A general technique for automatically optimizing programs through the use of proof plans (Extended Abstract)

The use of proof plans -formal patterns of reasoning for theorem proving -to control the {automatic) synthesis of efficient programs from standard definitional equations is described. A general framework for synthesizing efficient programs, using tools such as higher-order unification, has been developed and holds promise for encapsulating an otherwise diverse, and often ad hoc, range of transformation techniques. A prototype system has been implemented. Proof plans are used to control the (automatic) synthesis of functional programs, specified in a standard equational form, t', by using the proofs as programs principle. The goal is that the program extracted from a constructive proof of the specification is an optimization of that defined solely by £. Thus the theorem proving process is a form of program optimization allowing for the construction of an efficient, target, program from the definition of an inefficient, source, program. The general technique for controlling the syntheses of efficient programs involves using t' to specify the target program and then introducing a new sub-goal into the proof of that specification. Different optimizations are achieved by placing different characterizing restrictions on the form of this new sub-goal and hence on the subsequent proof. Meta-variables and higher-order unification are used in a technique called middle-out reasoning to circumvent eureka steps concerning, amongst other things, the identification of recursive data-types, and unknown constraint functions. Such problems typically require user intervention