Type-Directed Flow Analysis for Typed Intermediate Languages

Flow analysis is especially valuable for optimizing functional languages because control-flow information is not syntactically apparent in higher-order programs. Flow analyses typically operate on untyped languages. However, recent compilers for typed functional languages such as ML and Haskell use a typed intermediate language to expose data representations for optimization. This paper presents a polyvariant flow analysis framework for the predicative subset of system F, a common basis for typed intermediate languages. Analyses in this framework can take advantage of types to analyze programs more precisely. We study a specific analysis called SRT that uses types to control polyvariance. We prove that SRTrespects types: whenever it assigns abstract value \(\hat \upsilon\)to a variable and the type system assigns type σ to the same variable, then \(\left[ {\hat \upsilon } \right] \subseteq \left[ \sigma \right]\), where [ · ] denotes a set of values. SRT does not terminate 1569 1655 V 3 for some programs. We present several variants of SRT that are better suited to practical use.