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ajeffrey@roblox.com 2022-04-22 19:56:38 -05:00
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18
prototyping/Properties/TypeNormalization.agda
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@ -51,31 +51,19 @@ normal (S ∩ T) = normal-∩ⁿ (normal S) (normal T)
normalᶠ (S ⇒ T) = S ⇒ T normalᶠ (S ⇒ T) = S ⇒ T
normalᶠ (F ∩ G) = F ∩ G normalᶠ (F ∩ G) = F ∩ G
normal-∪ⁿ never never = never normal-∪ⁿ S (T₁ ∪ T₂) = (normal-∪ⁿ S T₁) ∪ T₂
normal-∪ⁿ never unknown = unknown normal-∪ⁿ S never = S
normal-∪ⁿ S unknown = unknown
normal-∪ⁿ never (T ⇒ U) = T ⇒ U normal-∪ⁿ never (T ⇒ U) = T ⇒ U
normal-∪ⁿ never (G₁ ∩ G₂) = G₁ ∩ G₂ normal-∪ⁿ never (G₁ ∩ G₂) = G₁ ∩ G₂
normal-∪ⁿ never (T₁ ∪ T₂) = (normal-∪ⁿ never) T₁ ∪ T₂
normal-∪ⁿ unknown never = unknown
normal-∪ⁿ unknown unknown = unknown
normal-∪ⁿ unknown (T ⇒ U) = unknown normal-∪ⁿ unknown (T ⇒ U) = unknown
normal-∪ⁿ unknown (G₁ ∩ G₂) = unknown normal-∪ⁿ unknown (G₁ ∩ G₂) = unknown
normal-∪ⁿ unknown (T₁ ∪ T₂) = (normal-∪ⁿ unknown T₁) ∪ T₂
normal-∪ⁿ (R ⇒ S) never = (R ⇒ S)
normal-∪ⁿ (R ⇒ S) unknown = unknown
normal-∪ⁿ (R ⇒ S) (T ⇒ U) = normalᶠ (normal-∪ᶠ (R ⇒ S) (T ⇒ U)) normal-∪ⁿ (R ⇒ S) (T ⇒ U) = normalᶠ (normal-∪ᶠ (R ⇒ S) (T ⇒ U))
normal-∪ⁿ (R ⇒ S) (G₁ ∩ G₂) = normalᶠ (normal-∪ᶠ (R ⇒ S) (G₁ ∩ G₂)) normal-∪ⁿ (R ⇒ S) (G₁ ∩ G₂) = normalᶠ (normal-∪ᶠ (R ⇒ S) (G₁ ∩ G₂))
normal-∪ⁿ (R ⇒ S) (T₁ ∪ T₂) = (normal-∪ⁿ (R ⇒ S) T₁) ∪ T₂
normal-∪ⁿ (F₁ ∩ F₂) never = (F₁ ∩ F₂)
normal-∪ⁿ (F₁ ∩ F₂) unknown = unknown
normal-∪ⁿ (F₁ ∩ F₂) (T ⇒ U) = normalᶠ (normal-∪ᶠ (F₁ ∩ F₂) (T ⇒ U)) normal-∪ⁿ (F₁ ∩ F₂) (T ⇒ U) = normalᶠ (normal-∪ᶠ (F₁ ∩ F₂) (T ⇒ U))
normal-∪ⁿ (F₁ ∩ F₂) (G₁ ∩ G₂) = normalᶠ (normal-∪ᶠ (F₁ ∩ F₂) (G₁ ∩ G₂)) normal-∪ⁿ (F₁ ∩ F₂) (G₁ ∩ G₂) = normalᶠ (normal-∪ᶠ (F₁ ∩ F₂) (G₁ ∩ G₂))
normal-∪ⁿ (F₁ ∩ F₂) (T₁ ∪ T₂) = (normal-∪ⁿ (F₁ ∩ F₂) T₁) ∪ T₂
normal-∪ⁿ (S₁ ∪ S₂) never = S₁ ∪ S₂
normal-∪ⁿ (S₁ ∪ S₂) unknown = unknown
normal-∪ⁿ (S₁ ∪ S₂) (T₁ ⇒ T₂) = normal-∪ⁿ S₁ (T₁ ⇒ T₂) ∪ S₂ normal-∪ⁿ (S₁ ∪ S₂) (T₁ ⇒ T₂) = normal-∪ⁿ S₁ (T₁ ⇒ T₂) ∪ S₂
normal-∪ⁿ (S₁ ∪ S₂) (G₁ ∩ G₂) = normal-∪ⁿ S₁ (G₁ ∩ G₂) ∪ S₂ normal-∪ⁿ (S₁ ∪ S₂) (G₁ ∩ G₂) = normal-∪ⁿ S₁ (G₁ ∩ G₂) ∪ S₂
normal-∪ⁿ (S₁ ∪ S₂) (T₁ ∪ T₂) = normal-∪ⁿ (S₁ ∪ S₂) T₁ ∪ T₂
-- normal-∪ⁿ never never = never -- normal-∪ⁿ never never = never
-- normal-∪ⁿ never unknown = unknown -- normal-∪ⁿ never unknown = unknown