mirror of
https://github.com/leanprover/lean4.git
synced 2026-03-17 18:34:06 +00:00
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.
90 lines
2.2 KiB
Lean4
90 lines
2.2 KiB
Lean4
def f (x : Nat) : Nat :=
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match x with
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| 30 => 31
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| y+1 => y
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| 0 => 10
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#eval f 20
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#eval f 0
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#eval f 30
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universe u
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theorem ex1 {α : Sort u} {a b : α} (h : a ≍ b) : a = b :=
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match α, a, b, h with
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| _, _, _, HEq.refl _ => rfl
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theorem ex2 {α : Sort u} {a b : α} (h : a ≍ b) : a = b :=
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match a, b, h with
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| _, _, HEq.refl _ => rfl
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theorem ex3 {α : Sort u} {a b : α} (h : a ≍ b) : a = b :=
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match b, h with
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| _, HEq.refl _ => rfl
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theorem ex4 {α β : Sort u} {b : β} {a a' : α} (h₁ : a = a') (h₂ : a' ≍ b) : a ≍ b :=
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match β, a', b, h₁, h₂ with
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| _, _, _, rfl, HEq.refl _ => HEq.refl _
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theorem ex5 {α β : Sort u} {b : β} {a a' : α} (h₁ : a = a') (h₂ : a' ≍ b) : a ≍ b :=
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match a', h₁, h₂ with
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| _, rfl, h₂ => h₂
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theorem ex6 {α β : Sort u} {b : β} {a a' : α} (h₁ : a = a') (h₂ : a' ≍ b) : a ≍ b :=
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by {
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subst h₁;
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assumption
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}
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theorem ex7 (a : Bool) (p q : Prop) (h₁ : a = true → p) (h₂ : a = false → q) : p ∨ q :=
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match (generalizing := false) h:a with
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| true => Or.inl $ h₁ h
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| false => Or.inr $ h₂ h
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theorem ex7' (a : Bool) (p q : Prop) (h₁ : a = true → p) (h₂ : a = false → q) : p ∨ q :=
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match a with
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| true => Or.inl $ h₁ rfl
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| false => Or.inr $ h₂ rfl
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def head {α} (xs : List α) (h : xs = [] → False) : α :=
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match he:xs with
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| [] => by contradiction
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| x::_ => x
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variable {α : Type u} {p : α → Prop}
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theorem ex8 {a1 a2 : {x // p x}} (h : a1.val = a2.val) : a1 = a2 :=
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match a1, a2, h with
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| ⟨_, _⟩, ⟨_, _⟩, rfl => rfl
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universe v
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variable {β : α → Type v}
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theorem ex9 {p₁ p₂ : Sigma (fun a => β a)} (h₁ : p₁.1 = p₂.1) (h : p₁.2 ≍ p₂.2) : p₁ = p₂ :=
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match p₁, p₂, h₁, h with
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| ⟨_, _⟩, ⟨_, _⟩, rfl, HEq.refl _ => rfl
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inductive F : Nat → Type
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| z : {n : Nat} → F (n+1)
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| s : {n : Nat} → F n → F (n+1)
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def f0 {α : Sort u} (x : F 0) : α :=
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nomatch x
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def f0' {α : Sort u} (x : F 0) : α :=
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nomatch id x
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def f1 {α : Sort u} (x : F 0 × Bool) : α :=
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nomatch x
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def f2 {α : Sort u} (x : Sum (F 0) (F 0)) : α :=
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nomatch x
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def f3 {α : Sort u} (x : Bool × F 0) : α :=
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nomatch x
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def f4 (x : Sum (F 0 × Bool) Nat) : Nat :=
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match x with
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| Sum.inr x => x
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#eval f4 $ Sum.inr 100
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