Detecting sharing of partial applications in functional programs

Abstract

A method is presented for detecting sharing of partial function applications in higher order functional programs. Such sharing occurs when there are several references to variables that are bound to a particular function application. In order to provide an interprocedural analysis, a non-standard semantics is defined for a lazy, higher-order functional language such that the meaning of a program is information about the sharing that occurred during its execution. An abstraction of this non-standard semantics is presented so that useful, although less complete, sharing information can be provided at compile-time. In the second part of this paper, we utilize sharing detection in order to provide an efficient method for ensuring full laziness during program execution. A refinement of the method used to generate Hughes' super-combinators is discussed. Super-combinators insure that no unnecessary computation is performed when sharing occurs in a program. Unfortunately, the algorithm used to generate super-combinators assumes that every function application is shared and some unnecessary overhead is incurred while executing super-combinators. The refined super-combinators, called super-duper combinators, presented in this paper incur no unnecessary overhead in the cases where no sharing occurs.