wtf

.gitignore

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+*.agdai

cubical-playground.agda-lib

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+include: src
+depend: standard-library

src/2022-10-03-notes.lagda.md

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 ```
-{#- OPTIONS --cubical -#}
+{-# OPTIONS --cubical #-}
 
 ----------
 

src/2022-10-10-notes.lagda.md

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+2022 Oct 10
+===
+
+```agda
+{-# OPTIONS --cubical #-}
+
+-- Hello
+```

src/Dedekind/Bool.agda

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+module Dedekind.Bool where
+
+-- Booleans
+data Bool : Set where
+  true : Bool
+  false : Bool
+
+

src/Dedekind/Integer.agda

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+module Dedekind.Integer where
+
+open import Dedekind.Natural using (ℕ)
+
+-- Integers
+data ℤ : Set where
+  pos : ℕ → ℤ
+  negsuc : ℕ → ℤ

src/Dedekind/Natural.agda

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+module Dedekind.Natural where
+
+open import Dedekind.Set using (⊤; ⊥)
+
+-- Natural
+data ℕ : Set where
+  zero : ℕ
+  suc : ℕ → ℕ
+
+NonZero : ℕ → Set
+NonZero zero = ⊥
+NonZero (suc n) = ⊤
+
+gcd : (x y : ℕ) .{{ _ : NonZero x }} .{{ _ : NonZero y }} → ℕ
+gcd x y = ?

src/Dedekind/Rational.agda

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+module Dedekind.Rational where
+
+open import Dedekind.Bool using (Bool)
+open import Dedekind.Integer using (ℤ)
+open import Dedekind.Natural using (ℕ; NonZero)
+
+-- Rational
+data ℚ : Set where
+  rat : ℤ → (d : ℕ) .{{ _ : NonZero d }} → ℚ
+
+_<_ : ℚ → ℚ → Bool
+x < y = ?

src/Dedekind/Real.agda

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+-- Dedekind cuts using Cubical Agda
+{-# OPTIONS --cubical #-}
+
+module Dedekind.Real where
+
+open import Dedekind.Rational using (ℚ; _<_)
+
+-- Dedekind cuts
+record ℝ : Set where
+  constructor real
+  field
+    lower : (ℚ → Bool)
+    closed : ∀ (x y : ℚ) → x < y
+
+-- Operations on reals
+_+_ : ℝ → ℝ → ℝ
+a + b = real 
+  (λ q → ℝ.lower a q)
+
+-- Properties of reals

src/Dedekind/Set.agda

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+module Dedekind.Set where
+
+record ⊥ : Set where
+
+record ⊤ : Set where
+  instance constructor tt

src/main.agda

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+{-# OPTIONS --guardedness #-}
+
+module main where
+
+open import Agda.Builtin.IO using (IO)
+open import Agda.Builtin.Unit using (⊤)
+open import Agda.Builtin.String using (String)
+
+postulate putStrLn : String → IO ⊤
+{-# FOREIGN GHC import qualified Data.Text as T #-}
+{-# COMPILE GHC putStrLn = putStrLn . T.unpack #-}
+
+main : IO ⊤
+main = putStrLn "Hello world!"