bd46319aee
Where before we had ```lean #check fun x : Nat => ?a -- fun x ↦ ?m.7 x : (x : Nat) → ?m.6 x ``` Now by default we have ```lean #check fun x : Nat => ?a -- fun x => ?a : (x : Nat) → ?m.6 x ``` In particular, delayed assignment metavariables such as `?m.7` pretty print using the name of the metavariable they are delayed assigned to, suppressing the bound variables used in the delayed assignment (hence `?a` rather than `?a x`). Hovering over `?a` shows `?m.7 x`. The benefit is that users can see the user-provided name in local contexts. A justification for this pretty printing choice is that `?m.7 x` is supposed to stand for `?a`, and furthermore it is just as opaque to assignment in defeq as `?a` is (however, when synthetic opaque metavariables are made assignable, delayed assignments can be a little less assignable than true synthetic opaque metavariables). The original pretty printing behavior can be recovered using `set_option pp.mvars.delayed true`. This PR also extends the documentation for holes and synthetic holes, with some technical details about what delayed assignments are. This likely should be moved to the reference manual, but for now it is included in this docstring. (This PR is a simplified version of #3494, which has a round-trippable notation for delayed assignments. The pretty printing in this PR is unlikely to round trip, but it is better than the current situation, which is that delayed assignment metavariables never round trip, and plus it does not require introducing a new notation.)
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"```lean\nFalse\n```\n***\nA *synthetic hole* (or *synthetic placeholder*), which stands for an unknown term that should be synthesized using tactics.\n- `?_` creates a fresh metavariable with an auto-generated name.\n- `?m` either refers to a pre-existing metavariable named `m` or creates a fresh metavariable with that name.\n\nIn particular, the synthetic hole syntax creates \"synthetic opaque metavariables\",\nthe same kind of metavariable used to represent goals in the tactic state.\n\nSynthetic holes are similar to holes in that `_` also creates metavariables,\nbut synthetic opaque metavariables have some different properties:\n- In tactics such as `refine`, only synthetic holes yield new goals.\n- During elaboration, unification will not solve for synthetic opaque metavariables, they are \"opaque\".\n This is to prevent counterintuitive behavior such as disappearing goals.\n- When synthetic holes appear under binders, they capture local variables using a more complicated mechanism known as delayed assignment.\n\n## Delayed assigned metavariables\n\nThis section gives an overview of some technical details of synthetic holes, which you should feel free to skip.\nUnderstanding delayed assignments is mainly useful for those who are working on tactics and other metaprogramming.\nIt is included here until there is a suitable place for it in the reference manual.\n\nWhen a synthetic hole appears under a binding construct, such as for example `fun (x : α) (y : β) => ?s`,\nthe system creates a *delayed assignment*. This consists of\n1. A metavariable `?m` of type `(x : α) → (y : β) → γ x y` whose local context is the local context outside the `fun`,\n where `γ x y` is the type of `?s`. Recall that `x` and `y` appear in the local context of `?s`.\n2. A delayed assigment record associating `?m` to `?s` and the variables `#[x, y]` in the local context of `?s`\n\nThen, this function elaborates as `fun (x : α) (y : β) => ?m x y`, where one should understand `x` and `y` here\nas being De Bruijn indexes, since Lean uses the locally nameless encoding of lambda calculus.\n\nOnce `?s` is fully solved for, in the sense that after metavariable instantiation it is a metavariable-free term `e`,\nthen we can make the assignment `?m := fun (x' : α) (y' : β) => e[x := x', y := y']`.\n(Implementation note: Lean only instantiates full applications `?m x' y'` of delayed assigned metavariables, to skip forming this function.)\nThis delayed assignment mechanism is essential to the operation of basic tactics like `intro`,\nand 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.\nWhile it would be easier to immediately assign `?s := ?m x y`,\ndelayed assigment preserves `?s` as an unsolved-for metavariable with a local context that still contains `x` and `y`,\nwhich is exactly what tactics like `intro` need.\n\nBy default, delayed assigned metavariables pretty print with what they are delayed assigned to.\nThe delayed assigned metavariables themselves can be pretty printed using `set_option pp.mvars.delayed true`.\n\nFor more information, see the \"Gruesome details\" module docstrings in `Lean.MetavarContext`.\n",
