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https://github.com/leanprover/lean4.git
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08eb78a5b2
This PR sets up the new integrated test/bench suite. It then migrates all benchmarks and some related tests to the new suite. There's also some documentation and some linting. For now, a lot of the old tests are left alone so this PR doesn't become even larger than it already is. Eventually, all tests should be migrated to the new suite though so there isn't a confusing mix of two systems.
58 lines
1.8 KiB
Lean4
58 lines
1.8 KiB
Lean4
set_option warn.sorry false
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axiom A : Type
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axiom B : Type
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axiom A.toB : A → B
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axiom B.toA : B → A
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open Lean.Order
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instance : PartialOrder A := sorry
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-- It’s important that the CCPO instance isn't completely axiomatic, so that
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-- `instCCPO.toOrder` is defeq to `instOrder`
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instance : CCPO A where
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has_csup := sorry
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instance : PartialOrder B := sorry
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instance : CCPO B where
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has_csup := sorry
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@[partial_fixpoint_monotone] axiom monotone_toA :
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∀ {α} [PartialOrder α] (f : α → B), monotone f → monotone (fun x => B.toA (f x))
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@[partial_fixpoint_monotone] axiom monotone_toB :
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∀ {α} [PartialOrder α] (f : α → A), monotone f → monotone (fun x => A.toB (f x))
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mutual
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noncomputable def f : A := g.toA
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partial_fixpoint
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noncomputable def g : B := f.toB
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partial_fixpoint
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end
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/--
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info: equations:
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theorem f.eq_1 : f = g.toA
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-/
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#guard_msgs in #print equations f
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/--
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info: f.fixpoint_induct (motive_1 : A → Prop) (motive_2 : B → Prop) (adm_1 : admissible motive_1)
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(adm_2 : admissible motive_2) (h_1 : ∀ (g : B), motive_2 g → motive_1 g.toA)
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(h_2 : ∀ (f : A), motive_1 f → motive_2 f.toB) : motive_1 f
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-/
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#guard_msgs in
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#check f.fixpoint_induct
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/--
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info: g.fixpoint_induct (motive_1 : A → Prop) (motive_2 : B → Prop) (adm_1 : admissible motive_1)
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(adm_2 : admissible motive_2) (h_1 : ∀ (g : B), motive_2 g → motive_1 g.toA)
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(h_2 : ∀ (f : A), motive_1 f → motive_2 f.toB) : motive_2 g
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-/
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#guard_msgs in
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#check g.fixpoint_induct
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/--
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info: f.mutual_fixpoint_induct (motive_1 : A → Prop) (motive_2 : B → Prop) (adm_1 : admissible motive_1)
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(adm_2 : admissible motive_2) (h_1 : ∀ (g : B), motive_2 g → motive_1 g.toA)
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(h_2 : ∀ (f : A), motive_1 f → motive_2 f.toB) : motive_1 f ∧ motive_2 g
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-/
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#guard_msgs in
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#check f.mutual_fixpoint_induct
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