doc: avoid universe issue in example type class code (#3098)

by allowing `Inhabited` to apply to any sort.

fixes #3096.
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Joachim Breitner 2023-12-21 17:57:26 +01:00 committed by GitHub
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@ -99,11 +99,11 @@ Let us start with the first step of the program above, declaring an appropriate
```lean
# namespace Ex
class Inhabited (a : Type u) where
class Inhabited (a : Sort u) where
default : a
#check @Inhabited.default
-- Inhabited.default : {a : Type u} → [self : Inhabited a] → a
-- Inhabited.default : {a : Sort u} → [self : Inhabited a] → a
# end Ex
```
Note `Inhabited.default` doesn't have any explicit argument.
@ -114,7 +114,7 @@ Now we populate the class with some instances:
```lean
# namespace Ex
# class Inhabited (a : Type _) where
# class Inhabited (a : Sort _) where
# default : a
instance : Inhabited Bool where
default := true
@ -138,7 +138,7 @@ instance : Inhabited Prop where
You can use the command `export` to create the alias `default` for `Inhabited.default`
```lean
# namespace Ex
# class Inhabited (a : Type _) where
# class Inhabited (a : Sort _) where
# default : a
# instance : Inhabited Bool where
# default := true
@ -174,7 +174,7 @@ instance [Inhabited a] [Inhabited b] : Inhabited (a × b) where
With this added to the earlier instance declarations, type class instance can infer, for example, a default element of ``Nat × Bool``:
```lean
# namespace Ex
# class Inhabited (a : Type u) where
# class Inhabited (a : Sort u) where
# default : a
# instance : Inhabited Bool where
# default := true
@ -191,8 +191,14 @@ instance [Inhabited a] [Inhabited b] : Inhabited (a × b) where
```
Similarly, we can inhabit type function with suitable constant functions:
```lean
# namespace Ex
# class Inhabited (a : Sort u) where
# default : a
# opaque default [Inhabited a] : a :=
# Inhabited.default
instance [Inhabited b] : Inhabited (a -> b) where
default := fun _ => default
# end Ex
```
As an exercise, try defining default instances for other types, such as `List` and `Sum` types.