d6f778bec4
@Kha I was tired of writing `arbitrary _` :) There 0 places in the stdlib where the type needs to be provided. If in the future we need to specify the type we can use `arbitrary (α := <type>)`
80 lines
5.8 KiB
Text
80 lines
5.8 KiB
Text
/-
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Copyright (c) 2019 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.Data.UInt
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universe u
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def bfix1 {α β : Type u} (base : α → β) (rec : (α → β) → α → β) : Nat → α → β
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| 0, a => base a
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| n+1, a => rec (bfix1 base rec n) a
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@[extern c inline "lean_fixpoint(#4, #5)"]
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def fixCore1 {α β : Type u} (base : @& (α → β)) (rec : (α → β) → α → β) : α → β :=
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bfix1 base rec USize.size
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@[inline] def fixCore {α β : Type u} (base : @& (α → β)) (rec : (α → β) → α → β) : α → β :=
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fixCore1 base rec
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@[inline] def fix1 {α β : Type u} [Inhabited β] (rec : (α → β) → α → β) : α → β :=
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fixCore1 (fun _ => arbitrary) rec
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@[inline] def fix {α β : Type u} [Inhabited β] (rec : (α → β) → α → β) : α → β :=
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fixCore1 (fun _ => arbitrary) rec
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def bfix2 {α₁ α₂ β : Type u} (base : α₁ → α₂ → β) (rec : (α₁ → α₂ → β) → α₁ → α₂ → β) : Nat → α₁ → α₂ → β
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| 0, a₁, a₂ => base a₁ a₂
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| n+1, a₁, a₂ => rec (bfix2 base rec n) a₁ a₂
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@[extern c inline "lean_fixpoint2(#5, #6, #7)"]
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def fixCore2 {α₁ α₂ β : Type u} (base : α₁ → α₂ → β) (rec : (α₁ → α₂ → β) → α₁ → α₂ → β) : α₁ → α₂ → β :=
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bfix2 base rec USize.size
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@[inline] def fix2 {α₁ α₂ β : Type u} [Inhabited β] (rec : (α₁ → α₂ → β) → α₁ → α₂ → β) : α₁ → α₂ → β :=
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fixCore2 (fun _ _ => arbitrary) rec
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def bfix3 {α₁ α₂ α₃ β : Type u} (base : α₁ → α₂ → α₃ → β) (rec : (α₁ → α₂ → α₃ → β) → α₁ → α₂ → α₃ → β) : Nat → α₁ → α₂ → α₃ → β
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| 0, a₁, a₂, a₃ => base a₁ a₂ a₃
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| n+1, a₁, a₂, a₃ => rec (bfix3 base rec n) a₁ a₂ a₃
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@[extern c inline "lean_fixpoint3(#6, #7, #8, #9)"]
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def fixCore3 {α₁ α₂ α₃ β : Type u} (base : α₁ → α₂ → α₃ → β) (rec : (α₁ → α₂ → α₃ → β) → α₁ → α₂ → α₃ → β) : α₁ → α₂ → α₃ → β :=
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bfix3 base rec USize.size
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@[inline] def fix3 {α₁ α₂ α₃ β : Type u} [Inhabited β] (rec : (α₁ → α₂ → α₃ → β) → α₁ → α₂ → α₃ → β) : α₁ → α₂ → α₃ → β :=
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fixCore3 (fun _ _ _ => arbitrary) rec
