94 lines
3.6 KiB
Text
94 lines
3.6 KiB
Text
/-
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Copyright (c) 2021 Gabriel Ebner. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Gabriel Ebner, Mario Carneiro
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-/
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module
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prelude
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public import Init.RCases
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public section
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namespace Lean
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namespace Parser.Attr
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/--
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The flag `(iff := false)` prevents `ext` from generating an `ext_iff` lemma.
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-/
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syntax extIff := atomic("(" &"iff" " := " &"false" ")")
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/--
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The flag `(flat := false)` causes `ext` to not flatten parents' fields when generating an `ext` lemma.
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-/
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syntax extFlat := atomic("(" &"flat" " := " &"false" ")")
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/--
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Registers an extensionality theorem.
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* When `@[ext]` is applied to a theorem, the theorem is registered for the `ext` tactic, and it generates an "`ext_iff`" theorem.
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The name of the theorem is from adding the suffix `_iff` to the theorem name.
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* When `@[ext]` is applied to a structure, it generates an `.ext` theorem and applies the `@[ext]` attribute to it.
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The result is an `.ext` and an `.ext_iff` theorem with the `.ext` theorem registered for the `ext` tactic.
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* An optional natural number argument, e.g. `@[ext 9000]`, specifies a priority for the `ext` lemma.
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Higher-priority lemmas are chosen first, and the default is `1000`.
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* The flag `@[ext (iff := false)]` disables generating an `ext_iff` theorem.
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* The flag `@[ext (flat := false)]` causes generated structure extensionality theorems to show inherited fields based on their representation,
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rather than flattening the parents' fields into the lemma's equality hypotheses.
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-/
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syntax (name := ext) "ext" (ppSpace extIff)? (ppSpace extFlat)? (ppSpace prio)? : attr
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end Parser.Attr
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-- TODO: rename this namespace?
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namespace Elab.Tactic.Ext
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/--
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Applies extensionality lemmas that are registered with the `@[ext]` attribute.
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* `ext pat*` applies extensionality theorems as much as possible,
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using the patterns `pat*` to introduce the variables in extensionality theorems using `rintro`.
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For example, the patterns are used to name the variables introduced by lemmas such as `funext`.
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* Without patterns,`ext` applies extensionality lemmas as much
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as possible but introduces anonymous hypotheses whenever needed.
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* `ext pat* : n` applies ext theorems only up to depth `n`.
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The `ext1 pat*` tactic is like `ext pat*` except that it only applies a single extensionality theorem.
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Unused patterns will generate warning.
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Patterns that don't match the variables will typically result in the introduction of anonymous hypotheses.
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-/
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syntax (name := ext) "ext" (colGt ppSpace rintroPat)* (" : " num)? : tactic
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/-- Apply a single extensionality theorem to the current goal. -/
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syntax (name := applyExtTheorem) "apply_ext_theorem" : tactic
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/--
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`ext1 pat*` is like `ext pat*` except that it only applies a single extensionality theorem rather
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than recursively applying as many extensionality theorems as possible.
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The `pat*` patterns are processed using the `rintro` tactic.
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If no patterns are supplied, then variables are introduced anonymously using the `intros` tactic.
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-/
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macro "ext1" xs:(colGt ppSpace rintroPat)* : tactic =>
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if xs.isEmpty then `(tactic| apply_ext_theorem <;> intros)
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else `(tactic| apply_ext_theorem <;> rintro $xs*)
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end Elab.Tactic.Ext
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end Lean
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attribute [ext] Prod PProd Sigma PSigma
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attribute [ext] funext propext Subtype.ext Array.ext Char.ext
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@[deprecated Subtype.ext_iff (since := "2025-10-26")]
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protected def Subtype.eq_iff := @Subtype.ext_iff
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attribute [grind ext] funext Array.ext
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attribute [ext] PUnit.ext
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protected theorem Unit.ext (x y : Unit) : x = y := rfl
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@[ext] protected theorem Thunk.ext : {a b : Thunk α} → a.get = b.get → a = b
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| {..}, {..}, heq => congrArg _ <| funext fun _ => heq
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