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Extending Equational Monadic Reasoning with Monad Transformers

Abstract : 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 with a non-standard use of Coq that combines impredicative polymorphism and parametricity.
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Contributor : David Nowak Connect in order to contact the contributor
Submitted on : Monday, November 9, 2020 - 8:43:46 AM
Last modification on : Tuesday, January 4, 2022 - 6:13:17 AM

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Reynald Affeldt, David Nowak. Extending Equational Monadic Reasoning with Monad Transformers. 26th International Conference on Types for Proofs and Programs, TYPES 2020, Mar 2020, Turin, Italy. ⟨10.4230/LIPIcs.TYPES.2020.2⟩. ⟨hal-02995160⟩



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