0fcee100e7
Now that the elaborator supports primitive projections for recursive inductive types (#5822), enable defining recursive inductive types with the `structure` command, which was set up in #5842. Example: ```lean structure Tree where n : Nat children : Fin n → Tree def Tree.size : Tree → Nat | {n, children} => Id.run do let mut s := 0 for h : i in [0 : n] do s := s + (children ⟨i, h.2⟩).size pure s ``` Note for kernel re-implementors: recursive structures are exercising the kernel feature where primitive projections are valid for one-constructor inductive types in general, so long as the structure isn't a `Prop` and doesn't have any non-`Prop` fields, not just ones that are non-indexed and non-recursive. Closes #2512
135 lines
2.6 KiB
Text
135 lines
2.6 KiB
Text
/-!
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# Tests for recursive structures
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-/
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/-!
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No parameters, variables, or universes.
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-/
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structure A1 where
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xs : List A1
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/-- info: A1 : Type -/
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#guard_msgs in #check A1
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/-!
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Projections
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-/
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section
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variable (a : A1)
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/-- info: a.xs : List A1 -/
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#guard_msgs in #check a.xs
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/-- info: a.xs : List A1 -/
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#guard_msgs in #check a.1
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end
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/-!
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A parameter
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-/
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structure A2 (n : Nat) where
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x : Fin n
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xs : List (A2 n)
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/-- info: A2 (n : Nat) : Type -/
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#guard_msgs in #check A2
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/-!
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Numeric projections
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-/
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section
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variable (a : A2 2)
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/-- info: a.x : Fin 2 -/
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#guard_msgs in #check a.x
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/-- info: a.xs : List (A2 2) -/
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#guard_msgs in #check a.xs
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/-- info: a.x : Fin 2 -/
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#guard_msgs in #check a.1
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/-- info: a.xs : List (A2 2) -/
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#guard_msgs in #check a.2
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end
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/-!
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A `variable`
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-/
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section
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variable (n : Nat)
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structure A3 where
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x : Fin n
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xs : List A3
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/-- info: A3 (n : Nat) : Type -/
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#guard_msgs in #check A3
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end
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/-!
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A variable and parameter with universe metavariables
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-/
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section
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variable (α : Type _)
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structure A4 (β : Type _) where
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x : α
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y : β
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xs : List (A4 β)
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/-- info: A4.{u_1, u_2} (α : Type u_1) (β : Type u_2) : Type (max u_1 u_2) -/
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#guard_msgs in #check A4
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end
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/-!
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Example from https://github.com/leanprover/lean4/issues/2512
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-/
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structure Foo where
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name : String
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children : List Foo
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/-!
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Defining a recursive function on a recursive structure
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-/
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structure Foo' where
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name : String
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n : Nat
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children : Fin n → Foo'
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def Foo'.preorder : Foo' → String
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| {name, n, children} => Id.run do
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let mut acc := name
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for h : i in [0:n] do
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acc := acc ++ (children ⟨i, h.2⟩).preorder
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return acc
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/-- info: Foo'.preorder : Foo' → String -/
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#guard_msgs in #check Foo'.preorder
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/-!
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Extending with default values.
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-/
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structure A5 extends A4 Nat Bool where
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x := 0
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y := true
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/-!
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Incidental new feature: checking projections when the structure is Prop.
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-/
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/-- error: failed to generate projections for 'Prop' structure, field 'x' is not a proof -/
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#guard_msgs in
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structure Exists' {α : Sort _} (p : α → Prop) : Prop where
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x : α
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h : p x
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/-!
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Testing numeric projections on recursive inductive types now that the elaborator isn't restricted to structure-likes.
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-/
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inductive I1 where
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| mk (x : Nat) (xs : I1)
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/-- info: fun v => v.1 : I1 → Nat -/
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#guard_msgs in #check fun (v : I1) => v.1
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/-- info: fun v => v.2 : I1 → I1 -/
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#guard_msgs in #check fun (v : I1) => v.2
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inductive I2 : Nat → Type where
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| mk (x : Nat) (xs : I2 (x + 1)) : I2 x
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/-- info: fun v => v.1 : I2 2 → Nat -/
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#guard_msgs in #check fun (v : I2 2) => v.1
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/-- info: fun v => v.2 : (v : I2 2) → I2 (v.1 + 1) -/
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#guard_msgs in #check fun (v : I2 2) => v.2
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