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ajeffrey@roblox.com 2022-05-13 12:32:03 -05:00
parent 424c896788
commit f8e9148efa
2 changed files with 28 additions and 17 deletions
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20
prototyping/Properties/TypeNormalization.agda
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@ -237,16 +237,16 @@ scalar-∩-fun-<:-never function S = scalar-∩-function-<:-never S
scalar-∩-fun-<:-never (T ⇒ U) S = scalar-∩-function-<:-never S scalar-∩-fun-<:-never (T ⇒ U) S = scalar-∩-function-<:-never S
scalar-∩-fun-<:-never (F ∩ G) S = <:-trans (<:-intersect <:-∩-left <:-refl) (scalar-∩-fun-<:-never F S) scalar-∩-fun-<:-never (F ∩ G) S = <:-trans (<:-intersect <:-∩-left <:-refl) (scalar-∩-fun-<:-never F S)
<:-tgtⁿ : ∀ {S T U} → (T <: U) → T <: tgtⁿ S U <:-tgtⁿ : ∀ {T U} → U <: tgtⁿ T U
<:-tgtⁿ {never} p = <:-unknown <:-tgtⁿ {never} = <:-unknown
<:-tgtⁿ {nil} p = p <:-tgtⁿ {nil} = <:-refl
<:-tgtⁿ {unknown} p = p <:-tgtⁿ {unknown} = <:-refl
<:-tgtⁿ {boolean} p = p <:-tgtⁿ {boolean} = <:-refl
<:-tgtⁿ {number} p = p <:-tgtⁿ {number} = <:-refl
<:-tgtⁿ {string} p = p <:-tgtⁿ {string} = <:-refl
<:-tgtⁿ {S ⇒ T} p = p <:-tgtⁿ {S ⇒ T} = <:-refl
<:-tgtⁿ {S ∪ T} p = p <:-tgtⁿ {S ∪ T} = <:-refl
<:-tgtⁿ {S ∩ T} p = p <:-tgtⁿ {S ∩ T} = <:-refl
flipper : ∀ {S T U} → ((S ∪ T) ∪ U) <: ((S ∪ U) ∪ T) flipper : ∀ {S T U} → ((S ∪ T) ∪ U) <: ((S ∪ U) ∪ T)
flipper = <:-trans <:-∪-assocr (<:-trans (<:-union <:-refl <:-∪-symm) <:-∪-assocl) flipper = <:-trans <:-∪-assocr (<:-trans (<:-union <:-refl <:-∪-symm) <:-∪-assocl)

25
prototyping/Properties/TypeSaturation.agda
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@ -202,7 +202,7 @@ data ⋓-Overload F G : Type → Set where
∪-∪-saturated : ∀ {F} → (FunType F) → (∪-saturate F ⋓ ∪-saturate F) ⊂:ᵒ ∪-saturate F ∪-∪-saturated : ∀ {F} → (FunType F) → (∪-saturate F ⋓ ∪-saturate F) ⊂:ᵒ ∪-saturate F
∪-∪-saturated function here = <:ᵒ-refl ∪-∪-saturated function here = <:ᵒ-refl
∪-∪-saturated (Sⁱ ⇒ Tⁿ) here = defn here (<:-trans (∪ⁿ-<:-∪ (normalⁱ Sⁱ) (normalⁱ Sⁱ)) (<:-∪-lub <:-refl <:-refl)) (<:-tgtⁿ (<:-trans <:-∪-left (∪-<:-∪ⁿ Tⁿ Tⁿ))) ∪-∪-saturated (Sⁱ ⇒ Tⁿ) here = defn here (<:-trans (∪ⁿ-<:-∪ (normalⁱ Sⁱ) (normalⁱ Sⁱ)) (<:-∪-lub <:-refl <:-refl)) (<:-trans (<:-trans <:-∪-left (∪-<:-∪ⁿ Tⁿ Tⁿ)) <:-tgtⁿ)
∪-∪-saturated (Fᶠ ∩ Gᶠ) o = ∩ᵘ-∪-saturated (∪-∪-saturated Fᶠ) (∪-∪-saturated Gᶠ) o ∪-∪-saturated (Fᶠ ∩ Gᶠ) o = ∩ᵘ-∪-saturated (∪-∪-saturated Fᶠ) (∪-∪-saturated Gᶠ) o
-- ∩-saturate is ⋓-closed -- ∩-saturate is ⋓-closed
