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open import Data.Empty | |
open import Relation.Nullary | |
infix 0 ⌊_⌋ | |
⌊_⌋ : ∀ {a} → Set a → Set a | |
⌊ A ⌋ = ¬ ¬ A | |
pure : ∀ {a} {A : Set a} → A → ⌊ A ⌋ | |
pure x = λ z → z x | |
_<*>_ : ∀ {a b} {A : Set a} {B : Set b} | |
→ ⌊ (A → B) ⌋ | |
→ ⌊ A ⌋ | |
→ ⌊ B ⌋ | |
fs <*> xs = λ z → xs (λ z₁ → fs (λ z₂ → z (z₂ z₁))) | |
_>>=_ : ∀ {a b} {A : Set a} {B : Set b} | |
→ ⌊ A ⌋ | |
→ (A → ⌊ B ⌋) | |
→ ⌊ B ⌋ | |
xs >>= f = λ z → xs (λ z₁ → f z₁ z) | |
open import Data.Sum | |
lem : ∀ {a} {A : Set a} → ⌊ A ⊎ ¬ A ⌋ | |
lem = λ z → z (inj₂ (λ x → z (inj₁ x))) | |
_↓_ : ∀ {a} {A : Set a} → ⌊ A ⌋ → A ⊎ ¬ A → A | |
_ ↓ inj₁ x = x | |
x ↓ inj₂ y = ⊥-elim (x y) |
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