### 33.5 Projection and Redundancy Elimination

Once a derivation succeeds, the Prolog system presents the
bindings for the variables in the query. In a CLP
system, the set of answer constraints is presented in analogy. A
complication in the CLP context are variables and associated
constraints that were not mentioned in the query. A motivating
example is the familiar `mortgage`

relation:

*% library('clpqr/examples/mg')*

mg(P,T,I,B,MP):-
{
T = 1,
B + MP = P * (1 + I)
}.
mg(P,T,I,B,MP):-
{
T > 1,
P1 = P * (1 + I) - MP,
T1 = T - 1
},
mg(P1, T1, I, B, MP).

A sample query yields:

clp(r) ?- `use_module(library('clpqr/examples/mg')).`
clp(r) ?- `mg(P,12,0.01,B,Mp).`
{B=1.1268250301319698*P-12.682503013196973*Mp}

Without projection of the answer constraints onto the query
variables we would observe the following interaction:

clp(r) ?- `mg(P,12,0.01,B,Mp).`
{B=12.682503013196973*_A-11.682503013196971*P},
{Mp= -(_A)+1.01*P},
{_B=2.01*_A-1.01*P},
{_C=3.0301*_A-2.0301*P},
{_D=4.060401000000001*_A-3.0604009999999997*P},
{_E=5.101005010000001*_A-4.10100501*P},
{_F=6.152015060100001*_A-5.152015060099999*P},
{_G=7.213535210701001*_A-6.213535210700999*P},
{_H=8.285670562808011*_A-7.285670562808009*P},
{_I=9.368527268436091*_A-8.36852726843609*P},
{_J=10.462212541120453*_A-9.46221254112045*P},
{_K=11.566834666531657*_A-10.566834666531655*P}

The variables `_A` ... `_K` are not part of the
query, they originate from the mortgage program
proper. Although the latter answer is equivalent to the former in terms
of linear algebra, most users would prefer the former.