feat: try? composite suggestions (#6979)

This PR adds support for more complex suggestions in `try?`. Example:
```lean
example (as : List α) (a : α) : concat as a = as ++ [a] := by
  try?
```
suggestion
```
Try this: · induction as, a using concat.induct
  · rfl
  · simp_all
```

src/Init/Try.lean

@@ -27,7 +27,10 @@ namespace Lean.Parser.Tactic
 
 syntax (name := tryTrace) "try?" optConfig : tactic
 
-/-- Helper tactic for implementing the tactic `try?`. -/
+/-- Helper internal tactic for implementing the tactic `try?`. -/
 syntax (name := attemptAll) "attempt_all " withPosition((ppDedent(ppLine) colGe "| " tacticSeq)+) : tactic
 
+/-- Helper internal tactic used to implement `evalSuggest` in `try?` -/
+syntax (name := tryResult) "try_suggestions " tactic* : tactic
+
 end Lean.Parser.Tactic

src/Lean/Elab/Tactic/Try.lean

@@ -13,11 +13,6 @@ import Lean.Elab.Tactic.Config
 import Lean.Elab.Tactic.SimpTrace
 import Lean.Elab.Tactic.Grind
 
-namespace Lean.Parser.Tactic
-/-- Internal tactic used to implement `evalSuggest` -/
-syntax (name := tryResult) "try_suggestions " tactic* : tactic
-end Lean.Parser.Tactic
-
 namespace Lean.Elab.Tactic
 open Meta
 /-!
@@ -52,7 +47,7 @@ private def appendSeqResult (suggestionSeqs : Array (Array (TSyntax `tactic))) (
 /-- Returns a tactic representing all given suggestions `tacs`. -/
 private def mkTrySuggestions (tacs : Array (TSyntax `tactic)) : TacticM (TSyntax `tactic) := do
   if tacs.isEmpty then
-    throwError "`mkSuggestions` failed"
+    throwError "`mkTrySuggestions` failed"
   else if tacs.size == 1 then
     return tacs[0]!
   else
@@ -130,16 +125,38 @@ private def getKindsSolvedAll (tacss : Array (Array (TSyntax `tactic))) : Array
         r := r.push k
     return r
 
-private def mkChainResultCore (tac1 : TSyntax `tactic) (tacs2 : Array (TSyntax `tactic)) : TacticM (Array (TSyntax `tactic)) := do
-  let tacs2 := tacs2.map getSuggestionsCore
+private def peekOne (tac1 : TSyntax `tactic) (tacss2 : Array (Array (TSyntax `tactic))) : TacticM (TSyntax `tactic) := do
+  let mut tacs2 := #[]
+  for s in tacss2 do
+    if s.isEmpty then
+      tacs2 := tacs2.push (← `(tactic| · sorry))
+    else
+      tacs2 := tacs2.push (← `(tactic| · $(s[0]!):tactic))
+  `(tactic| · $tac1:tactic
+              $tacs2*)
+
+private def mkChainResultCore (tac1 : TSyntax `tactic) (tacss2 : Array (TSyntax `tactic)) : TacticM (Array (TSyntax `tactic)) := do
+  let tacss2 := tacss2.map getSuggestionsCore
+  if (← isTracingEnabledFor `try.debug) then
+    trace[try.debug] "mkChainResultCore tac1{indentD tac1}"
+    let mut i : Nat := 0
+    for tacs2 in tacss2 do
+      i := i + 1
+      trace[try.debug] "goal #{i} tactics"
+      for tac2 in tacs2 do
+        trace[try.debug] "  {tac2}"
+    trace[try.debug] "mkChainResult -----"
   let mut acc := #[]
-  let solvedAll := getTacsSolvedAll tacs2
+  let solvedAll := getTacsSolvedAll tacss2
   for tac2 in solvedAll do
     acc := acc.push (← `(tactic| $tac1 <;> $tac2))
-  let tacs2 := eraseTacs tacs2 solvedAll
+  let tacss2 := eraseTacs tacss2 solvedAll
   -- TODO: mixed cases
-  trace[Meta.debug] "CHAIN tacs2: {tacs2}"
-  trace[Meta.debug] "CHAIN kinds: {getKindsSolvedAll tacs2}"
+  trace[try.debug] "kinds: {getKindsSolvedAll tacss2}"
+  if (!acc.isEmpty && tacss2.all fun s => !s.isEmpty)
+     -- We only include partial solutions if there are no other solutions.
+     || (acc.isEmpty && tacss2.any fun s => !s.isEmpty) then
+    acc := acc.push <| (← peekOne tac1 tacss2)
   return acc
 
