Type-changing rewriting and semantics-preserving transformation

  • Authors:

  • Sean Leather;Johan Jeuring;Andres Löh;Bram Schuur

  • Affiliations:

  • Utrecht University, Utrecht, Netherlands;Utrecht University and Open University Netherlands, Utrecht, Netherlands;Well-Typed LLP, Regensburg, Germany;Utrecht University, Utrecht, Netherlands

  • Venue:
  • Proceedings of the ACM SIGPLAN 2014 Workshop on Partial Evaluation and Program Manipulation
  • Year:
  • 2014

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Abstract

We have identified a class of regular, whole-program transformations that cannot be safely performed with typical transformation techniques because transformation requires changing the types of terms. In these transformations, we want to change typically large parts of a program from using one type to using another type while simultaneously preserving the original program semantics after transformation. In this paper, we present type-and-transform systems, an automated approach to the whole-program transformation of terms involving type A to terms involving the isomorphic type B using type-changing rewrite rules. Type-and-transform systems establish typing and semantics relations between all source and target subprograms such that a complete transformation can guarantee the equivalent semantics of a whole program. We describe the type-and-transform system for the lambda calculus with let-polymorphism and general recursion, including several examples from the literature and properties of the system.