a3ca15d2b2
building upon #3714, this (almost) implements the second half of #3302. The main effect is that we now get a better error message when `rfl` fails. For ```lean example : n+1+m = n + (1+m) := by rfl ``` instead of the wall of text ``` The rfl tactic failed. Possible reasons: - The goal is not a reflexive relation (neither `=` nor a relation with a @[refl] lemma). - The arguments of the relation are not equal. Try using the reflexivity lemma for your relation explicitly, e.g. `exact Eq.refl _` or `exact HEq.rfl` etc. n m : Nat ⊢ n + 1 + m = n + (1 + m) ``` we now get ``` error: tactic 'rfl' failed, the left-hand side n + 1 + m is not definitionally equal to the right-hand side n + (1 + m) n m : Nat ⊢ n + 1 + m = n + (1 + m) ``` Unfortunately, because of very subtle differences in semantics (which transparency setting is used when reducing the goal and whether the “implicit lambda” feature applies) I could not make this simply the only `rfl` implementation. So `rfl` remains a macro and is still expanded to `eq_refl` (difference transparency setting) and `exact Iff.rfl` and `exact HEq.rfl` (implicit lambda) to not break existing code. This can be revised later, so this still closes: #3302. A user might still be puzzled *why* to terms are not defeq. Explaining that better (“reduced to… and reduces to… etc.”) would also be great, but that’s not specific to `rfl`, so better left for some other time.
139 lines
5.2 KiB
Text
139 lines
5.2 KiB
Text
/-
|
||
Copyright (c) 2022 Newell Jensen. All rights reserved.
|
||
Released under Apache 2.0 license as described in the file LICENSE.
|
||
Authors: Newell Jensen, Thomas Murrills, Joachim Breitner
|
||
-/
|
||
prelude
|
||
import Lean.Meta.Tactic.Apply
|
||
import Lean.Elab.Tactic.Basic
|
||
import Lean.Meta.Tactic.Refl
|
||
|
||
/-!
|
||
# `rfl` tactic extension for reflexive relations
|
||
|
||
This extends the `rfl` tactic so that it works on any reflexive relation,
|
||
provided the reflexivity lemma has been marked as `@[refl]`.
|
||
-/
|
||
|
||
namespace Lean.Meta.Rfl
|
||
|
||
open Lean Meta
|
||
|
||
/-- Discrimation tree settings for the `refl` extension. -/
|
||
def reflExt.config : WhnfCoreConfig := {}
|
||
|
||
/-- Environment extensions for `refl` lemmas -/
|
||
initialize reflExt :
|
||
SimpleScopedEnvExtension (Name × Array DiscrTree.Key) (DiscrTree Name) ←
|
||
registerSimpleScopedEnvExtension {
|
||
addEntry := fun dt (n, ks) => dt.insertCore ks n
|
||
initial := {}
|
||
}
|
||
|
||
initialize registerBuiltinAttribute {
|
||
name := `refl
|
||
descr := "reflexivity relation"
|
||
add := fun decl _ kind => MetaM.run' do
|
||
let declTy := (← getConstInfo decl).type
|
||
let (_, _, targetTy) ← withReducible <| forallMetaTelescopeReducing declTy
|
||
let fail := throwError
|
||
"@[refl] attribute only applies to lemmas proving x ∼ x, got {declTy}"
|
||
let .app (.app rel lhs) rhs := targetTy | fail
|
||
if let .app (.const ``Eq [_]) _ := rel then
|
||
throwError "@[refl] attribute may not be used on `Eq.refl`."
|
||
unless ← withNewMCtxDepth <| isDefEq lhs rhs do fail
|
||
let key ← DiscrTree.mkPath rel reflExt.config
|
||
reflExt.add (decl, key) kind
|
||
}
|
||
|
||
open Elab Tactic
|
||
|
||
/-- `MetaM` version of the `rfl` tactic.
|
||
|
||
This tactic applies to a goal whose target has the form `x ~ x`, where `~` is a reflexive
|
||
relation, that is, equality or another relation which has a reflexive lemma tagged with the
|
||
attribute [refl].
|
||
-/
|
||
def _root_.Lean.MVarId.applyRfl (goal : MVarId) : MetaM Unit := goal.withContext do
|
||
-- NB: uses whnfR, we do not want to unfold the relation itself
|
||
let t ← whnfR <|← instantiateMVars <|← goal.getType
|
||
if t.getAppNumArgs < 2 then
|
||
throwTacticEx `rfl goal "expected goal to be a binary relation"
|
||
|
||
-- Special case HEq here as it has a different argument order.