@ -210,8 +210,18 @@ data ⋓-Overload F G : Type → Set where
∪-saturated F = ∪-∪-saturated (normal-∩-saturate F) ∪-saturated F = ∪-∪-saturated (normal-∩-saturate F)
-- ∩-saturate is ⋒-closed -- ∩-saturate is ⋒-closed
ov-⋒-∩ : ∀ {F G R S T U} → Overload F (R ⇒ S) → Overload G (T ⇒ U) → Overload (F ⋒ G) ((R ∩ T) ⇒ (S ∩ U)) ov-⋒-∩ : ∀ {F G R S T U} → FunType F → FunType G → Overload F (R ⇒ S) → Overload G (T ⇒ U) → (F ⋒ G) <:ᵒ ((R ∩ T) ⇒ (S ∩ U))
ov-⋒-∩ = {!!} ov-⋒-∩ function function here here = defn here (∩-<:-∩ⁿ never never) (<:-∩-glb <:-refl <:-refl)
ov-⋒-∩ function (T ⇒ U) here here = defn here (∩-<:-∩ⁿ never (normalⁱ T)) {!<:-tgtⁿ (∩ⁿ-<:-∩ unknown U)!}
ov-⋒-∩ function (G ∩ H) here (left o) = {!!}
ov-⋒-∩ function (G ∩ H) here (right o) = {!!}
ov-⋒-∩ (R ⇒ S) function here here = defn here (∩-<:-∩ⁿ {!!} {!!}) {!!}
ov-⋒-∩ (R ⇒ S) (T ⇒ U) here here = defn here (∩-<:-∩ⁿ {!!} {!!}) {!!}
ov-⋒-∩ (R ⇒ S) (G ∩ H) here (left o) = {!!}
ov-⋒-∩ (R ⇒ S) (G ∩ H) here (right o) = {!!}
ov-⋒-∩ (E ∩ F) function n o = {!!}
ov-⋒-∩ (E ∩ F) (T ⇒ U) n o = {!!}
ov-⋒-∩ (E ∩ F) (G ∩ H) n o = {!!}
∩-∩-saturated : ∀ {F} → (FunType F) → (∩-saturate F ⋒ ∩-saturate F) ⊂:ᵒ ∩-saturate F ∩-∩-saturated : ∀ {F} → (FunType F) → (∩-saturate F ⋒ ∩-saturate F) ⊂:ᵒ ∩-saturate F
∩-∩-saturated F = {!!} ∩-∩-saturated F = {!!}
@ -238,13 +248,13 @@ data ⋒-Overload-<: F G : Type → Set where
⋒-overload-<: : ∀ {F G S T} → FunType F → FunType G → Overload (F ⋒ G) (S ⇒ T) → ⋒-Overload-<: F G (S ⇒ T) ⋒-overload-<: : ∀ {F G S T} → FunType F → FunType G → Overload (F ⋒ G) (S ⇒ T) → ⋒-Overload-<: F G (S ⇒ T)
⋒-overload-<: function function here = defn (defn here here) <:-never <:-unknown ⋒-overload-<: function function here = defn (defn here here) <:-never <:-unknown
⋒-overload-<: function (T ⇒ U) here = defn (defn here here) (∩ⁿ-<:-∩ never (normalⁱ T)) (<:-tgtⁿ (∩-<:-∩ⁿ unknown U)) ⋒-overload-<: function (T ⇒ U) here = defn (defn here here) (∩ⁿ-<:-∩ never (normalⁱ T)) (<:-trans (∩-<:-∩ⁿ unknown U) <:-tgtⁿ)
⋒-overload-<: function (G ∩ H) (left o) with ⋒-overload-<: function G o ⋒-overload-<: function (G ∩ H) (left o) with ⋒-overload-<: function G o
⋒-overload-<: function (G ∩ H) (left o) | defn (defn o₁ o₂) o₃ o₄ = defn (defn o₁ (left o₂)) o₃ o₄ ⋒-overload-<: function (G ∩ H) (left o) | defn (defn o₁ o₂) o₃ o₄ = defn (defn o₁ (left o₂)) o₃ o₄
⋒-overload-<: function (G ∩ H) (right o) with ⋒-overload-<: function H o ⋒-overload-<: function (G ∩ H) (right o) with ⋒-overload-<: function H o
