Authenticated Data Structures as Functors in Isabelle/HOL

Authors Andreas Lochbihler , Ognjen Marić

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Andreas Lochbihler
  • Digital Asset, Zurich, Switzerland
Ognjen Marić
  • Digital Asset, Zurich, Switzerland

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Andreas Lochbihler and Ognjen Marić. Authenticated Data Structures as Functors in Isabelle/HOL. In 2nd Workshop on Formal Methods for Blockchains (FMBC 2020). Open Access Series in Informatics (OASIcs), Volume 84, pp. 6:1-6:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Merkle trees are ubiquitous in blockchains and other distributed ledger technologies (DLTs). They guarantee that the involved systems are referring to the same binary tree, even if each of them knows only the cryptographic hash of the root. Inclusion proofs allow knowledgeable systems to share subtrees with other systems and the latter can verify the subtrees' authenticity. Often, blockchains and DLTs use data structures more complicated than binary trees; authenticated data structures generalize Merkle trees to such structures. We show how to formally define and reason about authenticated data structures, their inclusion proofs, and operations thereon as datatypes in Isabelle/HOL. The construction lives in the symbolic model, i.e., we assume that no hash collisions occur. Our approach is modular and allows us to construct complicated trees from reusable building blocks, which we call Merkle functors. Merkle functors include sums, products, and function spaces and are closed under composition and least fixpoints. As a practical application, we model the hierarchical transactions of Canton, a practical interoperability protocol for distributed ledgers, as authenticated data structures. This is a first step towards formalizing the Canton protocol and verifying its integrity and security guarantees.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
  • Theory of computation → Higher order logic
  • Theory of computation → Cryptographic primitives
  • Merkle tree
  • functor
  • distributed ledger
  • datatypes
  • higher-order logic


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