Formal validation of transformation schemata

  • Mattias Waldau
Conference paper
Part of the Workshops in Computing book series (WORKSHOPS COMP.)

Abstract

We present a first-order theory Г, which is used to validate transformation schemata. The theory Г consists of two kinds of axioms. Δ is the subset of the axioms Г which can be executed using a SLD-reso-lution like inference system, and Г-Δ contains first-order programs, as defined by T. Sato [Sat90], and induction axioms. Induction is essential if we want to prove correctness of more elaborate transformation schemata, e.g., a scheme which makes a program tail-recursive.

We show how to prove the correctness of transformation schemata using an ordinary proof system for intuitionistic first-order logic. Let ϑ be a transformation scheme which is proved correct. If we apply the scheme ϑ to a (first-order) program, the resulting program computes the same set of solutions as the original one.

We exemplify the method by proving the correctness of unfold/fold transformation, and of a scheme, which replaces recursion by tail-recursion.

Keywords

Lution Verse 

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Copyright information

© Springer-Verlag London 1992

Authors and Affiliations

  • Mattias Waldau
    • 1
  1. 1.Computing Science DepartmentUppsala UniversityUppsalaSweden

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