + (1) * _r218 + (1) * _rp407 + (1) * _rp238 + (-1) * _rp211 % SH =:= (9) + (1) * _r218 + (1) * _rp471 + (1) * _rp407 + (1) * _rp238 + % (-1) * _rp211 % SG =:= (8) + (1) * _r218 + (1) * _rp374 + (1) * _rp238 + (-1) * _rp211 % SE =:= (8) + (1) * _r218 + (1) * _rp314 + (1) * _rp238 + (-1) * _rp211 % SJ =:= (12) + (1) * _r218 + (1) * _rp506 + (1) * _rp471 + (1) * _rp407 + % (1) * _rp238 + (-1) * _rp211 % Send =:= (15) + (1) * _r218 + (1) * _rp674 + (1) * _rp607 + (1) * _rp506 + % (1) * _rp471 + (1) * _rp407 + (1) * _rp238 + (-1) * _rp211 % SK =:= (14) + (1) * _r218 + (1) * _rp607 + (1) * _rp506 + (1) * _rp471 + % (1) * _rp407 + (1) * _rp238 + (-1) * _rp211 % % small_sched:- { SB >= SA + 7, SD >= SA + 7, SC >= SB + 3, SE >= SC + 1, SE >= SD + 8, SG >= SC + 1, SG >= SD + 8, SF >= SD + 8, SF >= SC + 1, SH >= SF + 1, SJ >= SH + 3, SK >= SG + 1, SK >= SE + 2, SK >= SJ + 2, Send >= SK + 1}. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Example from paper by De Backer and Beringer % ``A CLP language handling disjunctions of linear constraints'' % % ConstrainedMin[ x, {3x -2y =< 4, 3x+2y =< 28, 5 =< y},{x,y}] % {0, {x -> 0, y -> 5}} % ConstrainedMax[ x, {3x -2y =< 4, 3x+2y =< 28, 5 =< y},{x,y}] % 16 16 % {--, {x -> --, y -> 6}} % 3 3 % ConstrainedMin[y, {3x -2y =< 4, 3x+2y =< 28, 5 =< y},{x,y}] % 14 % {5, {x -> --, y -> 5}} % 3 % ConstrainedMax[ y, {3x -2y =< 4, 3x+2y =< 28, 5 =< y},{x,y}] % {14, {x -> 0, y -> 14}} test324:- {3*X - 2*Y =< -4, 3*X + 2*Y =< 28, 5 =< Y}. %, rmax(X). %3*X - 2*Y >= -4, 3*X + 2*Y =< 28, 5 =< Y.%, rmin(X). %3*X - 2*Y =< -4, 3*X + 2*Y =< 28, 5 =< Y.%, rmax(Y). %3*X - 2*Y =< -4, 3*X + 2*Y =< 28, 5 =< Y.%, rmin(Y). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% test111213:- { X11 + X12 + X13 + X14 + X15 =:= 1000, X21 + X22 + X23 + X24 + X25 =:= 1000, 4*X11 + 5*X21 - Y21 - Z21 =< 0, -4*X12 - 5*X22 + Y22 + Z22 =:= 0, -4*X13 - 5*X23 + Y24 - Y25 + Z24 - Z25 =:= 0, Y21 + Z21 =:= 0}. test0000:- { X1>=0,%positive(X1), X2>=0,%positive(X2), Y1>=0,%positive(Y1), Y2>=0,%positive(Y2), Y1 =:= X1 - X2, Y2 =:= X2 - X1}. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% test1231:- { U1-Z+W =:= 0, U2 +Z-V =:= 0, U3 -W + V =:= 0, U1 >=0, U2 >= 0, U3 >= 0, Z >= 0, V >= 0, W >= 0}. test1232:- { U1-Z+2*W =:= 0, U2 +2*Z-V =:= 0, U3-W+2*V =:= 0, U1 >= 0, U2 >= 0, U3 >= 0, Z >= 0, V >= 0, W >= 0}. test1233:- {X + 2*Z >=0, -Z +Y >= 1, -Y >= 2}. %============================================================================== %From lim@scorpio Tue Mar 8 11:57:12 1994 :- setval(limit, -1). bridge(Ende) :- setup(K,Ende,Disj), min_max(p(Disj,K,Ende),Ende,100,200). min_max(G,E,L,U) :- call(G), !, rmin(E). extract_vars(Term , Vars) :- extract_vars(Term, Vars0, []), =(Vars0, Vars). extract_vars(X, [X|T], T) :- var(X), !. extract_vars(X, [X|T], T) :- rvar(X), !. extract_vars(X, [X|T], T) :- pvar(X), !. extract_vars(X, T, T) :- atomic(X), !. extract_vars([X|Xs], T, T0) :- !, extract_vars(X, T, T1), extract_vars(Xs, T1, T0). extract_vars(X, T, T0) :- X =.. Xl, extract_vars(Xl, T, T0). setup(K,Ende,Disj):- jobs(L), make_vars(L,K), el([stop,_,Ende],K), precedence(M), make_precedence(M,K), max_nf(M1), make_max_nf(M1,K), max_ef(M2), make_max_ef(M2,K), min_af(M3), make_min_af(M3,K), min_sf(M4), make_min_sf(M4,K), min_nf(M5), make_min_nf(M5,K), resources(R), make_disj(R,K,[],Disj1), reverse(Disj1,Disj). p(Disj,K,Ende):- disjunct(Disj,0). make_vars([],[]). make_vars([H|T],[[H,D,A]|R]):- duration(H,D), make_vars(T,R). make_precedence([],_). make_precedence([[A,B]|R],L):- el([A,Ad,Aa],L), el([B,Bd,Ba],L), mgreatereqc(Ba,Aa,Ad), make_precedence(R,L). mgreatereqc(X,Y,Z) :- {X >= Y + Z}. smallereqd(X,Y,Z) :- {X =< Y + Z}. make_max_nf([],_). make_max_nf([[A,B,C]|R],L):- el([A,Ad,Aa],L), el([B,Bd,Ba],L), C1 is C + Ad, smallereqd(Ba,Aa,C1), make_max_nf(R,L). make_max_ef([],_). make_max_ef([[A,B,C]|R],L):- el([A,Ad,Aa],L), el([B,Bd,Ba],L), C1 is Ad + C - Bd, smallereqd(Ba,Aa,C1), make_max_ef(R,L). make_min_af([],_). make_min_af([[A,B,C]|R],L):- el([A,Ad,Aa],L), el([B,Bd,Ba],L), mgreatereqc(Ba,Aa,C), make_min_af(R,L). make_min_sf([],_). make_min_sf([[A,B,C]|R],L):- el([A,Ad,Aa],L), el([B,Bd,Ba],L), C1 is C - Bd, smallereqd(Ba,Aa,C1), make_min_sf(R,L). make_min_nf([],_). make_min_nf([[A,B,C]|R],L):- el([A,Ad,Aa],L), el([B,Bd,Ba],L), C1 is C + Ad, mgreatereqc(Ba,Ad,C1), make_min_nf(R,L). make_disj([],R,D,D). make_disj([[H,R]|T],K,Din,Dout):- el_list(R,K,R1), make_disj1(R1,Din,D1), make_disj(T,K,D1,Dout). make_disj1([],D,D). make_disj1([H|T],Din,Dout):- make_disj2(H,T,Din,D1), make_disj1(T,D1,Dout). make_disj2(H,[],D,D). make_disj2([A,B],[[C,D]|S],Din,Dout):- make_disj2([A,B],S,[[A,B,C,D]|Din],Dout). el_list([],_,[]). el_list([H|T],L,[[A,D]|S]):- el([H,D,A],L), el_list(T,L,S). disjunct([],_). /* disjunct([[A,B,C,D]|R],N):- writeln(disjunct(N)), N1 is N + 1, (N == 7 -> stop ; true ), disj(A,B,C,D), disjunct(R,N1). */ disjunct([[A,B,C,D]|R],N):- N1 is N + 1, getval(limit, L), (N == L -> stop, disj(A,B,C,D), true ; disj(A,B,C,D), disjunct(R,N1) ). disj(Aa,Ad,Ba,Bd):- mgreatereqc(Ba,Aa,Ad). disj(Aa,Ad,Ba,Bd):- mgreatereqc(Aa,Ba,Bd). reverse(L,K):- rev(L,[],K). rev([],L,L). rev([H|T],L,K):- rev(T,[H|L],K). el(X,[X|R]). el(X,[Y|R]):- el(X,R). /* DATA */ jobs([start,a1,a2,a3,a4,a5,a6,p1,p2,ue,s1,s2,s3,s4,s5,s6, b1,b2,b3,b4,b5,b6,ab1,ab2,ab3,ab4,ab5,ab6,m1,m2,m3,m4,m5,m6, l1,t1,t2,t3,t4,t5,ua,v1,v2,k1,k2,stop]). duration(start,0). duration(a1,4). duration(a2,2). duration(a3,2). duration(a4,2). duration(a5,2). duration(a6,5). duration(p1,20). duration(p2,13). duration(ue,10). duration(s1,8). duration(s2,4). duration(s3,4). duration(s4,4). duration(s5,4). duration(s6,10). duration(b1,1). duration(b2,1). duration(b3,1). duration(b4,1). duration(b5,1). duration(b6,1). duration(ab1,1). duration(ab2,1). duration(ab3,1). duration(ab4,1). duration(ab5,1). duration(ab6,1). duration(m1,16). duration(m2,8). duration(m3,8). duration(m4,8). duration(m5,8). duration(m6,20). duration(l1,2). duration(t1,12). duration(t2,12). duration(t3,12). duration(t4,12). duration(t5,12). duration(ua,10). duration(v1,15). duration(v2,10). duration(k1,0). duration(k2,0). duration(stop,0). precedence([[start,a1],[start,a2],[start,a3],[start,a4],[start,a5], [start,a6],[start,ue],[a1,s1],[a2,s2],[a5,s5], [a6,s6],[a3,p1],[a4,p2],[p1,s3],[p2,s4], [p1,k1],[p2,k1],[s1,b1],[s2,b2], [s3,b3],[s4,b4],[s5,b5],[s6,b6],[b1,ab1], [b2,ab2],[b3,ab3],[b4,ab4],[b5,ab5],[b6,ab6], [ab1,m1],[ab2,m2],[ab3,m3],[ab4,m4],[ab5,m5], [ab6,m6],[m1,t1],[m2,t1],[m2,t2],[m3,t2], [m3,t3],[m4,t3],[m4,t4],[m5,t4],[m5,t5], [m6,t5],[m1,k2],[m2,k2],[m3,k2],[m4,k2], [m5,k2],[m6,k2],[l1,t1],[l1,t2],[l1,t3], [l1,t4],[l1,t5],[t1,v1],[t5,v2],[t2,stop], [t3,stop],[t4,stop],[v1,stop],[v2,stop],[ua,stop], [k2,stop]]). max_nf([[start,l1,30],[a1,s1,3],[a2,s2,3],[a5,s5,3], [a6,s6,3],[p1,s3,3],[p2,s4,3]]). min_sf([[ua,m1,2],[ua,m2,2],[ua,m3,2],[ua,m4,2], [ua,m5,2],[ua,m6,2]]). max_ef([[s1,b1,4],[s2,b2,4],[s3,b3,4],[s4,b4,4],[s5,b5,4],[s6,b6,4]]). min_nf([[start,l1,30]]). min_af([[ue,s1,6],[ue,s2,6],[ue,s3,6],[ue,s4,6],[ue,s5,6],[ue,s6,6]]). resources([[kran,[l1,t1,t2,t3,t4,t5]], [maurer,[m1,m2,m3,m4,m5,m6]], [schal,[s1,s2,s3,s4,s5,s6]], [bagger,[a1,a2,a3,a4,a5,a6]], [ramme,[p1,p2]], [pumpe,[b1,b2,b3,b4,b5,b6]], [walze,[v1,v2]]]). b. stop.