Add Action monad #502
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Add Action monad #502
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JacquesCarette
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Dec 16, 2025
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JacquesCarette
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Very nice. Some picky comments.
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| {-# OPTIONS --safe --without-K #-} | ||
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| open import Categories.Category |
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please restrict all open import via using. Do use Categories.Category.Core when at top-level just for 'Category'.
| module A = Functor ActionF | ||
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| η : ∀ X → X ⇒ A.₀ X | ||
| η X = m.η ⊗₁ id ∘ unitorˡ.to |
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Shorthands has things for unitors and associators; probably best to use them throughout the file.
| Monoid⇒-Monad⇒ : ∀ {m n} → Monoid⇒ m n → Monad⇒-id (ActionM n) (ActionM m) | ||
| Monoid⇒-Monad⇒ {m} {n} f = record | ||
| { α = ntHelper record | ||
| { η = λ X → arr ⊗₁ id |
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do _ names that are not used in the rhs of a lambda.
JacquesCarette
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Dec 17, 2025
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Closes #498
I'd like to share the commutative diagrams I made while trying to understand how to implement this:
Associativity:
Left identity:
Right identity:
In the issue I noted that this could be extended to a strong monad transformer - that comes from the fact that any pair of monads with a distributive property compose, which I think should be proven separately.