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.
43 lines
1.2 KiB
Text
43 lines
1.2 KiB
Text
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inductive Formula
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| eqf : Nat → Nat → Formula
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| andf : Formula → Formula → Formula
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| impf : Formula → Formula → Formula
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| notf : Formula → Formula
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| orf : Formula → Formula → Formula
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| allf : (Nat → Formula) → Formula
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namespace Formula
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def implies (a b : Prop) : Prop := a → b
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def denote : Formula → Prop
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| eqf n1 n2 => n1 = n2
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| andf f1 f2 => denote f1 ∧ denote f2
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| impf f1 f2 => implies (denote f1) (denote f2)
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| orf f1 f2 => denote f1 ∨ denote f2
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| notf f => ¬ denote f
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| allf f => (n : Nat) → denote (f n)
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theorem denote_eqf (n1 n2 : Nat) : denote (eqf n1 n2) = (n1 = n2) :=
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rfl
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theorem denote_andf (f1 f2 : Formula) : denote (andf f1 f2) = (denote f1 ∧ denote f2) :=
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rfl
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theorem denote_impf (f1 f2 : Formula) : denote (impf f1 f2) = (denote f1 → denote f2) :=
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rfl
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theorem denote_orf (f1 f2 : Formula) : denote (orf f1 f2) = (denote f1 ∨ denote f2) :=
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rfl
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theorem denote_notf (f : Formula) : denote (notf f) = ¬ denote f :=
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rfl
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theorem denote_allf (f : Nat → Formula) : denote (allf f) = (∀ n, denote (f n)) :=
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rfl
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theorem ex : denote (allf (fun n₁ => allf (fun n₂ => impf (eqf n₁ n₂) (eqf n₂ n₁)))) = (∀ (n₁ n₂ : Nat), n₁ = n₂ → n₂ = n₁) :=
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rfl
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end Formula
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