3 Search Results for "Tebbi, Tobias"

Document
Invited Talk
DOI: 10.4230/LIPIcs.ITP.2025.40
Autosubst: On Mechanising Binders in a General-Purpose Proof Assistant (Invited Talk)

Authors: Kathrin Stark

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
The question of handling binders effectively regularly comes up when mechanising results in a proof assistant. Since the beginning of proof assistants, many solutions have been suggested: these include de Bruijn syntax, locally nameless binders, nominal syntax or HOAS. But even today - 20 years after the POPLMark Challenge [Brian E. Aydemir et al., 2005] - new tools and approaches to binding are still being published. Binders are still mentioned as being a complication of mechanised proofs over pen-and-paper proofs and the source of uninteresting technicalities and heaps of boilerplate - particularly, when working in a proof assistant without native support for binders or quotients. Autosubst [Steven Schäfer et al., 2015; Steven Schäfer et al., 2015], initially developed a decade ago as a teaching tool, addresses this problem by automating boilerplate code generation for a de Bruijn representation in the Rocq prover. Autosubst translates a specification into the corresponding pure or scoped de Bruijn algebra: It hence generates a corresponding instantiation operation for parallel substitutions, and several equational substitution lemmas. Central to its usability is a rewriting tactic that automatically decides equality up to substitutions, requiring minimal input and knowledge from the user’s side. This greatly simplifies using the otherwise notoriously difficult de Bruijn representation. Since then, Autosubst has been successfully used in several projects. In this talk, I will give an overview of the background and history of Autosubst and give an overview on the work, tools, and formalisations around it [Kathrin Stark et al., 2019; Kathrin Stark, 2020; Andreas Abel et al., 2019]. Moreover, this talk will highlight some of the more recent extensions [Yannick Forster and Kathrin Stark, 2020] as well as outline future challenges and directions.
Cite as

Kathrin Stark. Autosubst: On Mechanising Binders in a General-Purpose Proof Assistant (Invited Talk). In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 40:1-40:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{stark:LIPIcs.ITP.2025.40,
  author =	{Stark, Kathrin},
  title =	{{Autosubst: On Mechanising Binders in a General-Purpose Proof Assistant}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{40:1--40:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.40},
  URN =		{urn:nbn:de:0030-drops-246385},
  doi =		{10.4230/LIPIcs.ITP.2025.40},
  annote =	{Keywords: Syntax, binders, Rocq}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.11
Animating MRBNFs: Truly Modular Binding-Aware Datatypes in Isabelle/HOL

Authors: Jan van Brügge, Andrei Popescu, and Dmitriy Traytel

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
Nominal Isabelle provides powerful tools for meta-theoretic reasoning about syntax of logics or programming languages, in which variables are bound. It has been instrumental to major verification successes, such as Gödel’s incompleteness theorems. However, the existing tooling is not compositional. In particular, it does not support nested recursion, linear binding patterns, or infinitely branching syntax. These limitations are fundamental in the way nominal datatypes and functions on them are constructed within Nominal Isabelle. Taking advantage of recent theoretical advancements that overcome these limitations through a modular approach using the concept of map-restricted bounded natural functor (MRBNF), we develop and implement a new definitional package for binding-aware datatypes in Isabelle/HOL, called MrBNF. We describe the journey from the user specification to the end-product types, constants and theorems the tool generates. We validate MrBNF in two formalization case studies that so far were out of reach of nominal approaches: (1) Mazza’s isomorphism between the finitary and the infinitary affine λ-calculus, and (2) the POPLmark 2B challenge, which involves non-free binders for linear pattern matching.
Cite as

Jan van Brügge, Andrei Popescu, and Dmitriy Traytel. Animating MRBNFs: Truly Modular Binding-Aware Datatypes in Isabelle/HOL. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 11:1-11:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{vanbrugge_et_al:LIPIcs.ITP.2025.11,
  author =	{van Br\"{u}gge, Jan and Popescu, Andrei and Traytel, Dmitriy},
  title =	{{Animating MRBNFs: Truly Modular Binding-Aware Datatypes in Isabelle/HOL}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{11:1--11:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.11},
  URN =		{urn:nbn:de:0030-drops-246091},
  doi =		{10.4230/LIPIcs.ITP.2025.11},
  annote =	{Keywords: syntax with bindings, datatypes, inductive predicates, Isabelle/HOL}
}
Document
DOI: 10.4230/LIPIcs.RTA.2013.271
Unification Modulo Nonnested Recursion Schemes via Anchored Semi-Unification

Authors: Gert Smolka and Tobias Tebbi

Published in: LIPIcs, Volume 21, 24th International Conference on Rewriting Techniques and Applications (RTA 2013)

Abstract
A recursion scheme is an orthogonal rewriting system with rules of the form f(x1,...,xn) -> s. We consider terms to be equivalent if they rewrite to the same redex-free possibly infinite term after infinitary rewriting. For the restriction to the nonnested case, where nested redexes are forbidden, we prove the existence of principal unifiers modulo scheme equivalence. We give an algorithm computing principal unifiers by reducing the problem to a novel fragment of semi-unification we call anchored semi-unification. For anchored semi-unification, we develop a decision algorithm that returns a principal semi-unifier in the positive case.
Cite as

Gert Smolka and Tobias Tebbi. Unification Modulo Nonnested Recursion Schemes via Anchored Semi-Unification. In 24th International Conference on Rewriting Techniques and Applications (RTA 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 21, pp. 271-286, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{smolka_et_al:LIPIcs.RTA.2013.271,
  author =	{Smolka, Gert and Tebbi, Tobias},
  title =	{{Unification Modulo Nonnested Recursion Schemes via Anchored Semi-Unification}},
  booktitle =	{24th International Conference on Rewriting Techniques and Applications (RTA 2013)},
  pages =	{271--286},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-53-8},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{21},
  editor =	{van Raamsdonk, Femke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2013.271},
  URN =		{urn:nbn:de:0030-drops-40674},
  doi =		{10.4230/LIPIcs.RTA.2013.271},
  annote =	{Keywords: recursion schemes, semi-unification, infinitary rewriting}
}
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