Higher-order Binding-time Analysis

The partial evaluation process requires a binding-time analysis. Binding-time analysis seeks to determine which parts of a program's result is determined when some part of the input is known. Domain projections provide a very general way to encode a description of which parts of a data structure are static (known), and which are dynamic (not static). For first-order functional languages Launchbury [Lau91a] has developed an abstract interpretation technique for bindingtime analysis in which the basic abstract value is a projection. Unfortunately this technique does not generalise easily to higher-order languages. This paper develops such a generalisation: a projection-based abstract interpretation suitable for higher-order binding-time analysis. Launchbury [Lau91b] has shown that binding-time analysis and strictness analysis are equivalent problems at first order, and for projection-based analyses have exactly the same safety condition. We argue that the same is true at higher order, ..