42fbe3c18c
The new `partial def`s allow us to define `fix` in Lean, but the Lean implementation is not as efficient as the native one. The native one in C++ use weak pointers to prevent a closure allocation at every recursive invocation. This commit also fixes the `fixCore` helper functions that were broken after we switched to camelCase. We have updated the test `fix1.lean` to demonstrate the native implementation is faster. Here are the numbers on my desktop. ``` ./run.sh fix1.lean 24 721420279 Time for 'native fix': 816ms 721420279 Time for 'fix in lean': 1.34s ```
80 lines
5.6 KiB
Text
80 lines
5.6 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 n) a
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@[extern cpp 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 usizeSz
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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 (λ _, default β) 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 (λ _, default β) 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 n) a₁ a₂
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@[extern cpp 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 usizeSz
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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 (λ _ _, default β) 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 n) a₁ a₂ a₃
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@[extern cpp 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 usizeSz
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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 (λ _ _ _, default β) 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 n) a₁ a₂ a₃ a₄
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@[extern cpp 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 usizeSz
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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 (λ _ _ _ _, default β) 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 n) a₁ a₂ a₃ a₄ a₅
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@[extern cpp 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 usizeSz
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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 (λ _ _ _ _ _, default β) 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 n) a₁ a₂ a₃ a₄ a₅ a₆
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@[extern cpp 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 usizeSz
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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 (λ _ _ _ _ _ _, default β) rec
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