2020
DOI: 10.1007/s10817-019-09538-8
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A Library for Formalization of Linear Error-Correcting Codes

Abstract: One can perform equational reasoning about computational effects with a purely functional programming language thanks to monads. Even though equational reasoning for effectful programs is desirable, it is not yet mainstream. This is partly because it is difficult to maintain pencil-and-paper proofs of large examples. We propose a formalization of a hierarchy of effects using monads in the Coq proof assistant that makes monadic equational reasoning practical. Our main idea is to formalize the hierarchy of effec… Show more

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Cited by 4 publications
(3 citation statements)
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“…The last step is to provide an implementation for the interface of the probability monad. The probabilistic choice operator corresponds to the construction of a distribution d from two distributions d1 and d2 biased by a probability p: The combinator ConvDist.d is a generalization that handles the combination of any distribution of distributions: it is instantiated here with the binary distribution I2Dist.d p [4]. We finally prove that the probabilistic choice d have the expected properties, for example, skewed commutativity:…”
Section: A Model Of the Probability Monadmentioning
confidence: 87%
See 1 more Smart Citation
“…The last step is to provide an implementation for the interface of the probability monad. The probabilistic choice operator corresponds to the construction of a distribution d from two distributions d1 and d2 biased by a probability p: The combinator ConvDist.d is a generalization that handles the combination of any distribution of distributions: it is instantiated here with the binary distribution I2Dist.d p [4]. We finally prove that the probabilistic choice d have the expected properties, for example, skewed commutativity:…”
Section: A Model Of the Probability Monadmentioning
confidence: 87%
“…6.1). We also benefit from other libraries compatible with MathComp to formalize the model of the probability monad [4].…”
Section: Technical Aspects Of Formalization In Coqmentioning
confidence: 99%
“…In a separate vein, several recently-developed libraries of formalized coding theory are similar to the functional model in our work, but are not connected to an efficient implementation. Most notably, Affeldt, Garrigue, and Saikawa have developed a Coq library for error-correcting codes, including Hamming and acyclic LDPC [1], Reed-Solomon [2], and BCH [3] codes. This library is built atop MathComp, and includes many theoretical results about each of these codes as well as specific encoders and decoders.…”
Section: Related Workmentioning
confidence: 99%