From dc2cc5be773d3cf95fe67cd30f9843c7fc3854a2 Mon Sep 17 00:00:00 2001
From: Leni Aniva <v@leni.sh>
Date: Sat, 4 Nov 2023 15:00:51 -0700
Subject: [PATCH 01/12] test: Separate mvar coupling tests

---
 Pantograph/Goal.lean |   9 ++-
 Test/Common.lean     |  15 +++++
 Test/Holes.lean      | 129 ++++++++++++++++++++++++++++++-------------
 Test/Main.lean       |   4 +-
 Test/Proofs.lean     |  95 +------------------------------
 5 files changed, 116 insertions(+), 136 deletions(-)

diff --git a/Pantograph/Goal.lean b/Pantograph/Goal.lean
index 78a4194..eeb5a10 100644
--- a/Pantograph/Goal.lean
+++ b/Pantograph/Goal.lean
@@ -170,15 +170,18 @@ protected def GoalState.tryAssign (state: GoalState) (goalId: Nat) (expr: String
   tacticM { elaborator := .anonymous } |>.run' state.savedState.tactic
 
 /-- After finishing one branch of a proof (`graftee`), pick up from the point where the proof was left off (`target`) -/
-protected def GoalState.continue (target: GoalState) (graftee: GoalState): Except String GoalState :=
+protected def GoalState.continue (target: GoalState) (graftee: GoalState) (goals: Option (List MVarId) := .none): Except String GoalState :=
+  let goals := match goals with
+    | .some goals => goals
+    | .none => target.goals
   if target.root != graftee.root then
     .error s!"Roots of two continued goal states do not match: {target.root.name} != {graftee.root.name}"
   -- Ensure goals are not dangling
-  else if ¬ (target.goals.all (λ goal => graftee.mvars.contains goal)) then
+  else if ¬ (goals.all (λ goal => graftee.mvars.contains goal)) then
     .error s!"Some goals in target are not present in the graftee"
   else
     -- Set goals to the goals that have not been assigned yet, similar to the `focus` tactic.
-    let unassigned := target.goals.filter (λ goal =>
+    let unassigned := goals.filter (λ goal =>
       let mctx := graftee.mctx
       ¬(mctx.eAssignment.contains goal || mctx.dAssignment.contains goal))
     .ok {
diff --git a/Test/Common.lean b/Test/Common.lean
index f74e6a2..5b74a0f 100644
--- a/Test/Common.lean
+++ b/Test/Common.lean
@@ -1,4 +1,6 @@
 import Pantograph.Protocol
+import Pantograph.Goal
+import LSpec
 
 namespace Pantograph
 
@@ -15,6 +17,19 @@ def Goal.devolatilize (goal: Goal): Goal :=
       v with
       name := ""
     }
+deriving instance DecidableEq, Repr for Expression
+deriving instance DecidableEq, Repr for Variable
+deriving instance DecidableEq, Repr for Goal
 end Protocol
 
+def TacticResult.toString : TacticResult → String
+  | .success state => s!".success ({state.goals.length} goals)"
+  | .failure messages =>
+    let messages := "\n".intercalate messages.toList
+    s!".failure {messages}"
+  | .parseError error => s!".parseError {error}"
+  | .indexError index => s!".indexError {index}"
+
+def assertUnreachable (message: String): LSpec.TestSeq := LSpec.check message false
+
 end Pantograph
diff --git a/Test/Holes.lean b/Test/Holes.lean
index 64f2e2c..9b38087 100644
--- a/Test/Holes.lean
+++ b/Test/Holes.lean
@@ -1,31 +1,28 @@
 import LSpec
 import Pantograph.Goal
 import Pantograph.Serial
+import Test.Common
 
 namespace Pantograph.Test.Holes
 open Pantograph
 open Lean
 
-abbrev TestM := StateRefT LSpec.TestSeq (ReaderT Commands.Options M)
+abbrev TestM := StateRefT LSpec.TestSeq (ReaderT Protocol.Options M)
 
-deriving instance DecidableEq, Repr for Commands.Expression
-deriving instance DecidableEq, Repr for Commands.Variable
-deriving instance DecidableEq, Repr for Commands.Goal
-
-def add_test (test: LSpec.TestSeq): TestM Unit := do
+def addTest (test: LSpec.TestSeq): TestM Unit := do
   set $ (← get) ++ test
 
