The MonetDB kernel is an abstract machine, programmed in the MonetDB Assemblee Language (MAL). Each relational algebra operator corresponds to a MAL instruction. Each BAT algebra operator maps to a simple MAL instruction, which has zero degrees of freedom; it does not take complex expressions as parameter. Rather, complex expressions are broken down into a sequence of BAT algebra operators that each perform a simple operation on an entire column of values (``bulk processing''). This allows the implementation of the BAT algebra to forsake an expression interpreting engine; rather all BAT algebra operations in the implementation map onto simple array operations.
For instance, the BAT algebra expression
can be implemented at the C code level like:
for (i = j = 0; i < n; i++)
if (B.tail[i] == V)
R.tail[j++] = i;
The BAT algebra operators have the advantage that tight for-loops create high data access and instruction locality. Such simple loops are amenable to compiler optimization (loop pipelining, vectorization, blocking, strength reduction), and CPU out-of-order speculative execution.