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"```lean\nFalse\n```\n***\nA *synthetic hole* (or *synthetic placeholder*), which stands for an unknown term that should be synthesized using tactics.\n- `?_` creates a fresh metavariable with an auto-generated name.\n- `?m` either refers to a pre-existing metavariable named `m` or creates a fresh metavariable with that name.\n\nIn particular, the synthetic hole syntax creates \"synthetic opaque metavariables\",\nthe same kind of metavariable used to represent goals in the tactic state.\n\nSynthetic holes are similar to holes in that `_` also creates metavariables,\nbut synthetic opaque metavariables have some different properties:\n- In tactics such as `refine`, only synthetic holes yield new goals.\n- During elaboration, unification will not solve for synthetic opaque metavariables, they are \"opaque\".\n This is to prevent counterintuitive behavior such as disappearing goals.\n- When synthetic holes appear under binders, they capture local variables using a more complicated mechanism known as delayed assignment.\n\n## Delayed assigned metavariables\n\nThis section gives an overview of some technical details of synthetic holes, which you should feel free to skip.\nUnderstanding delayed assignments is mainly useful for those who are working on tactics and other metaprogramming.\nIt is included here until there is a suitable place for it in the reference manual.\n\nWhen a synthetic hole appears under a binding construct, such as for example `fun (x : α) (y : β) => ?s`,\nthe system creates a *delayed assignment*. This consists of\n1. A metavariable `?m` of type `(x : α) → (y : β) → γ x y` whose local context is the local context outside the `fun`,\n where `γ x y` is the type of `?s`. Recall that `x` and `y` appear in the local context of `?s`.\n2. A delayed assigment record associating `?m` to `?s` and the variables `#[x, y]` in the local context of `?s`\n\nThen, this function elaborates as `fun (x : α) (y : β) => ?m x y`, where one should understand `x` and `y` here\nas being De Bruijn indexes, since Lean uses the locally nameless encoding of lambda calculus.\n\nOnce `?s` is fully solved for, in the sense that after metavariable instantiation it is a metavariable-free term `e`,\nthen we can make the assignment `?m := fun (x' : α) (y' : β) => e[x := x', y := y']`.\n(Implementation note: Lean only instantiates full applications `?m x' y'` of delayed assigned metavariables, to skip forming this function.)\nThis delayed assignment mechanism is essential to the operation of basic tactics like `intro`,\nand 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.\nWhile it would be easier to immediately assign `?s := ?m x y`,\ndelayed assigment preserves `?s` as an unsolved-for metavariable with a local context that still contains `x` and `y`,\nwhich is exactly what tactics like `intro` need.\n\nBy default, delayed assigned metavariables pretty print with what they are delayed assigned to.\nThe delayed assigned metavariables themselves can be pretty printed using `set_option pp.mvars.delayed true`.\n\nFor more information, see the \"Gruesome details\" module docstrings in `Lean.MetavarContext`.\n",
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"```lean\nFalse\n```\n***\nA *synthetic hole* (or *synthetic placeholder*), which stands for an unknown term that should be synthesized using tactics.\n- `?_` creates a fresh metavariable with an auto-generated name.\n- `?m` either refers to a pre-existing metavariable named `m` or creates a fresh metavariable with that name.\n\nIn particular, the synthetic hole syntax creates \"synthetic opaque metavariables\",\nthe same kind of metavariable used to represent goals in the tactic state.\n\nSynthetic holes are similar to holes in that `_` also creates metavariables,\nbut synthetic opaque metavariables have some different properties:\n- In tactics such as `refine`, only synthetic holes yield new goals.\n- During elaboration, unification will not solve for synthetic opaque metavariables, they are \"opaque\".\n This is to prevent counterintuitive behavior such as disappearing goals.\n- When synthetic holes appear under binders, they capture local variables using a more complicated mechanism known as delayed assignment.\n\n## Delayed assigned metavariables\n\nThis section gives an overview of some technical details of synthetic holes, which you should feel free to skip.\nUnderstanding delayed assignments is mainly useful for those who are working on tactics and other metaprogramming.\nIt is included here until there is a suitable place for it in the reference manual.\n\nWhen a synthetic hole appears under a binding construct, such as for example `fun (x : α) (y : β) => ?s`,\nthe system creates a *delayed assignment*. This consists of\n1. A metavariable `?m` of type `(x : α) → (y : β) → γ x y` whose local context is the local context outside the `fun`,\n where `γ x y` is the type of `?s`. Recall that `x` and `y` appear in the local context of `?s`.