e44fd19074
Many thanks for Patrick Massot for providing the new section at https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/topic/semantic.20highlighting.20doc/near/294953547
47 lines
1.9 KiB
Markdown
47 lines
1.9 KiB
Markdown
## Auto Bound Implicit Arguments
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In the previous section, we have shown how implicit arguments make functions more convenient to use.
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However, functions such as `compose` are still quite verbose to define. Note that the universe
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polymorphic `compose` is even more verbose than the one previously defined.
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```lean
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universe u v w
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def compose {α : Type u} {β : Type v} {γ : Type w}
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(g : β → γ) (f : α → β) (x : α) : γ :=
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g (f x)
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```
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You can avoid the `universe` command by providing the universe parameters when defining `compose`.
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```lean
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def compose.{u, v, w}
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{α : Type u} {β : Type v} {γ : Type w}
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(g : β → γ) (f : α → β) (x : α) : γ :=
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g (f x)
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```
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Lean 4 supports a new feature called *auto bound implicit arguments*. It makes functions such as
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`compose` much more convenient to write. When Lean processes the header of a declaration,
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any unbound identifier is automatically added as an implicit argument *if* it is a single lower case or
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greek letter. With this feature, we can write `compose` as
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```lean
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def compose (g : β → γ) (f : α → β) (x : α) : γ :=
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g (f x)
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#check @compose
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-- {β : Sort u_1} → {γ : Sort u_2} → {α : Sort u_3} → (β → γ) → (α → β) → α → γ
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```
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Note that, Lean inferred a more general type using `Sort` instead of `Type`.
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Although we love this feature and use it extensively when implementing Lean,
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we realize some users may feel uncomfortable with it. Thus, you can disable it using
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the command `set_option autoImplicit false`.
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```lean
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set_option autoImplicit false
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/- The following definition produces `unknown identifier` errors -/
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-- def compose (g : β → γ) (f : α → β) (x : α) : γ :=
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-- g (f x)
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```
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The Lean language server provides [semantic highlighting](./semantic_highlighting.md) information to editors, and it provides
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visual feedback whether an identifier has been interpreted as an auto bound implicit argument.
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