-def start_goal (hole: String): TestM (Option GoalState) := do
+def startProof (expr: String): TestM (Option GoalState) := do
   let env ← Lean.MonadEnv.getEnv
-  let syn? := syntax_from_str env hole
-  add_test $ LSpec.check s!"Parsing {hole}" (syn?.isOk)
+  let syn? := syntax_from_str env expr
+  addTest $ LSpec.check s!"Parsing {expr}" (syn?.isOk)
   match syn? with
   | .error error =>
     IO.println error
     return Option.none
   | .ok syn =>
-    let expr? ← syntax_to_expr syn
-    add_test $ LSpec.check s!"Elaborating" expr?.isOk
+    let expr? ← syntax_to_expr_type syn
+    addTest $ LSpec.check s!"Elaborating" expr?.isOk
     match expr? with
     | .error error =>
       IO.println error
@@ -34,40 +31,21 @@ def start_goal (hole: String): TestM (Option GoalState) := do
       let goal ← GoalState.create (expr := expr)
       return Option.some goal
 
-def assert_unreachable (message: String): LSpec.TestSeq := LSpec.check message false
-
-def build_goal (nameType: List (String × String)) (target: String): Commands.Goal :=
+def buildGoal (nameType: List (String × String)) (target: String) (userName?: Option String := .none): Protocol.Goal :=
   {
+    userName?,
     target := { pp? := .some target},
     vars := (nameType.map fun x => ({
-      name := x.fst,
+      userName := x.fst,
       type? := .some { pp? := .some x.snd },
       isInaccessible? := .some false
     })).toArray
   }
--- Like `build_goal` but allow certain variables to be elided.
-def build_goal_selective (nameType: List (String × Option String)) (target: String): Commands.Goal :=
-  {
-    target := { pp? := .some target},
-    vars := (nameType.map fun x => ({
-      name := x.fst,
-      type? := x.snd.map (λ type => { pp? := type }),
-      isInaccessible? := x.snd.map (λ _ => false)
-    })).toArray
-  }
-
-def construct_sigma: TestM Unit := do
-  let goal? ← start_goal "∀ (n m: Nat), n + m = m + n"
-  add_test $ LSpec.check "Start goal" goal?.isSome
-  if let .some goal := goal? then
-    return ()
-
-
-def proof_runner (env: Lean.Environment) (tests: TestM Unit): IO LSpec.TestSeq := do
+def proofRunner (env: Lean.Environment) (tests: TestM Unit): IO LSpec.TestSeq := do
   let termElabM := tests.run LSpec.TestSeq.done |>.run {} -- with default options
 
   let coreContext: Lean.Core.Context := {
-    currNamespace := str_to_name "Aniva",
+    currNamespace := Name.append .anonymous "Aniva",
     openDecls := [],     -- No 'open' directives needed
     fileName := "<Pantograph>",
     fileMap := { source := "", positions := #[0], lines := #[1] }
@@ -83,17 +61,94 @@ def proof_runner (env: Lean.Environment) (tests: TestM Unit): IO LSpec.TestSeq :
   | .ok (_, a) =>
     return a
 
