Equality constraints are added to the store implicitly each time variables that have been mentioned in explicit constraints are bound—either to another such variable or to a number.

     clp(r) ?- {2*A+3*B=C/2}, C=10.0, A=B.
     A = 1.0,
     B = 1.0,
     C = 10.0

Is equivalent modulo rounding errors to

     clp(r) ?- {2*A+3*B=C/2, C=10, A=B}.
     A = 1.0,
     B = 0.9999999999999999,
     C = 10.0

The shortcut bypassing the use of {}/1 is allowed and makes sense because the interpretation of this equality in Prolog and clp(R) coincides. In general, equations involving interpreted functors, +/2 in this case, must be fed to the solver explicitly:

     clp(r) ?- X=3.0+1.0, X=4.0.

Moreover, variables known by clp(R) may be bound directly to floats only. Likewise, variables known by clp(Q) may be bound directly to rational numbers only; see CLPQR Fragments and Bits. Failing to do so is rewarded with an exception:

     clp(q) ?- {2*A+3*B=C/2}, C=10.0, A=B.
     ! Type error in argument 2 of = /2
     ! 'a rational number' expected, but 10.0 found
     ! goal:  _254=10.0

This is because 10.0 is not a rational constant. To make clp(Q) happy you have to say:

     clp(q) ?- {2*A+3*B=C/2}, C=rat(10,1), A=B.
     A = 1,
     B = 1,
     C = 10

If you use {}/1, you don't have to worry about such details.

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