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CHR/chr/examples/examples-lim1.math

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+% From lim@scorpio Thu Jun 17 14:09:28 1993
+% adapted for CHRs by thom fruehwirth 930617
+% replaced $= by =:= and then removed '$'
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% 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
+%
+
+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
+
+-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
+%
+%
+
+-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
+%
+
+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
+%
+
+-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.
+%
+
+0 =< X, X =< 10, X =:= 11.              % inconsistent
+0 =< X, X =< 10, X =:= 1.               % X =:= 1
+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 
+%
+%
+
+X1 + X2 >= 2,
+-X1 + X2 >= 1,
+X2 =< 3,
+X1 >= 0,
+X2 >= 0.
+% print_store.
+
+%
+%
+% Answer: X =:= 5
+%
+
+X >= 5,
+X =< 5.
+
+%
+% x1 + x2 =< 4,
+% 2x1 + 3x2 >= 18,
+% x1 >= 0,
+% x2 >= 0.
+%
+% Answer: inconsistent
+
+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
+%
+
+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
+% 
+%
+
+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 
+%
+%
+%example([X1,X2,X3,X4]) :-
+  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 
+%
+%
+
+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}}
+
+
+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).
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+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.
+
+X1>=0,%positive(X1),
+X2>=0,%positive(X2),
+Y1>=0,%positive(Y1),
+Y2>=0,%positive(Y2),
+Y1 =:= X1 - X2,
+Y2 =:= X2 - X1.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+U1-Z+W =:= 0,
+U2 +Z-V =:= 0,
+U3 -W + V =:= 0,
+U1 >=0,
+U2 >= 0,
+U3 >= 0,
+Z >= 0,
+V >= 0,
+W >= 0.
+
+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.
+
+X + 2*Z >=0,
+-Z +Y >= 1,
+-Y >= 2.
+
+