+/-- M-coupled goals -/
+def test_m_couple: TestM Unit := do
+  let state? ← startProof "(2: Nat) ≤ 5"
+  let state0 ← match state? with
+    | .some state => pure state
+    | .none => do
+      addTest $ assertUnreachable "Goal could not parse"
+      return ()
+
+  let state1 ← match ← state0.execute (goalId := 0) (tactic := "apply Nat.le_trans") with
+    | .success state => pure state
+    | other => do
+      addTest $ assertUnreachable $ other.toString
+      return ()
+  addTest $ LSpec.check "apply Nat.le_trans" ((← state1.serializeGoals (options := ← read)).map (·.target.pp?) =
+    #[.some "2 ≤ ?m", .some "?m ≤ 5", .some "Nat"])
+  addTest $ LSpec.test "(1 root)" state1.rootExpr?.isNone
+  -- Set m to 3
+  let state2 ← match ← state1.execute (goalId := 2) (tactic := "exact 3") with
+    | .success state => pure state
+    | other => do
+      addTest $ assertUnreachable $ other.toString
+      return ()
+  addTest $ LSpec.test "(1b root)" state2.rootExpr?.isNone
+  let state1b ← match state1.continue state2 with
+    | .error msg => do
+      addTest $ assertUnreachable $ msg
+      return ()
+    | .ok state => pure state
+  addTest $ LSpec.check "exact 3" ((← state1b.serializeGoals (options := ← read)).map (·.target.pp?) =
+    #[.some "2 ≤ 3", .some "3 ≤ 5"])
+  addTest $ LSpec.test "(2 root)" state1b.rootExpr?.isNone
+  return ()
+
+def test_proposition_generation: TestM Unit := do
+  let state? ← startProof "Σ' p:Prop, p"
+  let state0 ← match state? with
+    | .some state => pure state
+    | .none => do
+      addTest $ assertUnreachable "Goal could not parse"
+      return ()
+
+  let state1 ← match ← state0.execute (goalId := 0) (tactic := "apply PSigma.mk") with
+    | .success state => pure state
+    | other => do
+      addTest $ assertUnreachable $ other.toString
+      return ()
+  addTest $ LSpec.check "apply PSigma.mk" ((← state1.serializeGoals (options := ← read)).map (·.devolatilize) =
+    #[
+      buildGoal [] "?fst" (userName? := .some "snd"),
+      buildGoal [] "Prop" (userName? := .some "fst")
+      ])
+  if let #[goal1, goal2] := ← state1.serializeGoals (options := { (← read) with printExprAST := true }) then
+    addTest $ LSpec.test "(1 reference)" (goal1.target.sexp? = .some s!"(:mv {goal2.name})")
+  addTest $ LSpec.test "(1 root)" state1.rootExpr?.isNone
+
+  let state2 ← match ← state1.tryAssign (goalId := 0) (expr := "λ (x: Nat) => _") with
+    | .success state => pure state
+    | other => do
+      addTest $ assertUnreachable $ other.toString
+      return ()
+  addTest $ LSpec.check ":= λ (x: Nat), _" ((← state2.serializeGoals (options := ← read)).map (·.target.pp?) =
+    #[.some "Nat → Prop", .some "∀ (x : Nat), ?m.29 x"])
+  addTest $ LSpec.test "(2 root)" state2.rootExpr?.isNone
+
+  let state3 ← match ← state2.tryAssign (goalId := 1) (expr := "fun x => Eq.refl x") with
+    | .success state => pure state
+    | other => do
+      addTest $ assertUnreachable $ other.toString
+      return ()
+  addTest $ LSpec.check ":= Eq.refl" ((← state3.serializeGoals (options := ← read)).map (·.target.pp?) =
+    #[])
+  addTest $ LSpec.test "(3 root)" state3.rootExpr?.isSome
+  return ()
+
+
 def suite: IO LSpec.TestSeq := do
   let env: Lean.Environment ← Lean.importModules
     (imports := #["Init"].map (λ str => { module := str_to_name str, runtimeOnly := false }))
     (opts := {})
     (trustLevel := 1)
   let tests := [
-    ("Σ'", construct_sigma)
+    ("2 < 5", test_m_couple),
+    ("Proposition Generation", test_proposition_generation)
   ]
   let tests ← tests.foldlM (fun acc tests => do
     let (name, tests) := tests
-    let tests ← proof_runner env tests
+    let tests ← proofRunner env tests
     return acc ++ (LSpec.group name tests)) LSpec.TestSeq.done
 
   return LSpec.group "Holes" tests
diff --git a/Test/Main.lean b/Test/Main.lean
index 5b9a24a..cb7c055 100644
--- a/Test/Main.lean
+++ b/Test/Main.lean
@@ -1,5 +1,5 @@
 import LSpec
---import Test.Holes
+import Test.Holes
 import Test.Integration
 import Test.Proofs
 import Test.Serial
@@ -11,7 +11,7 @@ unsafe def main := do
   Lean.initSearchPath (← Lean.findSysroot)
 
   let suites := [
-    --Holes.suite,
+    Holes.suite,
     Integration.suite,
     Proofs.suite,
     Serial.suite
diff --git a/Test/Proofs.lean b/Test/Proofs.lean
index c08ecb2..8ec01a7 100644
--- a/Test/Proofs.lean
+++ b/Test/Proofs.lean
@@ -6,17 +6,6 @@ import Pantograph.Goal
 import Pantograph.Serial
 import Test.Common
 
