Author: Christian Holzbaur, ported to SWI-Prolog
by Leslie De Koninck, K.U. Leuven
This CLP(Q,R) system is a port of the CLP(Q,R) system of Sicstus
Prolog by Christian Holzbaur: Holzbaur C.: OFAI clp(q,r) Manual, Edition
1.3.3, Austrian Research Institute for Artificial Intelligence, Vienna,
TR-95-09, 1995.250http://www.ai.univie.ac.at/cgi-bin/tr-online?number+95-09
This manual is roughly based on the manual of the above mentioned
CLP(Q,R) implementation.
The CLP(Q,R) system consists of two components: the CLP(Q) library
for handling constraints over the rational numbers and the CLP(R)
library for handling constraints over the real numbers (using floating
point numbers as representation). Both libraries offer the same
predicates (with exception of
bb_inf/4 in CLP(Q) and bb_inf/5
in CLP(R)). It is allowed to use both libraries in one program, but
using both CLP(Q) and CLP(R) constraints on the same variable will
result in an exception.
Please note that the library(clpqr) library is not
an
autoload library and therefore this library must be loaded
explicitly before using it:
:- use_module(library(clpq)).
or
:- use_module(library(clpr)).
The following predicates are provided
to work with constraints:
- {}(+Constraints)
- Adds the constraints given by Constraints to the constraint
store.
- entailed(+Constraint)
- Succeeds if Constraint is necessarily true within the current
constraint store. This means that adding the negation of the constraint
to the store results in failure.
- inf(+Expression,
-Inf)
- Computes the infimum of Expression within the current state
of the constraint store and returns that infimum in Inf. This
predicate does not change the constraint store.
- sup(+Expression,
-Sup)
- Computes the supremum of Expression within the current state
of the constraint store and returns that supremum in Sup.
This predicate does not change the constraint store.
- minimize(+Expression)
- Minimizes Expression within the current constraint store.
This is the same as computing the infimum and equating the expression to
that infimum.
- maximize(+Expression)
- Maximizes Expression within the current constraint store.
This is the same as computing the supremum and equating the expression
to that supremum.
- bb_inf(+Ints,
+Expression, -Inf, -Vertex, +Eps)
- This predicate is offered in CLP(R) only. It computes the infimum of
Expression within the current constraint store, with the
additional constraint that in that infimum, all variables in Ints
have integral values. Vertex will contain the values of Ints
in the infimum. Eps denotes how much a value may differ from
an integer to be considered an integer. E.g. when
Eps = 0.001, then X = 4.999 will be considered as an integer
(5 in this case). Eps should be between 0 and 0.5.
- bb_inf(+Ints,
+Expression, -Inf, -Vertex)
- This predicate is offered in CLP(Q) only. It behaves the same as
bb_inf/5 but does not use
an error margin.
- bb_inf(+Ints,
+Expression, -Inf)
- The same as bb_inf/5 or bb_inf/4
but without returning the values of the integers. In CLP(R), an error
margin of 0.001 is used.
- dump(+Target,
+Newvars, -CodedAnswer)
- Returns the constraints on Target in the list CodedAnswer
where all variables of Target have been replaced by NewVars.
This operation does not change the constraint store. E.g. in
dump([X,Y,Z],[x,y,z],Cons)
Cons will contain the constraints on X, Y and Z, where
these variables have been replaced by atoms x, y and z.
The arguments of the predicates
defined in the subsection above are defined in
table
10. Failing to meet the syntax rules will result in an exception.
<Constraints> ::= <Constraint> single
constraint
| <Constraint> , <Constraints> conjunction
| <Constraint> ; <Constraints> disjunction
<Constraint>
::= <
Expression>
< <
Expression> less
than
| <Expression> > <Expression> greater
than
| <Expression> =< <Expression> less
or equal
| <=(<Expression>, <Expression>) less
or equal
| <Expression> >= <Expression> greater
or equal
| <Expression> =\= <Expression> not
equal
| <Expression> =:= <Expression> equal
| <Expression> = <Expression> equal
<Expression>
::= <
Variable> Prolog
variable
| <Number> Prolog
number
| +<Expression> unary
plus
| -<Expression> unary
minus
| <Expression> + <Expression> addition
| <Expression> - <Expression> substraction
| <Expression> * <Expression> multiplication
| <Expression> / <Expression> division
| abs(<Expression>) absolute
value
| sin(<Expression>) sine
| cos(<Expression>) cosine
| tan(<Expression>) tangent
| exp(<Expression>) exponent
| pow(<Expression>) exponent
| <Expression> ^ <Expression> exponent
| min(<Expression>, <Expression>) minimum
| max(<Expression>, <Expression>) maximum
Table 10 : CLP(Q,R) constraint BNF
Instead of using the {}/1
predicate, you can also use the standard unification mechanism to store
constraints. The following code samples are equivalent:
The CLP(Q,R) system deals only
passively with non-linear constraints. They remain in a passive state
until certain conditions are satisfied. These conditions, which are
called the isolation axioms, are given in
table 11.
A = B * C B or C is ground A = 5 * C
or A = B * 4
A and (B or C) are ground 20 = 5 * C or 20 = B
* 4
A = B / C C is ground A
= B / 3
A and B are ground 4 = 12 / C
X = min(Y,Z) Y and Z are
ground X = min(4,3)
X = max(Y,Z) Y and Z are ground X =
max(4,3)
X = abs(Y) Y is ground X = abs(-7)
X = pow(Y,Z) X and Y are
ground 8 = 2 ^ Z
X = exp(Y,Z) X and Z are ground 8 =
Y ^ 3
X = Y ^ Z Y and Z
are ground X = 2 ^ 3
X = sin(Y) X is ground 1
= sin(Y)
X = cos(Y) Y is ground X =
sin(1.5707)
X = tan(Y)
Table 11 : CLP(Q,R) isolating axioms
The clpq and clpr libraries are‘orphaned’, i.e., they
currently have no maintainer.
- Top-level output
The top-level output may contain variables not present in the original
query:
?- {X+Y>=1}.
{Y=1-X+_G2160, _G2160>=0}.
?-
Nonetheless, for linear constraints this kind of answer means
unconditional satisfiability.
- Dumping constraints
The first argument of dump/3
has to be a list of free variables at call-time:
?- {X=1},dump([X],[Y],L).
ERROR: Unhandled exception: Unknown message:
instantiation_error(dump([1],[_G11],_G6),1)
?-