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Of course, you could rename them to, e.g., "LHS" and "RHS" for "Left Hand
Side" and "Right Hand Side".  This would address the composition argument
in favor of CAR and CDR: CADR -> LRHS (left-hand-side of right-hand-side),
CDADADR -> RLRLRHS, and so on.   It's easy to provide these as macros.

Later, you can explain that the original names are CAR and CDR, and isn't
that silly, etc.
     Regards, Mark