FORTissimo: Automating the First-Order Theory of Rewriting

FORTissimo is about the first-order theory of rewriting, which is a decidable theory for left-linear right-ground rewrite systems in which well-known properties like confluence, normalization and termination are expressible. The decision procedure for this theory is based on tree automata techniques and a first implementation was conducted by Franziska Rapp during her master studies. The resulting tool FORT is equipped with a synthesis mode to generate rewrite systems that satisfy properties expressible in the first-order theory of rewriting.

  1. The aim of this project is to formalize the decision procedure in the proof assistant Isabelle/HOL such that the output of FORT can be certified. Moreover, the expressiveness and the performance of FORT should be increased, and its limitations better understood. More concretely, the project has the following three main objectives:
  2. Formalize the basic properties of automata on n-ary relations (cylindrification, projection) and ground tree transducers in Isabelle/HOL. Develop suitable certificates that can be produced by FORT and checked by the certifier obtained from the formalization in Isabelle via code generation.
  3. Improve the performance of FORT by adopting and developing state-of-the-art tree automata techniques. Investigate methods for formula normalization in order to speed up the computation of intermediate automata. Adopt parallel programming techniques to further improve the efficiency of FORT.

FORTissimo will start on September 1, 2017 and run for three years.


Current Members

  • Jamie Hochrainer
  • Johannes Koch
  • Alexander Lochmann
  • Aart Middeldorp (coordination)
  • Fabian Mitterwallner

Former Members

  • Bertram Felgenhauer
  • Fabian Mitterwallner
  • T. V. H. Prathamesh
  • Franziska Rapp
  • Kei Shirakizawa (guest)


FWF project number



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