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Extending Equational Monadic Reasoning with Monad Transformers

Authors Reynald Affeldt , David Nowak

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  • 21 pages

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Author Details

Reynald Affeldt
  • National Institute of Advanced Industrial Science and Technology (AIST), Tokyo, Japan
David Nowak
  • Univ. Lille, CNRS, Centrale Lille, UMR 9189 CRIStAL, F-59000 Lille, France


We thank all the participants of the JSPS-CNRS bilateral program "FoRmal tools for IoT sEcurity" (PRC2199) for fruitful discussions. We also thank Takafumi Saikawa for his comments. This work is based on joint work with Célestine Sauvage [Célestine Sauvage et al., 2020].

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Reynald Affeldt and David Nowak. Extending Equational Monadic Reasoning with Monad Transformers. In 26th International Conference on Types for Proofs and Programs (TYPES 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 188, pp. 2:1-2:21, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


There is a recent interest for the verification of monadic programs using proof assistants. This line of research raises the question of the integration of monad transformers, a standard technique to combine monads. In this paper, we extend Monae, a Coq library for monadic equational reasoning, with monad transformers and we explain the benefits of this extension. Our starting point is the existing theory of modular monad transformers, which provides a uniform treatment of operations. Using this theory, we simplify the formalization of models in Monae and we propose an approach to support monadic equational reasoning in the presence of monad transformers. We also use Monae to revisit the lifting theorems of modular monad transformers by providing equational proofs and explaining how to patch a known bug using a non-standard use of Coq that combines impredicative polymorphism and parametricity.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
  • Software and its engineering → Formal software verification
  • monads
  • monad transformers
  • Coq
  • impredicativity
  • parametricity


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