-namespace Pantograph
-
-def TacticResult.toString : TacticResult → String
-  | .success state => s!".success ({state.goals.length} goals)"
-  | .failure messages =>
-    let messages := "\n".intercalate messages.toList
-    s!".failure {messages}"
-  | .parseError error => s!".parseError {error}"
-  | .indexError index => s!".indexError {index}"
-end Pantograph
-
 namespace Pantograph.Test.Proofs
 open Pantograph
 open Lean
@@ -27,10 +16,6 @@ inductive Start where
 
 abbrev TestM := StateRefT LSpec.TestSeq (ReaderT Protocol.Options M)
 
-deriving instance DecidableEq, Repr for Protocol.Expression
-deriving instance DecidableEq, Repr for Protocol.Variable
-deriving instance DecidableEq, Repr for Protocol.Goal
-
 def addTest (test: LSpec.TestSeq): TestM Unit := do
   set $ (← get) ++ test
 
@@ -64,8 +49,6 @@ def startProof (start: Start): TestM (Option GoalState) := do
         let goal ← GoalState.create (expr := expr)
         return Option.some goal
 
-def assertUnreachable (message: String): LSpec.TestSeq := LSpec.check message false
-
 def buildGoal (nameType: List (String × String)) (target: String) (userName?: Option String := .none): Protocol.Goal :=
   {
     userName?,
@@ -303,80 +286,6 @@ def proof_or_comm: TestM Unit := do
       ]
     }
 
-/-- M-coupled goals -/
-def proof_m_couple: TestM Unit := do
-  let state? ← startProof (.expr "(2: Nat) ≤ 5")
-  let state0 ← match state? with
-    | .some state => pure state
-    | .none => do
-      addTest $ assertUnreachable "Goal could not parse"
-      return ()
-
-  let state1 ← match ← state0.execute (goalId := 0) (tactic := "apply Nat.le_trans") with
-    | .success state => pure state
-    | other => do
-      addTest $ assertUnreachable $ other.toString
-      return ()
-  addTest $ LSpec.check "apply Nat.le_trans" ((← state1.serializeGoals (options := ← read)).map (·.target.pp?) =
-    #[.some "2 ≤ ?m", .some "?m ≤ 5", .some "Nat"])
-  addTest $ LSpec.test "(1 root)" state1.rootExpr?.isNone
-  -- Set m to 3
-  let state2 ← match ← state1.execute (goalId := 2) (tactic := "exact 3") with
-    | .success state => pure state
-    | other => do
-      addTest $ assertUnreachable $ other.toString
-      return ()
-  addTest $ LSpec.test "(1b root)" state2.rootExpr?.isNone
-  let state1b ← match state1.continue state2 with
-    | .error msg => do
-      addTest $ assertUnreachable $ msg
-      return ()
-    | .ok state => pure state
-  addTest $ LSpec.check "exact 3" ((← state1b.serializeGoals (options := ← read)).map (·.target.pp?) =
-    #[.some "2 ≤ 3", .some "3 ≤ 5"])
-  addTest $ LSpec.test "(2 root)" state1b.rootExpr?.isNone
-  return ()
-
-def proof_proposition_generation: TestM Unit := do
-  let state? ← startProof (.expr "Σ' p:Prop, p")
-  let state0 ← match state? with
-    | .some state => pure state
-    | .none => do
-      addTest $ assertUnreachable "Goal could not parse"
-      return ()
-
-  let state1 ← match ← state0.execute (goalId := 0) (tactic := "apply PSigma.mk") with
-    | .success state => pure state
-    | other => do
-      addTest $ assertUnreachable $ other.toString
-      return ()
-  addTest $ LSpec.check "apply PSigma.mk" ((← state1.serializeGoals (options := ← read)).map (·.devolatilize) =
-    #[
-      buildGoal [] "?fst" (userName? := .some "snd"),
-      buildGoal [] "Prop" (userName? := .some "fst")
-      ])
-  if let #[goal1, goal2] := ← state1.serializeGoals (options := { (← read) with printExprAST := true }) then
-    addTest $ LSpec.test "(1 reference)" (goal1.target.sexp? = .some s!"(:mv {goal2.name})")
-  addTest $ LSpec.test "(1 root)" state1.rootExpr?.isNone
-
-  let state2 ← match ← state1.tryAssign (goalId := 0) (expr := "λ (x: Nat) => _") with
-    | .success state => pure state
-    | other => do
-      addTest $ assertUnreachable $ other.toString
-      return ()
-  addTest $ LSpec.check ":= λ (x: Nat), _" ((← state2.serializeGoals (options := ← read)).map (·.target.pp?) =
-    #[.some "Nat → Prop", .some "∀ (x : Nat), ?m.29 x"])
-  addTest $ LSpec.test "(2 root)" state2.rootExpr?.isNone
-
-  let state3 ← match ← state2.tryAssign (goalId := 1) (expr := "fun x => Eq.refl x") with
-    | .success state => pure state
-    | other => do
-      addTest $ assertUnreachable $ other.toString
-      return ()
-  addTest $ LSpec.check ":= Eq.refl" ((← state3.serializeGoals (options := ← read)).map (·.target.pp?) =
-    #[])
-  addTest $ LSpec.test "(3 root)" state3.rootExpr?.isSome
-  return ()
 
