feat: add Float.lean

src/Init/Data/Float.lean

@@ -0,0 +1,58 @@
+/-
+Copyright (c) 2020 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+-/
+prelude
+import Init.Core
+import Init.Data.ToString
+
+structure FloatSpec :=
+(float : Type)
+(val   : float)
+(lt    : float → float → Prop)
+(le    : float → float → Prop)
+(decEq : DecidableEq float)
+(decLt : DecidableRel lt)
+(decLe : DecidableRel le)
+
+-- Just show FloatSpec is inhabited.
+constant floatSpec : FloatSpec := {
+  float := Unit,
+  val   := (),
+  lt    := fun _ _ => True,
+  le    := fun _ _ => True,
+  decEq := inferInstanceAs (DecidableEq Unit),
+  decLt := fun _ _ => inferInstanceAs (Decidable True),
+  decLe := fun _ _ => inferInstanceAs (Decidable True)
+}
+
+def Float : Type := floatSpec.float
+instance : Inhabited Float := ⟨floatSpec.val⟩
+
+@[extern "lean_float_of_nat"] constant Float.ofNat : (@& Nat) → Float := arbitrary _
+@[extern "lean_float_add"]    constant Float.add : Float → Float → Float := arbitrary _
+@[extern "lean_float_sub"]    constant Float.sub : Float → Float → Float := arbitrary _
+@[extern "lean_float_mul"]    constant Float.mul : Float → Float → Float := arbitrary _
+@[extern "lean_float_div"]    constant Float.div : Float → Float → Float := arbitrary _
+
+def Float.lt  : Float → Float → Prop := floatSpec.lt
+def Float.le  : Float → Float → Prop := floatSpec.le
+
+instance : HasZero Float   := ⟨Float.ofNat 0⟩
+instance : HasOne Float    := ⟨Float.ofNat 1⟩
+instance : HasOfNat Float  := ⟨Float.ofNat⟩
+instance : HasAdd Float    := ⟨Float.add⟩
+instance : HasSub Float    := ⟨Float.sub⟩
+instance : HasMul Float    := ⟨Float.mul⟩
+instance : HasDiv Float    := ⟨Float.div⟩
+instance : HasLess Float   := ⟨Float.lt⟩
+instance : HasLessEq Float := ⟨Float.le⟩
+
+@[extern "lean_float_eq"] constant Float.decEq (a b : Float) : Decidable (a = b) := floatSpec.decEq a b
+@[extern "lean_float_lt"] constant Float.decLt (a b : Float) : Decidable (a < b) := floatSpec.decLt a b
+@[extern "lean_float_le"] constant Float.decLe (a b : Float) : Decidable (a ≤ b) := floatSpec.decLe a b
+
+@[extern "lean_float_to_string"] constant Float.toString : Float → String := arbitrary _
+
+instance : HasToString Float := ⟨Float.toString⟩