\n2. A delayed assigment record associating `?m` to `?s` and the variables `#[x, y]` in the local context of `?s`\n\nThen, this function elaborates as `fun (x : α) (y : β) => ?m x y`, where one should understand `x` and `y` here\nas being De Bruijn indexes, since Lean uses the locally nameless encoding of lambda calculus.\n\nOnce `?s` is fully solved for, in the sense that after metavariable instantiation it is a metavariable-free term `e`,\nthen we can make the assignment `?m := fun (x' : α) (y' : β) => e[x := x', y := y']`.\n(Implementation note: Lean only instantiates full applications `?m x' y'` of delayed assigned metavariables, to skip forming this function.)\nThis delayed assignment mechanism is essential to the operation of basic tactics like `intro`,\nand 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.\nWhile it would be easier to immediately assign `?s := ?m x y`,\ndelayed assigment preserves `?s` as an unsolved-for metavariable with a local context that still contains `x` and `y`,\nwhich is exactly what tactics like `intro` need.\n\nBy default, delayed assigned metavariables pretty print with what they are delayed assigned to.\nThe delayed assigned metavariables themselves can be pretty printed using `set_option pp.mvars.delayed true`.\n\nFor more information, see the \"Gruesome details\" module docstrings in `Lean.MetavarContext`.\n",
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"```lean\nFalse\n```\n***\nA *synthetic hole* (or *synthetic placeholder*), which stands for an unknown term that should be synthesized using tactics.\n- `?_` creates a fresh metavariable with an auto-generated name.\n- `?m` either refers to a pre-existing metavariable named `m` or creates a fresh metavariable with that name.\n\nIn particular, the synthetic hole syntax creates \"synthetic opaque metavariables\",\nthe same kind of metavariable used to represent goals in the tactic state.\n\nSynthetic holes are similar to holes in that `_` also creates metavariables,\nbut synthetic opaque metavariables have some different properties:\n- In tactics such as `refine`, only synthetic holes yield new goals.\n- During elaboration, unification will not solve for synthetic opaque metavariables, they are \"opaque\".\n This is to prevent counterintuitive behavior such as disappearing goals.\n- When synthetic holes appear under binders, they capture local variables using a more complicated mechanism known as delayed assignment.\n\n## Delayed assigned metavariables\n\nThis section gives an overview of some technical details of synthetic holes, which you should feel free to skip.\nUnderstanding delayed assignments is mainly useful for those who are working on tactics and other metaprogramming.\nIt is included here until there is a suitable place for it in the reference manual.\n\nWhen a synthetic hole appears under a binding construct, such as for example `fun (x : α) (y : β) => ?s`,\nthe system creates a *delayed assignment*. This consists of\n1. A metavariable `?m` of type `(x : α) → (y : β) → γ x y` whose local context is the local context outside the `fun`,\n where `γ x y` is the type of `?s`. Recall that `x` and `y` appear in the local context of `?s`.\n2. A delayed assigment record associating `?m` to `?s` and the variables `#[x, y]` in the local context of `?s`\n\nThen, this function elaborates as `fun (x : α) (y : β) => ?m x y`, where one should understand `x` and `y` here\nas being De Bruijn indexes, since Lean uses the locally nameless encoding of lambda calculus.\n\nOnce `?s` is fully solved for, in the sense that after metavariable instantiation it is a metavariable-free term `e`,\nthen we can make the assignment `?m := fun (x' : α) (y' : β) => e[x := x', y := y']`.\n(Implementation note: Lean only instantiates full applications `?m x' y'` of delayed assigned metavariables, to skip forming this function.)\nThis delayed assignment mechanism is essential to the operation of basic tactics like `intro`,\nand 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.\nWhile it would be easier to immediately assign `?s := ?m x y`,\ndelayed assigment preserves `?s` as an unsolved-for metavariable with a local context that still contains `x` and `y`,\nwhich is exactly what tactics like `intro` need.\n\nBy default, delayed assigned metavariables pretty print with what they are delayed assigned to.\nThe delayed assigned metavariables themselves can be pretty printed using `set_option pp.mvars.delayed true`.\n\nFor more information, see the \"Gruesome details\" module docstrings in `Lean.MetavarContext`.\n",
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