 def suite: IO LSpec.TestSeq := do
   let env: Lean.Environment ← Lean.importModules
@@ -388,9 +297,7 @@ def suite: IO LSpec.TestSeq := do
     ("Nat.add_comm manual", proof_nat_add_comm true),
     ("Nat.add_comm delta", proof_delta_variable),
     ("arithmetic", proof_arith),
-    ("Or.comm", proof_or_comm),
-    ("2 < 5", proof_m_couple),
-    ("Proposition Generation", proof_proposition_generation)
+    ("Or.comm", proof_or_comm)
   ]
   let tests ← tests.foldlM (fun acc tests => do
     let (name, tests) := tests

From 754fb69cffa23f97cd917bf9a59d88bb72c71b3a Mon Sep 17 00:00:00 2001
From: Leni Aniva <v@leni.sh>
Date: Sat, 4 Nov 2023 15:33:53 -0700
Subject: [PATCH 02/12] feat: Partial state continuation

---
 Pantograph/Goal.lean | 32 ++++++++++++++++--------------
 Test/Holes.lean      | 46 ++++++++++++++++++++++++++++++++++++++++++--
 Test/Proofs.lean     |  2 +-
 3 files changed, 63 insertions(+), 17 deletions(-)

diff --git a/Pantograph/Goal.lean b/Pantograph/Goal.lean
index eeb5a10..fd24232 100644
--- a/Pantograph/Goal.lean
+++ b/Pantograph/Goal.lean
@@ -169,30 +169,34 @@ protected def GoalState.tryAssign (state: GoalState) (goalId: Nat) (expr: String
       return .failure #[← exception.toMessageData.toString]
   tacticM { elaborator := .anonymous } |>.run' state.savedState.tactic
 
-/-- After finishing one branch of a proof (`graftee`), pick up from the point where the proof was left off (`target`) -/
-protected def GoalState.continue (target: GoalState) (graftee: GoalState) (goals: Option (List MVarId) := .none): Except String GoalState :=
-  let goals := match goals with
-    | .some goals => goals
-    | .none => target.goals
-  if target.root != graftee.root then
-    .error s!"Roots of two continued goal states do not match: {target.root.name} != {graftee.root.name}"
-  -- Ensure goals are not dangling
-  else if ¬ (goals.all (λ goal => graftee.mvars.contains goal)) then
-    .error s!"Some goals in target are not present in the graftee"
+/--
+Brings into scope a list of goals
+-/
+protected def GoalState.resume (state: GoalState) (goals: List MVarId): Except String GoalState :=
+  if ¬ (goals.all (λ goal => state.mvars.contains goal)) then
+    .error s!"Goals not in scope"
   else
     -- Set goals to the goals that have not been assigned yet, similar to the `focus` tactic.
     let unassigned := goals.filter (λ goal =>
-      let mctx := graftee.mctx
+      let mctx := state.mctx
       ¬(mctx.eAssignment.contains goal || mctx.dAssignment.contains goal))
     .ok {
+      state with
       savedState := {
-        term := graftee.savedState.term,
+        term := state.savedState.term,
         tactic := { goals := unassigned },
       },
-      root := target.root,
-      newMVars := graftee.newMVars,
     }
 
