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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.
79 lines
2.2 KiB
Lean4
79 lines
2.2 KiB
Lean4
inductive Vec (α : Type u) : Nat → Type u
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| nil : Vec α 0
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| cons : α → Vec α n → Vec α (n+1)
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def Vec.map (xs : Vec α n) (f : α → β) : Vec β n :=
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match xs with
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| nil => nil
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| cons a as => cons (f a) (map as f)
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def Vec.map' (f : α → β) : Vec α n → Vec β n
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| nil => nil
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| cons a as => cons (f a) (map' f as)
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def Vec.map2 (f : α → α → β) : Vec α n → Vec α n → Vec β n
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| nil, nil => nil
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| cons a as, cons b bs => cons (f a b) (map2 f as bs)
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def Vec.head (xs : Vec α (n+1)) : α :=
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match xs with
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| cons x _ => x
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theorem ex1 (xs ys : Vec α (n+1)) (h : xs = ys) : xs.head = ys.head := by
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induction xs -- error, use cases
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theorem ex2 (xs ys : Vec α (n+1)) (h : xs = ys) : xs.head = ys.head := by
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cases xs with
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| cons x xs =>
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trace_state -- `h` has been refined
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repeat admit
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inductive ExprType where
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| bool : ExprType
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| nat : ExprType
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inductive Expr : ExprType → Type
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| natVal : Nat → Expr ExprType.nat
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| boolVal : Bool → Expr ExprType.bool
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| eq : Expr α → Expr α → Expr ExprType.bool
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| add : Expr ExprType.nat → Expr ExprType.nat → Expr ExprType.nat
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def constProp : Expr α → Expr α
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| Expr.add a b =>
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match constProp a, constProp b with
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| Expr.natVal v, Expr.natVal w => Expr.natVal (v + w)
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| a, b => Expr.add a b
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| e => e
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abbrev denoteType : ExprType → Type
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| ExprType.bool => Bool
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| ExprType.nat => Nat
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instance : BEq (denoteType α) where
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beq a b :=
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match α, a, b with
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| ExprType.bool, a, b => a == b
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| ExprType.nat, a, b => a == b
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def eval : Expr α → denoteType α
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| Expr.natVal v => v
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| Expr.boolVal b => b
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| Expr.eq a b => eval a == eval b
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| Expr.add a b => eval a + eval b
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theorem ex3 (a b : Expr α) (h : a = b) : eval (constProp a) = eval b := by
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set_option trace.Meta.debug true in
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induction a
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trace_state -- b's type must have been refined, `h` too
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repeat admit
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inductive Foo : Nat → Nat → Type where
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| mk : Foo 1 2
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theorem ex4 (n m : Nat) (heq : n = m) (h : Foo n m) : False := by
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induction h using Foo.rec
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case mk => contradiction
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theorem ex5 (n : Nat) (h : Foo n n) : False := by
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induction h using Foo.rec -- error, target repeated
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