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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.
60 lines
1.9 KiB
Lean4
60 lines
1.9 KiB
Lean4
inductive Term
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| Var (i : Nat)
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| Cons (l : Term) (r : Term)
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def Subst := Nat → Nat
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def depth : Term → Nat
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| .Var _ => 0
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| .Cons l r => 1 + depth l + depth r
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def act (f : Subst) (t : Term) := match t with
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| .Var i => Term.Var (f i)
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| .Cons l r => Term.Cons (act f l) (act f r)
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def strangers (u v : Term) := ∀ f : Subst, act f u ≠ act f v
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abbrev P (c : Option Subst) u v := match c with
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| none => strangers u v
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| some f => act f u = act f v
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instance rel : WellFoundedRelation (Term × Term) := measure (λ (u, v) => depth u + depth v)
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theorem decr_left (l₁ r₁ l₂ r₂ : Term) :
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rel.rel (l₁, l₂) (Term.Cons l₁ r₁, Term.Cons l₂ r₂) := by
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suffices h : depth l₁ + depth l₂ < depth (Term.Cons l₁ r₁) + depth (Term.Cons l₂ r₂) from h
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admit
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theorem decr_right (l₁ r₁ l₂ r₂ : Term) (f : Subst) :
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rel.rel (act f r₁, act f r₂) (Term.Cons l₁ r₁, Term.Cons l₂ r₂) := by
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suffices h : depth (act f r₁) + depth (act f r₂) < depth (Term.Cons l₁ r₁) + depth (Term.Cons l₂ r₂) from h
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admit
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def robinson (u v : Term) : { f : Option Subst // P f u v } := match u, v with
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| .Cons l₁ r₁, .Cons l₂ r₂ => match robinson l₁ l₂ with
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| ⟨ none, h ⟩ => ⟨ none, sorry ⟩
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| ⟨ some f, h ⟩ => match robinson (act f r₁) (act f r₂) with
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| ⟨ none, h ⟩ => ⟨ none, sorry ⟩
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| ⟨ some g, h ⟩ => ⟨ some (g ∘ f), sorry ⟩
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| .Var i, .Cons l r => ⟨ none, sorry ⟩
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| .Cons l r, .Var i => ⟨ none, sorry ⟩
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| .Var i, .Var j =>
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if i = j then ⟨ some id, sorry ⟩
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else ⟨ some λ n => if n = i then j else n, sorry ⟩
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termination_by (u, v)
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decreasing_by
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· apply decr_left _ _ _ _
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· apply decr_right _ _ _ _ _
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attribute [simp] robinson
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set_option pp.proofs true
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#check robinson.eq_1
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#check robinson.eq_2
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#check robinson.eq_3
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#check robinson.eq_4
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theorem ex : (robinson (Term.Var 0) (Term.Var 0)).1 = some id := by
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unfold robinson
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admit
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