From 3db42fabef4833cb0193ce4605e43dc0254aa7b2 Mon Sep 17 00:00:00 2001
From: Benjamin Barenblat <bbaren@mit.edu>
Date: Wed, 22 Apr 2015 01:09:16 -0400
Subject: Initial commit of B

---
 Prelude/Eq.agda | 40 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 40 insertions(+)
 create mode 100644 Prelude/Eq.agda

(limited to 'Prelude/Eq.agda')

diff --git a/Prelude/Eq.agda b/Prelude/Eq.agda
new file mode 100644
index 0000000..4a7b84f
--- /dev/null
+++ b/Prelude/Eq.agda
@@ -0,0 +1,40 @@
+module B.Prelude.Eq where
+
+import Data.Bool as Bool
+open Bool using (Bool)
+import Data.Char as Char
+open Char using (Char)
+import Data.Nat as ℕ
+open ℕ using (ℕ)
+open import Function using (_$_)
+import Level
+open Level using (_⊔_)
+open import Relation.Nullary.Decidable using (⌊_⌋)
+open import Relation.Binary using (DecSetoid)
+
+record Eq {c} {ℓ} (t : Set c) : Set (Level.suc $ c ⊔ ℓ) where
+  field
+    decSetoid : DecSetoid c ℓ
+
+  _≟_ = DecSetoid._≟_ decSetoid
+
+  _==_ : DecSetoid.Carrier decSetoid
+       → DecSetoid.Carrier decSetoid
+       → Bool
+  x == y = ⌊ x ≟ y ⌋
+
+open Eq ⦃...⦄ public
+
+instance
+  Eq-Bool : Eq Bool
+  Eq-Bool = record { decSetoid = Bool.decSetoid }
+
+  Eq-Char : Eq Char
+  Eq-Char = record { decSetoid = Char.decSetoid }
+
+  -- TODO: Float
+
+  Eq-ℕ : Eq ℕ
+  Eq-ℕ =
+    let module DecTotalOrder = Relation.Binary.DecTotalOrder in
+    record { decSetoid = DecTotalOrder.Eq.decSetoid ℕ.decTotalOrder }
-- 
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