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def bfix4 {α₁ α₂ α₃ α₄ β : Type u} (base : α₁ → α₂ → α₃ → α₄ → β) (rec : (α₁ → α₂ → α₃ → α₄ → β) → α₁ → α₂ → α₃ → α₄ → β) : Nat → α₁ → α₂ → α₃ → α₄ → β
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| 0, a₁, a₂, a₃, a₄ => base a₁ a₂ a₃ a₄
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| n+1, a₁, a₂, a₃, a₄ => rec (bfix4 base rec n) a₁ a₂ a₃ a₄
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@[extern c inline "lean_fixpoint4(#7, #8, #9, #10, #11)"]
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def fixCore4 {α₁ α₂ α₃ α₄ β : Type u} (base : α₁ → α₂ → α₃ → α₄ → β) (rec : (α₁ → α₂ → α₃ → α₄ → β) → α₁ → α₂ → α₃ → α₄ → β) : α₁ → α₂ → α₃ → α₄ → β :=
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bfix4 base rec USize.size
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@[inline] def fix4 {α₁ α₂ α₃ α₄ β : Type u} [Inhabited β] (rec : (α₁ → α₂ → α₃ → α₄ → β) → α₁ → α₂ → α₃ → α₄ → β) : α₁ → α₂ → α₃ → α₄ → β :=
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fixCore4 (fun _ _ _ _ => arbitrary) rec
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def bfix5 {α₁ α₂ α₃ α₄ α₅ β : Type u} (base : α₁ → α₂ → α₃ → α₄ → α₅ → β) (rec : (α₁ → α₂ → α₃ → α₄ → α₅ → β) → α₁ → α₂ → α₃ → α₄ → α₅ → β) : Nat → α₁ → α₂ → α₃ → α₄ → α₅ → β
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| 0, a₁, a₂, a₃, a₄, a₅ => base a₁ a₂ a₃ a₄ a₅
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| n+1, a₁, a₂, a₃, a₄, a₅ => rec (bfix5 base rec n) a₁ a₂ a₃ a₄ a₅
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@[extern c inline "lean_fixpoint5(#8, #9, #10, #11, #12, #13)"]
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def fixCore5 {α₁ α₂ α₃ α₄ α₅ β : Type u} (base : α₁ → α₂ → α₃ → α₄ → α₅ → β) (rec : (α₁ → α₂ → α₃ → α₄ → α₅ → β) → α₁ → α₂ → α₃ → α₄ → α₅ → β) : α₁ → α₂ → α₃ → α₄ → α₅ → β :=
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bfix5 base rec USize.size
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@[inline] def fix5 {α₁ α₂ α₃ α₄ α₅ β : Type u} [Inhabited β] (rec : (α₁ → α₂ → α₃ → α₄ → α₅ → β) → α₁ → α₂ → α₃ → α₄ → α₅ → β) : α₁ → α₂ → α₃ → α₄ → α₅ → β :=
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fixCore5 (fun _ _ _ _ _ => arbitrary) rec
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def bfix6 {α₁ α₂ α₃ α₄ α₅ α₆ β : Type u} (base : α₁ → α₂ → α₃ → α₄ → α₅ → α₆ → β) (rec : (α₁ → α₂ → α₃ → α₄ → α₅ → α₆ → β) → α₁ → α₂ → α₃ → α₄ → α₅ → α₆ → β) : Nat → α₁ → α₂ → α₃ → α₄ → α₅ → α₆ → β
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| 0, a₁, a₂, a₃, a₄, a₅, a₆ => base a₁ a₂ a₃ a₄ a₅ a₆
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| n+1, a₁, a₂, a₃, a₄, a₅, a₆ => rec (bfix6 base rec n) a₁ a₂ a₃ a₄ a₅ a₆
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@[extern c inline "lean_fixpoint6(#9, #10, #11, #12, #13, #14, #15)"]
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def fixCore6 {α₁ α₂ α₃ α₄ α₅ α₆ β : Type u} (base : α₁ → α₂ → α₃ → α₄ → α₅ → α₆ → β) (rec : (α₁ → α₂ → α₃ → α₄ → α₅ → α₆ → β) → α₁ → α₂ → α₃ → α₄ → α₅ → α₆ → β) : α₁ → α₂ → α₃ → α₄ → α₅ → α₆ → β :=
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bfix6 base rec USize.size
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@[inline] def fix6 {α₁ α₂ α₃ α₄ α₅ α₆ β : Type u} [Inhabited β] (rec : (α₁ → α₂ → α₃ → α₄ → α₅ → α₆ → β) → α₁ → α₂ → α₃ → α₄ → α₅ → α₆ → β) : α₁ → α₂ → α₃ → α₄ → α₅ → α₆ → β :=
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fixCore6 (fun _ _ _ _ _ _ => arbitrary) rec
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