Abstract

We present a new fixpoint theorem which guarantees the existence and the finite computability of the least common solution of a countable system of recursive equations over a wellfounded domain. The functions are only required to be increasing and delay-monotone, the latter being a property much weaker than monotonicity. We hold that wellfoundedness is a natural condition as it guarantees termination of every fixpoint computation algorithm. Our fixpoint theorem covers, under the wellfoundedness condition, all the known `synchronous' versions of fixpoint theorems. To demonstrate its power and versatility we contrast an application in data flow analysis, where known versions are applicable as well, to a practically relevant application in program optimization, which due to its second order effects, requires the full strength of our new theorem. In fact, the new theorem is central for establishing the optimality of the partial dead code elimination algorithm considered, which is implemented in the new release of the Sun SPARCompiler language systems.

Citations