The solver interface for both Q and R consists of the following
predicates, which are exported from module(linear)
.
{
+Constraint}
 ? clpr:{Ar+Br=10}, Ar=Br, clpq:{Aq+Bq=10}, Aq=Bq. Aq = 5, Ar = 5.0, Bq = 5, Br = 5.0
Although clp(Q) and clp(R) are independent modules, you are asking for trouble if you (accidently) share variables between them:
 ? clpr:{A+B=10}, clpq:{A=B}. ! Type error in argument 2 of clpq:=/2 ! a rational number expected, but 5.0 found ! goal: _118=5.0
This is because both solvers eventually compute values for the variables and Reals are incompatible with Rationals.
Here is the constraint grammar:
Constraint  ::= C
 
 C , C  { conjunction }
 
C  ::= Expr =:= Expr  { equation }

 Expr = Expr  { equation }
 
 Expr < Expr  { strict inequation }
 
 Expr > Expr  { strict inequation }
 
 Expr =< Expr  { nonstrict inequation }
 
 Expr >= Expr  { nonstrict inequation }
 
 Expr =\= Expr  { disequation }
 
Expr  ::= variable  { Prolog variable }

 number  { floating point or integer }
 
 + Expr  { unary plus }
 
  Expr  { unary minus }
 
 Expr + Expr  { addition }
 
 Expr  Expr  { subtraction }
 
 Expr * Expr  { multiplication }
 
 Expr / Expr  { division }
 
 abs( Expr)  { absolute value }
 
 sin( Expr)  { trigonometric sine }
 
 cos( Expr)  { trigonometric cosine }
 
 tan( Expr)  { trigonometric tangent }
 
 pow( Expr, Expr)  { raise to the power }
 
 exp( Expr, Expr)  { raise to the power }
 
 min( Expr, Expr)  { minimum of the two arguments }
 
 max( Expr, Expr)  { maximum of the two arguments }
 
 #( Const)  { symbolic numerical constants }

Conjunctive constraints {
C,
C}
have been made part of the syntax
to control the granularity of constraint submission, which will be exploited by
future versions of this software.
Symbolic numerical constants are provided for compatibility only;
see CLPQR Monash Examples.
entailed(
+Constraint)
clp(q) ? {A =< 4}, entailed(A=\=5). {A=<4} clp(q) ? {A =< 4}, entailed(A=\=3). no
inf(
+Expr,
Inf)
inf(
+Expr,
Inf,
+Vector,
Vertex)
sup(
+Expr,
Sup)
sup(
+Expr,
Sup,
+Vector,
Vertex)
clp(q) ? { 2*X+Y =< 16, X+2*Y =< 11, X+3*Y =< 15, Z = 30*X+50*Y }, sup(Z, Sup, [X,Y], Vertex). Sup = 310, Vertex = [7,2], {Z=30*X+50*Y}, {X+1/2*Y=<8}, {X+3*Y=<15}, {X+2*Y=<11}
minimize(
+Expr)
minimize(Expr) : inf(Expr, Expr).
maximize(
+Expr)
clp(q) ? { 2*X+Y =< 16, X+2*Y =< 11, X+3*Y =< 15, Z = 30*X+50*Y }, maximize(Z). X = 7, Y = 2, Z = 310
bb_inf(
+Ints,
+Expr,
Inf)
clp(q) ? {X >= Y+Z, Y > 1, Z > 1}, bb_inf([Y,Z],X,Inf). Inf = 4, {Y>1}, {Z>1}, {XYZ>=0}
bb_inf(
+Ints,
+Expr,
Inf,
Vertex,
+Eps)
abs(round(
X)
X) <
Eps. The predicate
bb_inf/3
uses Eps = 0.001
. With clp(Q),
Eps = 0
makes sense. Vertex is a list of the
same length as Ints and contains the (integral) values for
Ints, such that the infimum is produced when assigned. Note that
this will only generate one particular solution, which is different from
the situation with minimize/1
, where the general solution is
exhibited.
bb_inf/5
works properly for nonstrict inequalities only!
Disequations (=\=
) and higher dimensional strict inequalities
(>
,<
) are beyond its scope. Strict bounds on the decision
variables are honored however:
clp(q) ? {X >= Y+Z, Y > 1, Z > 1}, bb_inf([Y,Z],X,Inf,Vertex,0). Inf = 4, Vertex = [2,2], {Y>1}, {Z>1}, {XYZ>=0}
The limitation(s) can be addressed by:
{X + Y > 0}
becomes {X
+ Y >= 1}
for integral X
and Y
;
ordering(
+Spec)
dump(
+Target,
NewVars,
CodedAnswer)
clp(q) ? {A+B =< 10, A>=4}, dump([A,B],Vs,Cs), dump([B],Bp,Cb). Cb = [_A=<6], Bp = [_A], Cs = [_B>=4,_C+_B=<10], Vs = [_C,_B], {A>=4}, {A+B=<10}
The current version of dump/3
is incomplete with respect to
nonlinear constraints. It only reports nonlinear constraints that are
connected to the target variables. The following example has no
solution. From the toplevel's report we have a chance to deduce this
fact, but dump/3
currently has no means to collect global
constraints ...
q(X) : {X>=10}, {sin(Z)>3}. clp(r) ? q(X), dump([X],V,C). C = [_A>=10.0], V = [_A], clpr:{3.0sin(_B)<0.0}, {X>=10.0}
projecting_assert/1(
:Clause)
assert/1
in order to ensure that only
the relevant and projected constraints get stored in the database.
It will transform the clause into one with plain variables
and extra body goals that set up the relevant constraint
when called.