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{-# OPTIONS --cubical-compatible #-}
module Padova2025.ComputationalContent.DoubleNegation (⊥ : Set) where

Sarcastic interpretation of classical logic

Explain.

open import Padova2025.ProvingBasics.Connectives.Disjunction
open import Padova2025.ProvingBasics.Connectives.More
open import Padova2025.ProgrammingBasics.Lists

infix 3 ¬_
¬_ : Set → Set  -- enter `¬` as `\neg`
¬ P = (P → ⊥)

return : {A : Set} → A → ¬ ¬ A
return = {!!}

⊥-elim : {A : Set} → ⊥ → ¬ ¬ A
⊥-elim = {!!}

escape : ¬ ¬ ⊥ → ⊥
escape = {!!}

oracle : {A : Set} → ¬ ¬ (A ⊎ ¬ A)
oracle = {!!}

infixl 1 _>>=_ _⟫=_

_>>=_ : {A B : Set} → ¬ ¬ A → (A → ¬ ¬ B) → ¬ ¬ B
_>>=_ = {!!}

_⟫=_ : {A B : Set} → ¬ ¬ A → (A → ¬ ¬ B) → ¬ ¬ B
_⟫=_ = _>>=_

liftA2 : {A B C : Set} → (A → B → C) → ¬ ¬ A → ¬ ¬ B → ¬ ¬ C
liftA2 = {!!}

sequence : {X : Set} {P : X → Set} {xs : List X} → All (λ x → ¬ ¬ P x) xs → ¬ ¬ All P xs
sequence = {!!}