ab318dda2d
no need to enter `derive_functional_induction` anymore. (Will remove the support for `derive_functional_induction` after the next stage0 update, since we are already using it in Init.)
30 lines
1.1 KiB
Text
30 lines
1.1 KiB
Text
set_option autoImplicit false
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def ackermann : Nat → Nat → Nat
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| 0, m => m + 1
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| n+1, 0 => ackermann n 1
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| n+1, m+1 => ackermann n (ackermann (n + 1) m)
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/--
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info: ackermann.induct (motive : Nat → Nat → Prop) (case1 : ∀ (m : Nat), motive 0 m)
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(case2 : ∀ (n : Nat), motive n 1 → motive n.succ 0)
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(case3 : ∀ (n m : Nat), motive (n + 1) m → motive n (ackermann (n + 1) m) → motive n.succ m.succ) :
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∀ (a a_1 : Nat), motive a a_1
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-/
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#guard_msgs in
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#check ackermann.induct
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-- TODO: Remove when `List.attach` is upstreamed from std
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def List.attach {α} : (l : List α) → List {x // x ∈ l}
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| [] => []
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| x::xs => ⟨x, List.mem_cons_self _ _⟩ :: xs.attach.map (fun ⟨y, hy⟩ => ⟨y, mem_cons_of_mem _ hy⟩)
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inductive Tree | node : List Tree → Tree
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def Tree.rev : Tree → Tree | node ts => .node (ts.attach.map (fun ⟨t, _ht⟩ => t.rev) |>.reverse)
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/--
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info: Tree.rev.induct (motive : Tree → Prop)
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(case1 : ∀ (ts : List Tree), (∀ (t : Tree), t ∈ ts → motive t) → motive (Tree.node ts)) : ∀ (a : Tree), motive a
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-/
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#guard_msgs in
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#check Tree.rev.induct
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