FORTissimo   

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.

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:

  1. 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.

  2. 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.

  3. Improve the expressiveness of FORT by adding support for combinations of rewrite systems and the generation of witnesses for existentially quantified variables. Investigate to what extent properties on open terms can be simulated in FORT, and whether certain fragments of the first-order theory of rewriting are decidable for larger classes of rewrite systems.


Members



FWF

FORTissimo is supported by FWF (P30301) from September 1, 2017 until March 1, 2022.

Contact

aart middeldorp at uibk dot ac dot at

Publications

Reducing Rewrite Properties to Properties on Ground Terms
Alexander Lochmann
Archive of Formal Proofs, 2022

First-Order Theory of Rewriting
Alexander Lochmann and Bertram Felgenhauer
Archive of Formal Proofs, 2022

Regular Tree Relations
Alexander Lochmann, Bertram Felgenhauer, Christian Sternagel, René Thiemann, and Thomas Sternagel
Archive of Formal Proofs, 2021

Formalized Signature Extension Results for Confluence, Commutation and Unique Normal Forms
Alexander Lochmann, Fabian Mitterwallner, and Aart Middeldorp
Proceedings of the 10th International Workshop on Confluence (IWC 2021), pp. 25 – 30, 2021
supporting website

Certifying Proofs in the First-Order Theory of Rewriting
Fabian Mitterwallner, Alexander Lochmann, Aart Middeldorp, and Bertram Felgenhauer
Proceedings of the 27th International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS 2021), Lecture Notes in Computer Science 12652, pp. 127 – 144, 2021
supporting website

A Verified Decision Procedure for the First-Order Theory of Rewriting for Linear Variable-Separated Rewrite Systems
Alexander Lochmann, Aart Middeldorp, Fabian Mitterwallner, and Bertram Felgenhauer
Proceedings of the 10th ACM SIGPLAN International Conference on Certified Programs and Proofs (CPP 2021), pages 250 – 263, 2021
supporting website

Formalized Proofs of the Infinity and Normal Form Predicates in the First-Order Theory of Rewriting
Alexander Lochmann and Aart Middeldorp
Proceedings of the 26th International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS 2020), Lecture Notes in Computer Science 12079, pp. 25 – 40, 2020
supporting website

A Verified Ground Confluence Tool for Linear Variable-Separated Rewrite Systems in Isabelle/HOL
Bertram Felgenhauer, Aart Middeldorp, T. V. H. Prathamesh, and Franziska Rapp
Proceedings of the 8th ACM SIGPLAN International Conference on Certified Programs and Proofs (CPP 2019), ACM, pp. 132 – 143, 2019
supporting website

Minsky Machines
Bertram Felgenhauer
Archive of Formal Proofs, 2018

Towards a Verified Decision Procedure for Confluence of Ground Term Rewrite Systems in Isabelle/HOL
Bertram Felgenhauer, Aart Middeldorp, T. V. H. Prathamesh, and Franziska Rapp
Proceedings of the 7th International Workshop on Confluence (IWC 2018), pp. 46 – 50, 2018
supporting website

FORT 2.0
Franziska Rapp and Aart Middeldorp
Proceedings of the 9th International Joint Conference on Automated Reasoning (IJCAR-9), Lecture Notes in Artificial Intelligence 10900, pp. 81 – 88, 2018