 private def mkChainResult (tac1 : TSyntax `tactic) (tacs2 : Array (TSyntax `tactic)) : TacticM (TSyntax `tactic) := do
@@ -178,6 +195,7 @@ private def evalSuggestGrindTrace (tac : TSyntax `tactic) : TacticM (TSyntax `ta
     let trace ← evalGrindCore tac config only params fallback?
     let tac ← grindTraceToGrind tac
     let tac' ← mkGrindOnly configStx fallback? trace
+    trace[try.debug] "`grind` succeeded"
     mkTrySuggestions #[tac, tac']
   | _ => throwUnsupportedSyntax
 
@@ -188,6 +206,7 @@ private def evalSuggestSimpTrace (tac : TSyntax `tactic) : TacticM (TSyntax `tac
     let { ctx, simprocs, .. } ← mkSimpContext tac (eraseLocal := false)
     let stats ← simpLocation ctx (simprocs := simprocs) none <| (loc.map expandLocation).getD (.targets #[] true)
     let tac' ← mkSimpCallStx tac stats.usedTheorems
+    trace[try.debug] "`simp` succeeded"
     mkTrySuggestions #[tac, tac']
   | _ => throwUnsupportedSyntax
 
@@ -215,11 +234,14 @@ private def evalSuggestChain (tac1 tac2 : TSyntax `tactic) : TacticM (TSyntax `t
   let goals ← getGoals
   setGoals []
   let mut tac2s := #[]
+  let mut i : Nat := 0
   for goal in goals do
     setGoals [goal]
-    let tac2' ← (evalSuggest tac2) <|> `(tactic| sorry)
+    let tac2' : TSyntax `tactic ← (evalSuggest tac2) <|> `(tactic| sorry)
+    i := i + 1
+    trace[try.debug] "`<;>` goal #{i}, tactic{indentD tac2'}"
     unless (← getGoals).isEmpty do
-      throwError "unsolved goals, `<;>` in `try?` requires all goals to be solved"
+      throwError "unsolved goals, `<;>` in `try?` requires all goals to be solved{indentD tac2}\n{goalsToMessageData (← getGoals)}"
     tac2s := tac2s.push tac2'
   if tac2s.all isSorry then
     throwError "`<;>` failed"
@@ -269,8 +291,11 @@ where
   go (i : Nat) (saved? : Option SavedState) (acc : Array (TSyntax `tactic)) : TacticM (TSyntax `tactic) := do
     if i < tacs.size then
       match (← observing (evalSuggestTacticSeq tacs[i]!)) with
-      | .ok tac s => go (i+1) (saved? <|> some s) (appendSuggestion acc tac)
-      | _ => go (i+1) saved? acc
+      | .ok tac s =>
+        trace[try.debug] "`attempt_all` argument succeeded{indentD tac}"
+        go (i+1) (saved? <|> some s) (appendSuggestion acc tac)
+      | _ =>
+        go (i+1) saved? acc
     else
       if let some saved := saved? then
         saved.restore
@@ -281,6 +306,7 @@ where
 -- `evalSuggest` implementation
 @[export lean_eval_suggest_tactic]
 private partial def evalSuggestImpl (tac : TSyntax `tactic) : TacticM (TSyntax `tactic) := do
+  trace[try.debug] "{tac}"
   match tac with
   | `(tactic| $tac1 <;> $tac2) => evalSuggestChain tac1 tac2
   | `(tactic| first $[| $tacs]*) => evalSuggestFirst tacs
@@ -343,17 +369,17 @@ private def setGrindParams (tac : TSyntax `tactic) (params : Array (TSyntax ``Pa
   ⟨tac.raw.setArg 3 (mkNullNode paramsStx)⟩
 
