In this paper we present a new fixed point theorem applicable for a countable system of recursive equations over a wellfounded domain. Wellfoundedness is an essential feature of many computer science applications as it guarantees termination of the corresponding fixed point computation algorithms. Besides being a natural restriction, it marks a new area of application, where not even monotonicity is required. We demonstrate the power and versatility of our fixed point theorem, which under the wellfoundedness condition covers all the known `synchronous' versions of fixed point theorems, by means of applications in data flow analysis and program optimization. Keywords Fixed point, chaotic iteration, vector iteration, data flow analysis, program optimization, workset algorithm, partial dead code elimination. Contents 1 Introduction 1 2 Theory 2 2.1 The Main Theorem : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 2.2 Vector Iterations : : : : : : : : : : : : : : : : : :...

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.