2a67a49f31
This PR deprecates the tactics `simp_arith`, `simp_arith!`, `simp_all_arith` and `simp_all_arith!`. Users can just use the `+arith` option.
45 lines
1.6 KiB
Text
45 lines
1.6 KiB
Text
structure Pos where
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protected succ :: protected pred : Nat
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deriving Repr
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protected def Pos.add : Pos → Pos → Pos
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| .succ x, .succ y => .succ (x + y).succ
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instance : Add Pos := ⟨Pos.add⟩
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instance (x : Nat) : OfNat Pos x.succ := ⟨.succ x⟩
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/-- View for `Pos` type. -/
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inductive PosView where
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| one
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| succ (x : Pos)
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/--
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Convert `Pos` into `PosView`.
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Remark: nonrecursive views do not impact performance of the generated code if marked as `[inline]`
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-/
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@[inline] def Pos.view (p : Pos) : PosView :=
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match p with
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| { pred := 0 } => PosView.one
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| { pred := Nat.succ n } => PosView.succ ⟨n⟩
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/--
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Helper theorem for proving termination.
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In the future, we should be able to mark it as a forward reasoning theorem for `decreasing_tactic`,
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and it will be applied automatically for us. -/
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theorem sizeof_lt_of_view_eq (h : Pos.view p₁ = PosView.succ p₂) : sizeOf p₂ < sizeOf p₁ := by
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match p₁, p₂ with
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| { pred := Nat.succ n }, { pred := Nat.succ m } => simp [Pos.view] at h; simp +arith [h]
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| { pred := Nat.succ n }, { pred := 0 } => simp [Pos.view] at h; simp +arith [h]
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| { pred := 0 }, _ => simp [Pos.view] at h
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/-- `1` as notation for `PosView.one` -/
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instance : OfNat PosView (nat_lit 1) where
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ofNat := PosView.one
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def f (p : Pos) : Pos :=
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match h : p.view with -- It would also be nice to have a feature to force Lean to applies "views" automatically for us.
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| 1 => 1
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| .succ x =>
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have : sizeOf x < sizeOf p := sizeof_lt_of_view_eq h -- See comment at `sizeof_lt_of_view_eq`
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f x + x + 1
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