term ::= ...
| A *synthetic hole* (or *synthetic placeholder*), which stands for an unknown term that should be synthesized using tactics.
- `?_` creates a fresh metavariable with an auto-generated name.
- `?m` either refers to a pre-existing metavariable named `m` or creates a fresh metavariable with that name.
In particular, the synthetic hole syntax creates "synthetic opaque metavariables",
the same kind of metavariable used to represent goals in the tactic state.
Synthetic holes are similar to holes in that `_` also creates metavariables,
but synthetic opaque metavariables have some different properties:
- In tactics such as `refine`, only synthetic holes yield new goals.
- During elaboration, unification will not solve for synthetic opaque metavariables, they are "opaque".
This is to prevent counterintuitive behavior such as disappearing goals.
- When synthetic holes appear under binders, they capture local variables using a more complicated mechanism known as delayed assignment.
## Delayed assigned metavariables
This section gives an overview of some technical details of synthetic holes, which you should feel free to skip.
Understanding delayed assignments is mainly useful for those who are working on tactics and other metaprogramming.
It is included here until there is a suitable place for it in the reference manual.
When a synthetic hole appears under a binding construct, such as for example `fun (x : α) (y : β) => ?s`,
the system creates a *delayed assignment*. This consists of
1. A metavariable `?m` of type `(x : α) → (y : β) → γ x y` whose local context is the local context outside the `fun`,
where `γ x y` is the type of `?s`. Recall that `x` and `y` appear in the local context of `?s`.
2. A delayed assigment record associating `?m` to `?s` and the variables `#[x, y]` in the local context of `?s`
Then, this function elaborates as `fun (x : α) (y : β) => ?m x y`, where one should understand `x` and `y` here
as being De Bruijn indexes, since Lean uses the locally nameless encoding of lambda calculus.
Once `?s` is fully solved for, in the sense that after metavariable instantiation it is a metavariable-free term `e`,
then we can make the assignment `?m := fun (x' : α) (y' : β) => e[x := x', y := y']`.
(Implementation note: Lean only instantiates full applications `?m x' y'` of delayed assigned metavariables, to skip forming this function.)
This delayed assignment mechanism is essential to the operation of basic tactics like `intro`,
and a good mental model is that it is a way to "apply" the metavariable `?s` by substituting values in for some of its local variables.
While it would be easier to immediately assign `?s := ?m x y`,
delayed assigment preserves `?s` as an unsolved-for metavariable with a local context that still contains `x` and `y`,
which is exactly what tactics like `intro` need.
By default, delayed assigned metavariables pretty print with what they are delayed assigned to.
The delayed assigned metavariables themselves can be pretty printed using `set_option pp.mvars.delayed true`.
For more information, see the "Gruesome details" module docstrings in `Lean.MetavarContext`.
term ::= ...
| A *synthetic hole* (or *synthetic placeholder*), which stands for an unknown term that should be synthesized using tactics.
- `?_` creates a fresh metavariable with an auto-generated name.
- `?m` either refers to a pre-existing metavariable named `m` or creates a fresh metavariable with that name.
In particular, the synthetic hole syntax creates "synthetic opaque metavariables",
the same kind of metavariable used to represent goals in the tactic state.
Synthetic holes are similar to holes in that `_` also creates metavariables,
but synthetic opaque metavariables have some different properties:
- In tactics such as `refine`, only synthetic holes yield new goals.
- During elaboration, unification will not solve for synthetic opaque metavariables, they are "opaque".
This is to prevent counterintuitive behavior such as disappearing goals.
- When synthetic holes appear under binders, they capture local variables using a more complicated mechanism known as delayed assignment.
## Delayed assigned metavariables
This section gives an overview of some technical details of synthetic holes, which you should feel free to skip.
Understanding delayed assignments is mainly useful for those who are working on tactics and other metaprogramming.
It is included here until there is a suitable place for it in the reference manual.
When a synthetic hole appears under a binding construct, such as for example `fun (x : α) (y : β) => ?s`,
the system creates a *delayed assignment*. This consists of
1. A metavariable `?m` of type `(x : α) → (y : β) → γ x y` whose local context is the local context outside the `fun`,
where `γ x y` is the type of `?s`. Recall that `x` and `y` appear in the local context of `?s`.
2. A delayed assigment record associating `?m` to `?s` and the variables `#[x, y]` in the local context of `?s`
Then, this function elaborates as `fun (x : α) (y : β) => ?m x y`, where one should understand `x` and `y` here
as being De Bruijn indexes, since Lean uses the locally nameless encoding of lambda calculus.
Once `?s` is fully solved for, in the sense that after metavariable instantiation it is a metavariable-free term `e`,
then we can make the assignment `?m := fun (x' : α) (y' : β) => e[x := x', y := y']`.
(Implementation note: Lean only instantiates full applications `?m x' y'` of delayed assigned metavariables, to skip forming this function.)
This delayed assignment mechanism is essential to the operation of basic tactics like `intro`,
and a good mental model is that it is a way to "apply" the metavariable `?s` by substituting values in for some of its local variables.
While it would be easier to immediately assign `?s := ?m x y`,
delayed assigment preserves `?s` as an unsolved-for metavariable with a local context that still contains `x` and `y`,
which is exactly what tactics like `intro` need.
By default, delayed assigned metavariables pretty print with what they are delayed assigned to.
The delayed assigned metavariables themselves can be pretty printed using `set_option pp.mvars.delayed true`.
For more information, see the "Gruesome details" module docstrings in `Lean.MetavarContext`.