  Taylor introduced a variable binding scheme for logic variables in his PARMA
system, that uses cycles of bindings rather than the linear chains of bindings
used in the standard WAM representation. Both the HAL and dProlog languages
make use of the PARMA representation in their Herbrand constraint solvers.
Unfortunately, PARMA's trailing scheme is considerably more expensive in both
time and space consumption. The aim of this paper is to present several
techniques that lower the cost.
  First, we introduce a trailing analysis for HAL using the classic PARMA
trailing scheme that detects and eliminates unnecessary trailings. The
analysis, whose accuracy comes from HAL's determinism and mode declarations,
has been integrated in the HAL compiler and is shown to produce space
improvements as well as speed improvements. Second, we explain how to modify
the classic PARMA trailing scheme to halve its trailing cost. This technique is
illustrated and evaluated both in the context of dProlog and HAL. Finally, we
explain the modifications needed by the trailing analysis in order to be
combined with our modified PARMA trailing scheme. Empirical evidence shows that
the combination is more effective than any of the techniques when used in
isolation.
  To appear in Theory and Practice of Logic Programming.
