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Some edits inspired by Sergey
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MatthewDaggitt committed Sep 20, 2024
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Expand Up @@ -159,8 +159,8 @@ Relatedly, `agda-stdlib` has been used as a test bed for the design of the Agda

Agda’s unique support for dependently-parameterised modules [@ivardeBruin2023] has also significantly influenced the library’s design.
Although type classes are a common mechanism for creating interfaces and overloading syntax in other functional languages such as Haskell [@haskell2010], and other ITPs like Coq and Lean's MathLib use them extensively as a core feature of their design, the developers of `agda-stdlib` has so far found little need to exploit such an approach.
While Agda supports a very general form of instance search, the ability to use qualified, parameterised modules as first-class objects appears to reduce the need for it compared to the languages mentioned above.
Additionally, module parameters enable the safe and scalable embedding of non-constructive mathematics into a constructive system.
While Agda supports a very general form of instance search, the ability to use qualified, parameterised modules appears to reduce the need for it compared to the languages mentioned above.
Additionally, parameterised modules enable the safe and scalable embedding of non-constructive mathematics into a constructive system.
Since Agda is entirely constructive, the vast majority of `agda-stdlib` is also constructive.
Non-constructive methods, such as classical reasoning, can be achieved by passing the relevant axioms as module parameters.
This enables users to write provably "safe" non-constructive code, i.e. without having to *postulate* such axioms.
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