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Remove todo

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pingu
2025-12-22 21:31:24 +01:00
parent 94688e685b
commit 411109a2ee
1 changed files with 4 additions and 3 deletions
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@@ -30,7 +30,6 @@ data Formula : Type where
⊥ : Formula ⊥ : Formula
atom : Nat → Formula atom : Nat → Formula
∼_ : Formula → Formula ∼_ : Formula → Formula
◇_ : Formula → Formula
□_ : Formula → Formula □_ : Formula → Formula
_∧_ : Formula → Formula → Formula _∧_ : Formula → Formula → Formula
_∨_ : Formula → Formula → Formula _∨_ : Formula → Formula → Formula
@@ -47,6 +46,9 @@ X ⇔ Y = (X ⇒ Y) ∧ (Y ⇒ X)
⊤ : Formula ⊤ : Formula
⊤ = ∼ ⊥ ⊤ = ∼ ⊥
◇_ : Formula → Formula
◇ p = ∼ (□ (∼ p))
infix 9 _∈_ infix 9 _∈_
data _∈_ {A : Type} : A → List A → Type where data _∈_ {A : Type} : A → List A → Type where
zero : (x : A) (xs : List A) → x ∈ (x ∷ xs) zero : (x : A) (xs : List A) → x ∈ (x ∷ xs)
@@ -61,12 +63,12 @@ infix 2 _,_⊩_
_,_⊩_ : {W : Type} (Model : M W) (x : W) (p : Formula) → Type _,_⊩_ : {W : Type} (Model : M W) (x : W) (p : Formula) → Type
Model , x ⊩ ⊥ = Bottom Model , x ⊩ ⊥ = Bottom
Model , x ⊩ atom n = n ∈ M.L Model x Model , x ⊩ atom n = n ∈ M.L Model x
Model , x ⊩ (∼ (□ (∼ p))) = ∃ λ y → M.R Model x y → Model , y ⊩ p -- Alias for ◇ p
Model , x ⊩ (∼ p) = ¬ (Model , x ⊩ p) Model , x ⊩ (∼ p) = ¬ (Model , x ⊩ p)
Model , x ⊩ (p ∧ q) = (Model , x ⊩ p) × (Model , x ⊩ q) Model , x ⊩ (p ∧ q) = (Model , x ⊩ p) × (Model , x ⊩ q)
Model , x ⊩ (p ∨ q) = (Model , x ⊩ p) ∪ (Model , x ⊩ q) Model , x ⊩ (p ∨ q) = (Model , x ⊩ p) ∪ (Model , x ⊩ q)
Model , x ⊩ p ⇒ q = Model , x ⊩ p → Model , x ⊩ q Model , x ⊩ p ⇒ q = Model , x ⊩ p → Model , x ⊩ q
Model , x ⊩ (□ p) = ∀ y → M.R Model x y → Model , y ⊩ p Model , x ⊩ (□ p) = ∀ y → M.R Model x y → Model , y ⊩ p
Model , x ⊩ (◇ p) = ∃ λ y → M.R Model x y → Model , y ⊩ p
data R : Nat → Nat → Type where data R : Nat → Nat → Type where
zeroone : R 0 1 zeroone : R 0 1
@@ -121,4 +123,3 @@ data _⊢_ : Context → Formula → Type where
¬ₑ : Γ ⊢ X → Γ ⊢ ∼ X → Γ ⊢ ⊥ ¬ₑ : Γ ⊢ X → Γ ⊢ ∼ X → Γ ⊢ ⊥
□ₑ : Γ ⊢ □ X → X ∈ Δ → Γ ++ boxed Δ ⊢ Y □ₑ : Γ ⊢ □ X → X ∈ Δ → Γ ++ boxed Δ ⊢ Y
□ᵢ : X ∈ Δ → Γ ++ boxed Δ ⊢ □ X □ᵢ : X ∈ Δ → Γ ++ boxed Δ ⊢ □ X
-- TODO: Add ◇