+/--
+Brings into scope all goals from `branch`
+-/
+protected def GoalState.continue (target: GoalState) (branch: GoalState): Except String GoalState :=
+  if target.root != branch.root then
+    .error s!"Roots of two continued goal states do not match: {target.root.name} != {branch.root.name}"
+  else
+    target.resume (goals := branch.goals)
+
 protected def GoalState.rootExpr? (goalState: GoalState): Option Expr :=
   let expr := goalState.mctx.eAssignment.find! goalState.root
   let (expr, _) := instantiateMVarsCore (mctx := goalState.mctx) (e := expr)
diff --git a/Test/Holes.lean b/Test/Holes.lean
index 9b38087..8692c2a 100644
--- a/Test/Holes.lean
+++ b/Test/Holes.lean
@@ -85,7 +85,7 @@ def test_m_couple: TestM Unit := do
       addTest $ assertUnreachable $ other.toString
       return ()
   addTest $ LSpec.test "(1b root)" state2.rootExpr?.isNone
-  let state1b ← match state1.continue state2 with
+  let state1b ← match state2.continue state1 with
     | .error msg => do
       addTest $ assertUnreachable $ msg
       return ()
@@ -136,6 +136,47 @@ def test_proposition_generation: TestM Unit := do
   addTest $ LSpec.test "(3 root)" state3.rootExpr?.isSome
   return ()
 
+def test_partial_continuation: TestM Unit := do
+  let state? ← startProof "(2: Nat) ≤ 5"
+  let state0 ← match state? with
+    | .some state => pure state
+    | .none => do
+      addTest $ assertUnreachable "Goal could not parse"
+      return ()
+
+  let state1 ← match ← state0.execute (goalId := 0) (tactic := "apply Nat.le_trans") with
+    | .success state => pure state
+    | other => do
+      addTest $ assertUnreachable $ other.toString
+      return ()
+  addTest $ LSpec.check "apply Nat.le_trans" ((← state1.serializeGoals (options := ← read)).map (·.target.pp?) =
+    #[.some "2 ≤ ?m", .some "?m ≤ 5", .some "Nat"])
+
+  let state2 ← match ← state1.execute (goalId := 2) (tactic := "apply Nat.succ") with
+    | .success state => pure state
+    | other => do
+      addTest $ assertUnreachable $ other.toString
+      return ()
+  addTest $ LSpec.check "apply Nat.succ" ((← state2.serializeGoals (options := ← read)).map (·.target.pp?) =
+    #[.some "Nat"])
+
+  -- Execute a partial continuation
+  let coupled_goals := state1.goals ++ state2.goals
+  let state1b ← match state2.resume (goals := coupled_goals) with
+    | .error msg => do
+      addTest $ assertUnreachable $ msg
+      return ()
+    | .ok state => pure state
+  addTest $ LSpec.check "(continue)" ((← state1b.serializeGoals (options := ← read)).map (·.target.pp?) =
+    #[.some "2 ≤ Nat.succ ?m", .some "Nat.succ ?m ≤ 5", .some "Nat"])
+  addTest $ LSpec.test "(2 root)" state1b.rootExpr?.isNone
+
+  -- Continuation should fail if the state does not exist:
+  match state0.resume coupled_goals with
+  | .error error => addTest $ LSpec.check "(continuation failure message)" (error = "Goals not in scope")
+  | .ok _ => addTest $ assertUnreachable "(continuation failure)"
+  return ()
+
 
 def suite: IO LSpec.TestSeq := do
   let env: Lean.Environment ← Lean.importModules
@@ -144,7 +185,8 @@ def suite: IO LSpec.TestSeq := do
     (trustLevel := 1)
   let tests := [
     ("2 < 5", test_m_couple),
-    ("Proposition Generation", test_proposition_generation)
+    ("Proposition Generation", test_proposition_generation),
+    ("Partial Continuation", test_partial_continuation)
   ]
   let tests ← tests.foldlM (fun acc tests => do
     let (name, tests) := tests
diff --git a/Test/Proofs.lean b/Test/Proofs.lean
index 8ec01a7..0d5fb4e 100644
--- a/Test/Proofs.lean
+++ b/Test/Proofs.lean
@@ -253,7 +253,7 @@ def proof_or_comm: TestM Unit := do
   addTest $ LSpec.check "  assumption" state4_2.goals.isEmpty
   addTest $ LSpec.check "(4_2 root)" state4_2.rootExpr?.isNone
   -- Ensure the proof can continue from `state4_2`.
-  let state2b ← match state2.continue state4_2 with
+  let state2b ← match state4_2.continue state2 with
     | .error msg => do
       addTest $ assertUnreachable $ msg
       return ()