 /-- Given a set of declaration names, returns `grind` parameters of the form `= <declName>` -/
-private def mkGrindEqnParams (declNames : Std.HashSet Name) : MetaM (Array (TSyntax ``Parser.Tactic.grindParam)) := do
-  declNames.toArray.mapM fun declName => do
+private def mkGrindEqnParams (declNames : Array Name) : MetaM (Array (TSyntax ``Parser.Tactic.grindParam)) := do
+  declNames.mapM fun declName => do
     `(Parser.Tactic.grindParam| = $(← toIdent declName))
 
 private def mkGrindStx (info : Try.Info) : MetaM (TSyntax `tactic) := do
   let grind ← `(tactic| grind?)
   let mut tacs := #[grind]
   unless info.eqnCandidates.isEmpty do
-    tacs := tacs.push (setGrindParams grind (← mkGrindEqnParams info.eqnCandidates))
+    tacs := tacs.push (setGrindParams grind (← mkGrindEqnParams info.eqnCandidates.elems))
   unless info.unfoldCandidates.isEmpty do
-    tacs := tacs.push (setGrindParams grind (← mkGrindEqnParams info.unfoldCandidates))
+    tacs := tacs.push (setGrindParams grind (← mkGrindEqnParams info.unfoldCandidates.elems))
   mkFirstStx tacs
 
 /-! Other generators -/
@@ -400,7 +426,7 @@ where
     `(tactic| induction $terms,* using $indFn <;> $cont)
 
 private def mkAllFunIndStx (info : Try.Info) (cont : TSyntax `tactic) : MetaM (TSyntax `tactic) := do
-  let tacs ← info.funIndCandidates.toArray.mapM (mkFunIndStx · cont)
+  let tacs ← info.funIndCandidates.elems.mapM (mkFunIndStx · cont)
   mkFirstStx tacs
 
 /-! Main code -/

src/Lean/Meta/Tactic/Try.lean

@@ -12,6 +12,7 @@ builtin_initialize registerTraceClass `try
 builtin_initialize registerTraceClass `try.collect
 builtin_initialize registerTraceClass `try.collect.funInd
 
+builtin_initialize registerTraceClass `try.debug
 builtin_initialize registerTraceClass `try.debug.funInd
 
 end Lean

src/Lean/Meta/Tactic/Try/Collect.lean

@@ -21,19 +21,35 @@ structure FunIndCandidate where
   majors : Array FVarId
   deriving Hashable, BEq
 
+/-- `Set` with insertion order preserved. -/
+structure OrdSet (α : Type) [Hashable α] [BEq α] where
+  elems : Array α := #[]
+  set : Std.HashSet α := {}
+  deriving Inhabited
+
+def OrdSet.insert {_ : Hashable α} {_ : BEq α} (s : OrdSet α) (a : α) : OrdSet α :=
+  if s.set.contains a then
+    s
+  else
+    let { elems, set } := s
+    { elems := elems.push a, set := set.insert a }
+
+def OrdSet.isEmpty {_ : Hashable α} {_ : BEq α} (s : OrdSet α) : Bool :=
+  s.elems.isEmpty
+
 structure Result where
   /-- All constant symbols occurring in the gal. -/
-  allConsts : Std.HashSet Name  := {}
+  allConsts : OrdSet Name  := {}
   /-- Unfolding candiates. -/
-  unfoldCandidates : Std.HashSet Name  := {}
+  unfoldCandidates : OrdSet Name  := {}
   /-- Equation function candiates. -/
-  eqnCandidates : Std.HashSet Name  := {}
+  eqnCandidates : OrdSet Name  := {}
   /-- Function induction candidates. -/
-  funIndCandidates : Std.HashSet FunIndCandidate := {}
+  funIndCandidates : OrdSet FunIndCandidate := {}
   /-- Induction candidates. -/
   indCandidates : Array InductionCandidate := #[]
   /-- Relevant declarations by `libSearch` -/
-  libSearchResults : Std.HashSet (Name × Grind.EMatchTheoremKind) := {}
+  libSearchResults : OrdSet (Name × Grind.EMatchTheoremKind) := {}
 
