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A Type- and Control-Flow Analysis for System F

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Book cover Implementation and Application of Functional Languages (IFL 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8241))

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Abstract

We present a monovariant flow analysis for System F (with recursion). The flow analysis yields both control-flow information, approximating the \(\lambda \)- and \(\varLambda \)-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 \(\varLambda \)-expressions may be applied to which type expressions (and, hence, which type expressions may instantiate which type variables), while the type flow filters the \(\lambda \)- and \(\varLambda \)-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) \(\lambda \)- and \(\varLambda \)-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.

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Notes

  1. 1.

    Although there are many type-based [27] control-flow analyses, where the analyses are expressed as a sophisticated type systems, the language under analysis is typically a simply-typed language.

  2. 2.

    These abstraction functions are “shallow” in the sense that they do not abstract and join the embedded run-time type and value environments.

  3. 3.

    Again, we draw a distinction between flow analyses expressed as sophisticated type systems and flow analyses of languages with sophisticated type systems.

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Acknowledgments

Many thanks to Jan Midtgaard for the excellent survey “Control-flow analysis of functional programs” [22] and companion bibliography and for valuable feedback on an earlier draft. Thanks to Jurriaan Hage, Fritz Henglein, and Peter Thiemann for thoughtful conversation at IFL’12. This material is based upon work supported by the National Science Foundation under Grant No. 1065099.

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  1. Computer Science Department, Rochester Institute of Technology, Rochester, NY , 14623, USA

    Matthew Fluet

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  1. University of Oxford, Oxford, United Kingdom

    Ralf Hinze

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Fluet, M. (2013). A Type- and Control-Flow Analysis for System F. In: Hinze, R. (eds) Implementation and Application of Functional Languages. IFL 2012. Lecture Notes in Computer Science(), vol 8241. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41582-1_8

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