A type- and control-flow analysis for System F

Abstract

We present a monovariant flow analysis for System F (with recursion). The flow analysis yields both control-flow information, approximating the λ- and Λ-expressions that may be bound to variables, and type-flow information, approximating the type expressions that may instantiate type variables. Moreover, the two flows are mutually beneficial: the control flow determines which Λ-expressions may be applied to which type expressions (and, hence, which type expressions may instantiate which type variables), while the type flow filters the λ- and Λ-expressions that may be bound to variables (by rejecting expressions with static types that are incompatible with the static type of the variable under the type flow). As is typical for a monovariant control-flow analysis, control-flow information is expressed as an abstract environment mapping variables to sets of (syntactic) λ- and Λ-expressions that occur in the program under analysis. Similarly, type-flow information is expressed as an abstract environment mapping type variables to sets of (syntactic) types that occur in the program under analysis. Compatibility of static types (with free type variables) under a type flow is decided by interpreting the abstract environment as productions for a regular-tree grammar and querying if the languages generated by taking the types in question as starting terms have a non-empty intersection. © 2013 Springer-Verlag.