⋒-overload-<: function (G ∩ H) (right o) | defn (defn o₁ o₂) o₃ o₄ = defn (defn o₁ (right o₂)) o₃ o₄ ⋒-overload-<: function (G ∩ H) (right o) | defn (defn o₁ o₂) o₃ o₄ = defn (defn o₁ (right o₂)) o₃ o₄
⋒-overload-<: (R ⇒ S) function here = defn (defn here here) (∩ⁿ-<:-∩ (normalⁱ R) never) (<:-tgtⁿ (∩-<:-∩ⁿ S unknown)) ⋒-overload-<: (R ⇒ S) function here = defn (defn here here) (∩ⁿ-<:-∩ (normalⁱ R) never) (<:-trans (∩-<:-∩ⁿ S unknown) <:-tgtⁿ)
⋒-overload-<: (R ⇒ S) (T ⇒ U) here = defn (defn here here) (∩ⁿ-<:-∩ (normalⁱ R) (normalⁱ T)) (<:-tgtⁿ (∩-<:-∩ⁿ S U)) ⋒-overload-<: (R ⇒ S) (T ⇒ U) here = defn (defn here here) (∩ⁿ-<:-∩ (normalⁱ R) (normalⁱ T)) (<:-trans (∩-<:-∩ⁿ S U) <:-tgtⁿ)
⋒-overload-<: (R ⇒ S) (G ∩ H) (left o) with ⋒-overload-<: (R ⇒ S) G o ⋒-overload-<: (R ⇒ S) (G ∩ H) (left o) with ⋒-overload-<: (R ⇒ S) G o
⋒-overload-<: (R ⇒ S) (G ∩ H) (left o) | defn (defn o₁ o₂) o₃ o₄ = defn (defn o₁ (left o₂)) o₃ o₄ ⋒-overload-<: (R ⇒ S) (G ∩ H) (left o) | defn (defn o₁ o₂) o₃ o₄ = defn (defn o₁ (left o₂)) o₃ o₄
⋒-overload-<: (R ⇒ S) (G ∩ H) (right o) with ⋒-overload-<: (R ⇒ S) H o ⋒-overload-<: (R ⇒ S) (G ∩ H) (right o) with ⋒-overload-<: (R ⇒ S) H o
@ -301,7 +311,8 @@ data ⋓-Closure-<: F : Type → Set where
⋓-closure-<:ᵒ (defn o p q) = defn (ov o) p q ⋓-closure-<:ᵒ (defn o p q) = defn (ov o) p q
⋓-closure-<:-∩ : ∀ {F R S T U} → (FunType F) → (F ⋒ F) ⊂:ᵒ F → ⋓-Closure F (R ⇒ S) → ⋓-Closure F (T ⇒ U) → ⋓-Closure-<: F ((R ∩ T) ⇒ (S ∩ U)) ⋓-closure-<:-∩ : ∀ {F R S T U} → (FunType F) → (F ⋒ F) ⊂:ᵒ F → ⋓-Closure F (R ⇒ S) → ⋓-Closure F (T ⇒ U) → ⋓-Closure-<: F ((R ∩ T) ⇒ (S ∩ U))
⋓-closure-<:-∩ Fᶠ p (ov n) (ov o) = ⋓-closure-<:ᵒ (p (ov-⋒-∩ n o)) ⋓-closure-<:-∩ Fᶠ p (ov n) (ov o) with ov-⋒-∩ Fᶠ Fᶠ n o
⋓-closure-<:-∩ Fᶠ p (ov n) (ov o) | defn q q₁ q₂ = ⋓-closure-<:ᵒ (<:ᵒ-trans-<: (p q) q₁ q₂)
⋓-closure-<:-∩ Fᶠ p c (union d d₁) with ⋓-closure-<:-∩ Fᶠ p c d | ⋓-closure-<:-∩ Fᶠ p c d₁ ⋓-closure-<:-∩ Fᶠ p c (union d d₁) with ⋓-closure-<:-∩ Fᶠ p c d | ⋓-closure-<:-∩ Fᶠ p c d₁
⋓-closure-<:-∩ Fᶠ p c (union d d₁) | defn e e₁ e₂ | defn f f₁ f₂ = defn (union e f) (<:-trans <:-∩-distl-∪ (<:-union e₁ f₁)) (<:-trans (<:-union e₂ f₂) ∩-distl-∪-<:) ⋓-closure-<:-∩ Fᶠ p c (union d d₁) | defn e e₁ e₂ | defn f f₁ f₂ = defn (union e f) (<:-trans <:-∩-distl-∪ (<:-union e₁ f₁)) (<:-trans (<:-union e₂ f₂) ∩-distl-∪-<:)
⋓-closure-<:-∩ Fᶠ p (union c c₁) d with ⋓-closure-<:-∩ Fᶠ p c d | ⋓-closure-<:-∩ Fᶠ p c₁ d ⋓-closure-<:-∩ Fᶠ p (union c c₁) d with ⋓-closure-<:-∩ Fᶠ p c d | ⋓-closure-<:-∩ Fᶠ p c₁ d