99 lines
4.1 KiB
Text
99 lines
4.1 KiB
Text
/-
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Copyright (c) 2020 Microsoft Corporation. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Leonardo de Moura
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-/
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prelude
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import Init.Core
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import Init.Data.ToString
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structure FloatSpec :=
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(float : Type)
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(val : float)
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(lt : float → float → Prop)
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(le : float → float → Prop)
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(decLt : DecidableRel lt)
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(decLe : DecidableRel le)
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-- Just show FloatSpec is inhabited.
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constant floatSpec : FloatSpec := {
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float := Unit,
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val := (),
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lt := fun _ _ => True,
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le := fun _ _ => True,
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decLt := fun _ _ => inferInstanceAs (Decidable True),
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decLe := fun _ _ => inferInstanceAs (Decidable True)
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}
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structure Float :=
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(val : floatSpec.float)
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instance : Inhabited Float := ⟨{ val := floatSpec.val }⟩
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@[extern "lean_float_of_nat"] constant Float.ofNat : (@& Nat) → Float := arbitrary _
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@[extern c inline "#1 + #2"] constant Float.add : Float → Float → Float := arbitrary _
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@[extern c inline "#1 - #2"] constant Float.sub : Float → Float → Float := arbitrary _
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@[extern c inline "#1 * #2"] constant Float.mul : Float → Float → Float := arbitrary _
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@[extern c inline "#1 / #2"] constant Float.div : Float → Float → Float := arbitrary _
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def Float.lt : Float → Float → Prop :=
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fun a b => match a, b with
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def Float.le : Float → Float → Prop := fun a b => floatSpec.le a.val b.val
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instance : HasZero Float := ⟨Float.ofNat 0⟩
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instance : HasOne Float := ⟨Float.ofNat 1⟩
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instance : HasOfNat Float := ⟨Float.ofNat⟩
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instance : HasAdd Float := ⟨Float.add⟩
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instance : HasSub Float := ⟨Float.sub⟩
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instance : HasMul Float := ⟨Float.mul⟩
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instance : HasDiv Float := ⟨Float.div⟩
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instance : HasLess Float := ⟨Float.lt⟩
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instance : HasLessEq Float := ⟨Float.le⟩
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@[extern c inline "#1 == #2"] constant Float.beq (a b : Float) : Bool := arbitrary _
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instance : HasBeq Float := ⟨Float.beq⟩
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@[extern c inline "#1 < #2"] constant Float.decLt (a b : Float) : Decidable (a < b) :=
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match a, b with
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| ⟨a⟩, ⟨b⟩ => floatSpec.decLt a b
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@[extern c inline "#1 <= #2"] constant Float.decLe (a b : Float) : Decidable (a ≤ b) :=
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match a, b with
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instance floatDecLt (a b : Float) : Decidable (a < b) := Float.decLt a b
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instance floatDecLe (a b : Float) : Decidable (a ≤ b) := Float.decLe a b
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@[extern "lean_float_to_string"] constant Float.toString : Float → String := arbitrary _
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instance : HasToString Float := ⟨Float.toString⟩
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abbrev Nat.toFloat (n : Nat) : Float :=
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Float.ofNat n
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@[extern "sin"] constant Float.sin : Float → Float := arbitrary _
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@[extern "cos"] constant Float.cos : Float → Float := arbitrary _
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@[extern "tan"] constant Float.tan : Float → Float := arbitrary _
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@[extern "asin"] constant Float.asin : Float → Float := arbitrary _
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@[extern "acos"] constant Float.acos : Float → Float := arbitrary _
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@[extern "atan"] constant Float.atan : Float → Float := arbitrary _
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@[extern "atan2"] constant Float.atan2 : Float → Float → Float := arbitrary _
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@[extern "sinh"] constant Float.sinh : Float → Float := arbitrary _
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@[extern "cosh"] constant Float.cosh : Float → Float := arbitrary _
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@[extern "tanh"] constant Float.tanh : Float → Float := arbitrary _
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@[extern "asinh"] constant Float.asinh : Float → Float := arbitrary _
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@[extern "acosh"] constant Float.acosh : Float → Float := arbitrary _
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@[extern "atanh"] constant Float.atanh : Float → Float := arbitrary _
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@[extern "exp"] constant Float.exp : Float → Float := arbitrary _
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@[extern "exp2"] constant Float.exp2 : Float → Float := arbitrary _
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@[extern "log"] constant Float.log : Float → Float := arbitrary _
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@[extern "log2"] constant Float.log2 : Float → Float := arbitrary _
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@[extern "log10"] constant Float.log10 : Float → Float := arbitrary _
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@[extern "pow"] constant Float.pow : Float → Float → Float := arbitrary _
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@[extern "sqrt"] constant Float.sqrt : Float → Float := arbitrary _
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@[extern "cbrt"] constant Float.cbrt : Float → Float := arbitrary _
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instance : HasPow Float Float := ⟨Float.pow⟩
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