|
||
if t.isAppOfArity ``HEq 4 then
|
||
let gs ← goal.applyConst ``HEq.refl
|
||
unless gs.isEmpty do
|
||
throwTacticEx `rfl goal <| MessageData.tagged `Tactic.unsolvedGoals <| m!"unsolved goals\n{
|
||
goalsToMessageData gs}"
|
||
return
|
||
|
||
let rel := t.appFn!.appFn!
|
||
let lhs := t.appFn!.appArg!
|
||
let rhs := t.appArg!
|
||
|
||
let success ← approxDefEq <| isDefEqGuarded lhs rhs
|
||
unless success do
|
||
let explanation := MessageData.ofLazyM (es := #[lhs, rhs]) do
|
||
let (lhs, rhs) ← addPPExplicitToExposeDiff lhs rhs
|
||
return m!"the left-hand side{indentExpr lhs}\nis not definitionally equal to the right-hand side{indentExpr rhs}"
|
||
throwTacticEx `rfl goal explanation
|
||
|
||
if rel.isAppOfArity `Eq 1 then
|
||
-- The common case is equality: just use `Eq.refl`
|
||
let us := rel.appFn!.constLevels!
|
||
let α := rel.appArg!
|
||
goal.assign (mkApp2 (mkConst ``Eq.refl us) α lhs)
|
||
else
|
||
-- Else search through `@refl` keyed by the relation
|
||
-- We change the type to `lhs ~ lhs` so that we do not the (possibly costly) `lhs =?= rhs` check
|
||
-- again.
|
||
goal.setType (.app t.appFn! lhs)
|
||
let s ← saveState
|
||
let mut ex? := none
|
||
for lem in ← (reflExt.getState (← getEnv)).getMatch rel reflExt.config do
|
||
try
|
||
let gs ← goal.apply (← mkConstWithFreshMVarLevels lem)
|
||
if gs.isEmpty then return () else
|
||
throwError MessageData.tagged `Tactic.unsolvedGoals <| m!"unsolved goals\n{
|
||
goalsToMessageData gs}"
|
||
catch e =>
|
||
unless ex?.isSome do
|
||
ex? := some (← saveState, e) -- stash the first failure of `apply`
|
||
s.restore
|
||
if let some (sErr, e) := ex? then
|
||
sErr.restore
|
||
throw e
|
||
else
|
||
throwTacticEx `rfl goal m!"no @[refl] lemma registered for relation{indentExpr rel}"
|
||
|
||
/-- Helper theorem for `Lean.MVarId.liftReflToEq`. -/
|
||
private theorem rel_of_eq_and_refl {α : Sort _} {R : α → α → Prop}
|
||
{x y : α} (hxy : x = y) (h : R x x) : R x y :=
|
||
hxy ▸ h
|
||
|
||
/--
|
||
Convert a goal of the form `x ~ y` into the form `x = y`, where `~` is a reflexive
|
||
relation, that is, a relation which has a reflexive lemma tagged with the attribute `@[refl]`.
|
||
If this can't be done, returns the original `MVarId`.
|
||
-/
|
||
def _root_.Lean.MVarId.liftReflToEq (mvarId : MVarId) : MetaM MVarId := do
|
||
mvarId.checkNotAssigned `liftReflToEq
|
||
let .app (.app rel _) _ ← withReducible mvarId.getType' | return mvarId
|
||
if rel.isAppOf `Eq then
|
||
-- No need to lift Eq to Eq
|
||
return mvarId
|
||
for lem in ← (reflExt.getState (← getEnv)).getMatch rel reflExt.config do
|
||
let res ← observing? do
|
||
-- First create an equality relating the LHS and RHS
|
||
-- and reduce the goal to proving that LHS is related to LHS.
|
||
let [mvarIdEq, mvarIdR] ← mvarId.apply (← mkConstWithFreshMVarLevels ``rel_of_eq_and_refl)
|
||
| failure
|
||
-- Then fill in the proof of the latter by reflexivity.
|
||
let [] ← mvarIdR.apply (← mkConstWithFreshMVarLevels lem) | failure
|
||
return mvarIdEq
|
||
if let some mvarIdEq := res then
|
||
return mvarIdEq
|
||
return mvarId
|
||
|
||
end Lean.Meta.Rfl
|