Constraint programming over reals

Author(s): Christian Holzbaur, Daniel Cabeza.

Version: 1.10#6 (2004/8/7, 21:46:39 CEST)

Version of last change: 1.9#227 (2003/12/22, 16:55:52 CET)

Note: This package is currently being adapted to the new characteristics of the Ciao module system. This new version now works right now to some extent, but it under further development at the moment. Use with (lots of) caution.

Usage and interface (`clpr`)

• Library usage: `:- use_package(clpr).` or `:- module(...,...,[clpr]).`

Other information (`clpr`)

Some CLP(R) examples

(Other examples can be found in the source and library directories.)

• 'Reversible' Fibonacci (clpr):

```:- module(_, [fib/2], []).
:- use_package(clpr).

fib(X,Y):- X .=. 0, Y .=. 0.
fib(X,Y):- X .=. 1, Y .=. 1.
fib(N,F) :-
N .>. 1,
N1 .=. N - 1,
N2 .=. N - 2,
fib(N1, F1),
fib(N2, F2),
F .=. F1+F2.

```
• Dirichlet problem for Laplace's equation (clpr):

```
%
% Solve the Dirichlet problem for Laplace's equation using
% Leibman's five-point finit-differenc approximation.
% The goal ?- go1 is a normal example, while the goal ?- go2
% shows output constraints for a small region where the boundary conditions
% are not specified.
%
:- use_package(clpq).
:- use_module(library(format)).

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]).

printmat([]).
printmat([H|T]):-
printvec(H),
printmat(T).

printvec([]):- nl.
printvec([H|T]):-
printrat(H),
printvec(T).

printrat(rat(N,D)) :- !,
X is N/D,
format(" ~2f",X).
printrat(N) :-
X is N*100,
format(" ~2d",X).

go1:-
X =  [
[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]
],
laplace(X),
printmat(X).

% 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
% 100.00 51.11 32.52 24.56 21.11 20.12 21.11 24.56 32.52 51.11 100.00
% 100.00 71.91 54.41 44.63 39.74 38.26 39.74 44.63 54.41 71.91 100.00
% 100.00 82.12 68.59 59.80 54.97 53.44 54.97 59.80 68.59 82.12 100.00
% 100.00 87.97 78.03 71.00 66.90 65.56 66.90 71.00 78.03 87.97 100.00
% 100.00 91.71 84.58 79.28 76.07 75.00 76.07 79.28 84.58 91.71 100.00
% 100.00 94.30 89.29 85.47 83.10 82.30 83.10 85.47 89.29 94.30 100.00
% 100.00 96.20 92.82 90.20 88.56 88.00 88.56 90.20 92.82 96.20 100.00
% 100.00 97.67 95.59 93.96 92.93 92.58 92.93 93.96 95.59 97.67 100.00
% 100.00 98.89 97.90 97.12 96.63 96.46 96.63 97.12 97.90 98.89 100.00
% 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00

go2([B31, M32, M33, B34, B42, B43, B12, B13, B21, M22, M23, B24]) :-
laplace([
[_B11, B12, B13, _B14],
[B21, M22, M23, B24],
[B31, M32, M33, B34],
[_B41, B42, B43, _B44]
]).

%
% B34.=. -4*M22+B12+B21+4*M33-B43,
% M23.=.4*M22-M32-B12-B21,
% B31.=. -M22+4*M32-M33-B42,
% B24.=.15*M22-4*M32-4*B12-4*B21-M33-B13 ?

```

Known bugs and planned improvements (`clpr`)

• clp(Q) and clp(R) cannot be used simultaneously in the same program, or even within the same toplevel session.