facc356a0a
Typos were found with ``` pip install codespell --upgrade codespell --summary --ignore-words-list enew,forin,fro,happend,hge,ihs,iterm,spred --skip stage0 --check-filenames codespell --summary --ignore-words-list enew,forin,fro,happend,hge,ihs,iterm,spred --skip stage0 --check-filenames --regex '[A-Z][a-z]*' codespell --summary --ignore-words-list enew,forin,fro,happend,hge,ihs,iterm,spred --skip stage0 --check-filenames --regex "\b[a-z']*" ```
66 lines
2 KiB
Text
66 lines
2 KiB
Text
module
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public axiom P : Nat → Prop
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public axiom P.intro : P n
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public inductive AckFuel : (n m : Nat) → Type where
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| step1 : AckFuel 0 m
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| step2 : AckFuel n 1 → AckFuel (n + 1) 0
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| step3 : (∀ m', P m' → AckFuel n m') → AckFuel (n + 1) m → AckFuel (n+1) (m + 1)
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namespace Test1
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/-- info: Try this: termination_by structural x _ x => x -/
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#guard_msgs in
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public def ackermann_fuel : (n m : Nat) → (fuel : AckFuel n m) → Nat
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| 0, m, .step1 => m+1
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| n + 1, 0, .step2 f => ackermann_fuel n 1 f
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| n + 1, m + 1, .step3 f1 f2 =>
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ackermann_fuel n (ackermann_fuel (n + 1) m f2) (f1 _ (by exact P.intro))
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termination_by?
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end Test1
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namespace Test2
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/-- info: Try this: termination_by structural x _ x => x -/
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#guard_msgs in
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public def ackermann_fuel : (n m : Nat) → (fuel : AckFuel n m) → Nat
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| 0, m, .step1 => m+1
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| n + 1, 0, .step2 f => ackermann_fuel n 1 f
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| n + 1, m + 1, .step3 f1 f2 =>
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ackermann_fuel n (ackermann_fuel (n + 1) m f2) (f1 _ (by as_aux_lemma => exact P.intro))
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termination_by?
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end Test2
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namespace Test3
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/-- info: Try this: termination_by structural x _ x => x -/
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#guard_msgs in
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@[expose] public def ackermann_fuel : (n m : Nat) → (fuel : AckFuel n m) → Nat
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| 0, m, .step1 => m+1
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| n + 1, 0, .step2 f => ackermann_fuel n 1 f
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| n + 1, m + 1, .step3 f1 f2 =>
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ackermann_fuel n (ackermann_fuel (n + 1) m f2) (f1 _ (by exact P.intro))
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termination_by?
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end Test3
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namespace Test4
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-- This checks that when unfolding abstracted proofs, we do not unfold function calls
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-- that were actually there, like the one to `Function.cons` below
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/--
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error: failed to infer structural recursion:
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Cannot use parameter #3:
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unexpected occurrence of recursive application
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ackermann_fuel
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-/
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#guard_msgs in
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public def ackermann_fuel : (n m : Nat) → (fuel : AckFuel n m) → Nat
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| 0, m, .step1 => m+1
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| n + 1, 0, .step2 f => ackermann_fuel n 1 f
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| n + 1, m + 1, .step3 f1 f2 =>
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Function.const _
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( ackermann_fuel n (ackermann_fuel (n + 1) m f2) (f1 _ (by exact P.intro))
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)
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ackermann_fuel
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termination_by structural _ _ fuel => fuel
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end Test4
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