 structure Context where
   config : Try.Config

tests/lean/run/grind_constProp.lean

@@ -205,7 +205,15 @@ def evalExpr (e : Expr) : EvalM Val := do
 @[grind] theorem UnaryOp.simplify_eval (op : UnaryOp) : (op.simplify a).eval σ = (Expr.una op a).eval σ := by
   grind [UnaryOp.simplify.eq_def]
 
-/-- info: Try this: (induction e using Expr.simplify.induct) <;> grind -/
+/--
+info: Try these:
+• (induction e using Expr.simplify.induct) <;> grind
+• ·
+  induction e using Expr.simplify.induct
+  · grind only [Expr.simplify, BinOp.simplify, Expr.eval, BinaryOp.simplify_eval]
+  · grind only [UnaryOp.simplify_eval, UnaryOp.simplify, Expr.simplify, Expr.eval]
+  · simp
+-/
 #guard_msgs (info) in
 example (e : Expr) : e.simplify.eval σ = e.eval σ := by
   try?
@@ -304,7 +312,20 @@ theorem State.cons_le_of_eq (h₁ : σ' ≼ σ) (h₂ : σ.find? x = some v) : (
 @[grind] theorem State.join_le_left_of (h : σ₁ ≼ σ₂) (σ₃ : State) : σ₁.join σ₃ ≼ σ₂ := by
   grind
 
-/-- info: Try this: (induction σ₁, σ₂ using State.join.induct) <;> grind -/
+/--
+info: Try these:
+• (induction σ₁, σ₂ using State.join.induct) <;> grind
+• ·
+  induction σ₁, σ₂ using State.join.induct
+  ·
+    grind only [State.join_le_left, State.find?, State.join, State.join_le_left_of, State.le, = State.find?_nil,
+      State.bot_le, State.le_refl]
+  ·
+    grind only [State.join, State.join_le_left, State.length_erase_le, State.find?, State.join_le_left_of, State.le, =
+      State.find?_erase_eq, State.erase_le, State.le_refl, cases Or]
+  · grind only [State.join, State.join_le_left, State.length_erase_le, State.join_le_left_of, State.le, State.erase_le]
+  · grind only [State.join, State.join_le_left, State.length_erase_le, State.join_le_left_of, State.le, State.erase_le]
+-/
 #guard_msgs (info) in
 example (σ₁ σ₂ : State) : σ₁.join σ₂ ≼ σ₂ := by
   try?

tests/lean/run/try_trace1.lean

@@ -1,4 +1,5 @@
 set_option grind.warning false
+%reset_grind_attrs
 
 /--
 info: Try these:
@@ -97,3 +98,19 @@ example : app (app as bs) cs = app as (app bs cs) := by
   intro _ _ _
   -- `as`, `bs`, and `cs` now have inaccessible names.
   try?
+
+def concat : List α → α → List α
+  | .nil,       b => .cons b .nil
+  | .cons a as, b => .cons a (concat as b)
+
+attribute [simp] concat
+
+/--
+info: Try this: ·
+  induction as, a using concat.induct
+  · rfl
+  · simp_all
+-/
+#guard_msgs (info) in
+example (as : List α) (a : α) : concat as a = as ++ [a] := by
+  try?