Binding time analysis for high order untyped functional languages

When some inputs of a program are known at compile-time, certain expressions can be processed statically; this is the basis of the notion of partial evaluation. Identifying these early computations can be determined independently of the actual values of the input by a static analysis called binding time analysis. Then, to process a program, one simply follows the binding time information: evaluate compile-time expressions and defer the others to run-time. Using abstract interpretation, we present a binding time analysis for an untyped functional language which provides an effective treatment of both higher order functions and data structures. To our knowledge it is the first such analysis. It has been implemented and is used in a partial evaluator for a side-effect free dialect of Scheme. The analysis is general enough, however, to be valid for non-strict typed functional languages such as Haskell. Our approach and the system we have developed solve and go beyond the open problem of partially evaluating higher order functions described in [3] since we also provide a method to handle data structures. Our analysis improves on previous work [5, 15, 4] in that: (1) it treats both higher order functions and data structures, (2) it does not impose syntactic restrictions on the program being processed, and (3) it does not require a preliminary phase to collect the set of possible functions that may occur at each site of application.