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39 lines
No EOL
1.3 KiB
TeX
39 lines
No EOL
1.3 KiB
TeX
\section{Implementation in Agda}
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\begin{frame}[t, fragile]{Goals}
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\begin{itemize}[<+->]
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\item Formalize the delay monad categorically and show that it is..
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\begin{itemize}
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\item strong
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\item commutative
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\end{itemize}
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\item Formalize K and show that it is..
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\begin{itemize}
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\item strong
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\item commutative
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\item an equational lifting monad
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\end{itemize}
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\item Take the category of setoids and show that $K$ instantiates to $D_\approx$
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\end{itemize}
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\end{frame}
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\begin{frame}[t, fragile, blank]{Category Theory in Agda}{Setoid-enriched Categories}
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\begin{minted}{agda}
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record Category (o ℓ e : Level) : Set (suc (o ⊔ ℓ ⊔ e)) where
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field
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Obj : Set o
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_⇒_ : Obj → Obj → Set ℓ
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_≈_ : ∀ {A B} → (A ⇒ B) → (A ⇒ B) → Set e
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id : ∀ {A} → (A ⇒ A)
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_∘_ : ∀ {A B C} → (B ⇒ C) → (A ⇒ B) → (A ⇒ C)
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field
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assoc : ∀ {A B C D} {f : A ⇒ B} {g : B ⇒ C} {h : C ⇒ D}
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→ (h ∘ g) ∘ f ≈ h ∘ (g ∘ f)
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identityˡ : ∀ {A B} {f : A ⇒ B} → id ∘ f ≈ f
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identityʳ : ∀ {A B} {f : A ⇒ B} → f ∘ id ≈ f
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equiv : ∀ {A B} → IsEquivalence (_≈_ {A} {B})
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∘-resp-≈ : ∀ {A B C} {f h : B ⇒ C} {g i : A ⇒ B} → f ≈ h → g ≈ i → f ∘ g ≈ h ∘ i
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\end{minted}
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\end{frame} |