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Documents authored by Tassi, Enrico

Document
DOI: 10.4230/LIPIcs.ITP.2025.27
Inductive Predicates via Least Fixpoints in Higher-Order Separation Logic

Authors: Robbert Krebbers, Luko van der Maas, and Enrico Tassi

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

Abstract
Inductive predicates play a key role in program verification using separation logic. There are many methods for defining such predicates in separation logic, which all have different conditions and thus support different classes of predicates. The most common methods are: (1) through a structurally-recursive definition (commonly used to define representation predicates for the verification of data structures), and (2) through step-indexing (commonly used to give a semantics of Hoare triples for partial program correctness). A lesser-known method is to define such inductive predicates internally in higher-order separation logic through a least fixpoint of a monotone function. The contributions of this paper are fourfold. First, we present the folklore result (from the Iris library) that one can define least (and greatest) fixpoints internally in separation logic by extending the standard second-order impredicative encoding with some modalities. Second, we show that these fixpoints are useful to define representation predicates where the mathematical and in-memory data structures do not correspond. Third, we show that these fixpoints can be used to define Hoare triples and weakest preconditions for total program correctness in Iris. Fourth, we present a prototype command (akin to Rocq’s Inductive), written in Rocq-Elpi, to generate the least fixpoint and its reasoning principles (constructors and induction principles) from a high-level specification.
Cite as

Robbert Krebbers, Luko van der Maas, and Enrico Tassi. Inductive Predicates via Least Fixpoints in Higher-Order Separation Logic. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 27:1-27:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{krebbers_et_al:LIPIcs.ITP.2025.27,
  author =	{Krebbers, Robbert and van der Maas, Luko and Tassi, Enrico},
  title =	{{Inductive Predicates via Least Fixpoints in Higher-Order Separation Logic}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{27:1--27:21},
  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.2025.27},
  URN =		{urn:nbn:de:0030-drops-246258},
  doi =		{10.4230/LIPIcs.ITP.2025.27},
  annote =	{Keywords: Separation Logic, Program Verification, Data Structures, Iris, Rocq prover}
}
Document
System Description
DOI: 10.4230/LIPIcs.FSCD.2020.34
Hierarchy Builder: Algebraic hierarchies Made Easy in Coq with Elpi (System Description)

Authors: Cyril Cohen, Kazuhiko Sakaguchi, and Enrico Tassi

Published in: LIPIcs, Volume 167, 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)

Abstract
It is nowadays customary to organize libraries of machine checked proofs around hierarchies of algebraic structures. One influential example is the Mathematical Components library on top of which the long and intricate proof of the Odd Order Theorem could be fully formalized. Still, building algebraic hierarchies in a proof assistant such as Coq requires a lot of manual labor and often a deep expertise in the internals of the prover. Moreover, according to our experience, making a hierarchy evolve without causing breakage in client code is equally tricky: even a simple refactoring such as splitting a structure into two simpler ones is hard to get right. In this paper we describe HB, a high level language to build hierarchies of algebraic structures and to make these hierarchies evolve without breaking user code. The key concepts are the ones of factory, builder and abbreviation that let the hierarchy developer describe an actual interface for their library. Behind that interface the developer can provide appropriate code to ensure backward compatibility. We implement the HB language in the hierarchy-builder addon for the Coq system using the Elpi extension language.
Cite as

Cyril Cohen, Kazuhiko Sakaguchi, and Enrico Tassi. Hierarchy Builder: Algebraic hierarchies Made Easy in Coq with Elpi (System Description). In 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 167, pp. 34:1-34:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{cohen_et_al:LIPIcs.FSCD.2020.34,
  author =	{Cohen, Cyril and Sakaguchi, Kazuhiko and Tassi, Enrico},
  title =	{{Hierarchy Builder: Algebraic hierarchies Made Easy in Coq with Elpi}},
  booktitle =	{5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)},
  pages =	{34:1--34:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-155-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{167},
  editor =	{Ariola, Zena M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2020.34},
  URN =		{urn:nbn:de:0030-drops-123562},
  doi =		{10.4230/LIPIcs.FSCD.2020.34},
  annote =	{Keywords: Algebraic Hierarchy, Packed Classes, Coq, Elpi, Metaprogramming, \lambdaProlog}
}
Document
DOI: 10.4230/LIPIcs.ITP.2019.29
Deriving Proved Equality Tests in Coq-Elpi: Stronger Induction Principles for Containers in Coq

Authors: Enrico Tassi

Published in: LIPIcs, Volume 141, 10th International Conference on Interactive Theorem Proving (ITP 2019)

Abstract
We describe a procedure to derive equality tests and their correctness proofs from inductive type declarations in Coq. Programs and proofs are derived compositionally, reusing code and proofs derived previously. The key steps are two. First, we design appropriate induction principles for data types defined using parametric containers. Second, we develop a technique to work around the modularity limitations imposed by the purely syntactic termination check Coq performs on recursive proofs. The unary parametricity translation of inductive data types turns out to be the key to both steps. Last but not least, we provide an implementation of the procedure for the Coq proof assistant based on the Elpi [Dunchev et al., 2015] extension language.
Cite as

Enrico Tassi. Deriving Proved Equality Tests in Coq-Elpi: Stronger Induction Principles for Containers in Coq. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 29:1-29:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{tassi:LIPIcs.ITP.2019.29,
  author =	{Tassi, Enrico},
  title =	{{Deriving Proved Equality Tests in Coq-Elpi: Stronger Induction Principles for Containers in Coq}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{29:1--29:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-122-1},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{141},
  editor =	{Harrison, John and O'Leary, John and Tolmach, Andrew},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2019.29},
  URN =		{urn:nbn:de:0030-drops-110841},
  doi =		{10.4230/LIPIcs.ITP.2019.29},
  annote =	{Keywords: Coq, Containers, Induction, Equality test, Parametricity translation}
}
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