And-Parallel Execution - Automatic Granularity Control

• In general it cannot be done (well) completely at compile-time: work done by a call often depends on the size of its input (difficult to approximate at compile time, even using abstract interpretation):

    
  q([],[]).
  q([X|RX],[X1|RX1]) :- 
          X1 is X +1,
          q(RX,RX1).

• Approach [DLH PLDI89, DLHL / LH TR94]:
  • generate at compile-time functions (to be evaluated at run-time) that efficiently approximate task size,
  • transform programs to carry out run-time granularity control.
  • Note: size computations can be done on-the-fly [ICLP 95].

• Example (with q above):

  ..., q(X,Y) & r(X), ...

  Cost is equal to (cost function ). Assuming threshold is 4 units:

  ..., length(X,LX), 
       Cost is LX*2+1,
       ( Cost > 4 -> q(X,Y) & r(Z)
                ;  q(X,y),  r(X) ), ...