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How do you do equational reasoning for user defined equational relations with agda-stdlib?

原文 2022-10-03 13:09:51 5 1 equality/ agda/ theorem-proving

agda-stdlib has facilities for doing equational reasoning for various specific library defined relations ( example ). It also has a type that identifies equality relations defined here . What is the easiest way for me to get access to the same facilities for equational reason I get with propositional equality.

1 answers

The kit is defined in Relation.Binary.Reasoning.Setoid .

You only need to define a proof S that your relation defines a Setoid and then you can open import Relation.Binary.Reasoning.Setoid S to get the equational reasoning combinators.

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Related Question Isabelle / isar: Implementing equational reasoning How do you compare structs for equality in C? How do you compare a nullable int to an int How do you test functions and closures for equality? how do you compare two arbitrary COM objects (can you get CLSID for arbitrary object?) How do you test to see if a double is equal to NaN? How do you detect if all the variables in two objects of the same type are the same? How do I check if a string with a user given input is equal to a certain letter/ word in Python When you override __eq__ in a class, do you also need to override __hash__? Equality in Agda - irrelevant arguments

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How do you do equational reasoning for user defined equational relations with agda-stdlib?

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solution1 3 ACCPTED 2022-10-03 14:10:42

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3 ACCPTED 2022-10-03 14:10:42