89686fcd02
This PR "monomorphizes" the structure `Std.PRange shape α`, replacing it with nine distinct structures `Std.Rcc`, `Std.Rco`, `Std.Rci` etc., one for each possible shape of a range's bounds. This change was necessary because the shape polymorphism is detrimental to attempts of automation. **BREAKING CHANGE:** While range/slice notation itself is unchanged, this essentially breaks the entire remaining (polymorphic) range and slice API except for the dot-notation(`toList`, `iter`, ...). It is not possible to deprecate old declarations that were formulated in a shape-polymorphic way that is not available anymore.
150 lines
2.9 KiB
Text
150 lines
2.9 KiB
Text
/-!
|
||
# Tests for recursive structures
|
||
-/
|
||
|
||
/-!
|
||
No parameters, variables, or universes.
|
||
-/
|
||
structure A1 where
|
||
xs : List A1
|
||
|
||
/-- info: A1 : Type -/
|
||
#guard_msgs in #check A1
|
||
|
||
/-!
|
||
Projections
|
||
-/
|
||
section
|
||
variable (a : A1)
|
||
/-- info: a.xs : List A1 -/
|
||
#guard_msgs in #check a.xs
|
||
/-- info: a.xs : List A1 -/
|
||
#guard_msgs in #check a.1
|
||
end
|
||
|
||
/-!
|
||
A parameter
|
||
-/
|
||
structure A2 (n : Nat) where
|
||
x : Fin n
|
||
xs : List (A2 n)
|
||
|
||
/-- info: A2 (n : Nat) : Type -/
|
||
#guard_msgs in #check A2
|
||
|
||
/-!
|
||
Numeric projections
|
||
-/
|
||
section
|
||
variable (a : A2 2)
|
||
/-- info: a.x : Fin 2 -/
|
||
#guard_msgs in #check a.x
|
||
/-- info: a.xs : List (A2 2) -/
|
||
#guard_msgs in #check a.xs
|
||
/-- info: a.x : Fin 2 -/
|
||
#guard_msgs in #check a.1
|
||
/-- info: a.xs : List (A2 2) -/
|
||
#guard_msgs in #check a.2
|
||
end
|
||
|
||
/-!
|
||
A `variable`
|
||
-/
|
||
section
|
||
variable (n : Nat)
|
||
|
||
structure A3 where
|
||
x : Fin n
|
||
xs : List A3
|
||
|
||
/-- info: A3 (n : Nat) : Type -/
|
||
#guard_msgs in #check A3
|
||
end
|
||
|
||
/-!
|
||
A variable and parameter with universe metavariables
|
||
-/
|
||
section
|
||
variable (α : Type _)
|
||
|
||
structure A4 (β : Type _) where
|
||
x : α
|
||
y : β
|
||
xs : List (A4 β)
|
||
|
||
/-- info: A4.{u_1, u_2} (α : Type u_1) (β : Type u_2) : Type (max u_1 u_2) -/
|
||
#guard_msgs in #check A4
|
||
end
|
||
|
||
/-!
|
||
Example from https://github.com/leanprover/lean4/issues/2512
|
||
-/
|
||
structure Foo where
|
||
name : String
|
||
children : List Foo
|
||
|
||
/-!
|
||
Defining a recursive function on a recursive structure
|
||
-/
|
||
structure Foo' where
|
||
name : String
|
||
n : Nat
|
||
children : Fin n → Foo'
|
||
|
||
def Foo'.preorder : Foo' → String
|
||
| {name, n, children} => Id.run do
|
||
let mut acc := name
|
||
for h : i in *...n do
|
||
acc := acc ++ (children ⟨i, h⟩).preorder
|
||
return acc
|
||
|
||
/-- info: Foo'.preorder : Foo' → String -/
|
||
#guard_msgs in #check Foo'.preorder
|
||
|
||
/-!
|
||
Extending with default values.
|
||
-/
|
||
structure A5 extends A4 Nat Bool where
|
||
x := 0
|
||
y := true
|
||
|
||
/-!
|
||
Default value whose type depends on the recursive structure.
|
||
Reported in https://github.com/leanprover/lean4/issues/6140
|
||
-/
|
||
|
||
structure RecS where
|
||
n : Nat
|
||
recS : Option RecS := none
|
||
|
||
/-- info: { n := 0 } : RecS -/
|
||
#guard_msgs in #check ({ n := 0 } : RecS)
|
||
|
||
/-!
|
||
Incidental new feature: checking projections when the structure is Prop.
|
||
-/
|
||
/--
|
||
error: failed to generate projection `Exists'.x` for the 'Prop'-valued type `Exists'`, field must be a proof, but it has type
|
||
α
|
||
-/
|
||
#guard_msgs in
|
||
structure Exists' {α : Sort _} (p : α → Prop) : Prop where
|
||
x : α
|
||
h : p x
|
||
|
||
/-!
|
||
Testing numeric projections on recursive inductive types now that the elaborator isn't restricted to structure-likes.
|
||
-/
|
||
inductive I1 where
|
||
| mk (x : Nat) (xs : I1)
|
||
/-- info: fun v => v.1 : I1 → Nat -/
|
||
#guard_msgs in #check fun (v : I1) => v.1
|
||
/-- info: fun v => v.2 : I1 → I1 -/
|
||
#guard_msgs in #check fun (v : I1) => v.2
|
||
|
||
inductive I2 : Nat → Type where
|
||
| mk (x : Nat) (xs : I2 (x + 1)) : I2 x
|
||
/-- info: fun v => v.1 : I2 2 → Nat -/
|
||
#guard_msgs in #check fun (v : I2 2) => v.1
|
||
/-- info: fun v => v.2 : (v : I2 2) → I2 (v.1 + 1) -/
|
||
#guard_msgs in #check fun (v : I2 2) => v.2
|