From db706070ad56bdbdcadf8d119259868258b18e20 Mon Sep 17 00:00:00 2001
From: Leni Aniva <v@leni.sh>
Date: Sat, 4 Nov 2023 15:51:09 -0700
Subject: [PATCH 03/12] feat: Add goal.continue command

---
 Pantograph.lean          | 25 +++++++++++++++++++++++++
 Pantograph/Protocol.lean | 15 +++++++++++++++
 2 files changed, 40 insertions(+)

diff --git a/Pantograph.lean b/Pantograph.lean
index 00782d5..0984db8 100644
--- a/Pantograph.lean
+++ b/Pantograph.lean
@@ -38,6 +38,7 @@ def execute (command: Protocol.Command): MainM Lean.Json := do
   | "options.print"  => run options_print
   | "goal.start"     => run goal_start
   | "goal.tactic"    => run goal_tactic
+  | "goal.continue"  => run goal_continue
   | "goal.delete"    => run goal_delete
   | "goal.print"    => run goal_print
   | cmd =>
@@ -170,6 +171,30 @@ def execute (command: Protocol.Command): MainM Lean.Json := do
         return .error $ errorIndex s!"Invalid goal id index {goalId}"
       | .ok (.failure messages) =>
         return .ok { tacticErrors? := .some messages }
+  goal_continue (args: Protocol.GoalContinue): MainM (CR Protocol.GoalContinueResult) := do
+    let state ← get
+    match state.goalStates.get? args.target with
+    | .none => return .error $ errorIndex s!"Invalid state index {args.target}"
+    | .some target => do
+      let nextState? ← match args.branch?, args.goals? with
+        | .some branchId, .none => do
+          match state.goalStates.get? branchId with
+          | .none => return .error $ errorIndex s!"Invalid state index {branchId}"
+          | .some branch => pure $ target.continue branch
+        | .none, .some goals =>
+          let goals := goals.map (λ name => { name := str_to_name name })
+          pure $ target.resume goals
+        | _, _ => return .error <| errorI "arguments" "Exactly one of {branch, goals} must be supplied"
+      match nextState? with
+      | .error error => return .ok { error? := .some error }
+      | .ok nextGoalState =>
+        let (goalStates, nextStateId) := state.goalStates.insert nextGoalState
+        set { state with goalStates }
+        let goals ← nextGoalState.serializeGoals (parent := .some target) (options := state.options)
+        return .ok {
+          nextStateId? := .some nextStateId,
+          goals? := .some goals,
+        }
   goal_delete (args: Protocol.GoalDelete): MainM (CR Protocol.GoalDeleteResult) := do
     let state ← get
     let goalStates := args.stateIds.foldl (λ map id => map.remove id) state.goalStates
diff --git a/Pantograph/Protocol.lean b/Pantograph/Protocol.lean
index fd790bb..2469a6c 100644
--- a/Pantograph/Protocol.lean
+++ b/Pantograph/Protocol.lean
@@ -163,6 +163,21 @@ structure GoalTacticResult where
   -- Existence of this field shows the tactic parsing has failed
   parseError?: Option String := .none
   deriving Lean.ToJson
+structure GoalContinue where
+  -- State from which the continuation acquires the context
+  target: Nat
+
+  -- One of the following must be supplied
+  -- The state which is an ancestor of `target` where goals will be extracted from
+  branch?: Option Nat := .none
+  -- Or, the particular goals that should be brought back into scope
+  goals?: Option (List String) := .none
+  deriving Lean.FromJson
+structure GoalContinueResult where
+  error?: Option String := .none
+  nextStateId?: Option Nat := .none
+  goals?: Option (Array Goal) := .none
+  deriving Lean.ToJson
 
 -- Remove goal states
 structure GoalDelete where

From d809a960f99e339f0849c2c8a1fec76ceb3c3976 Mon Sep 17 00:00:00 2001
From: Leni Aniva <v@leni.sh>
Date: Sat, 4 Nov 2023 15:53:57 -0700
Subject: [PATCH 04/12] feat: Goal continuation fails if target has goals

---
 Pantograph/Goal.lean | 4 +++-
 Test/Holes.lean      | 5 +++++
 2 files changed, 8 insertions(+), 1 deletion(-)

diff --git a/Pantograph/Goal.lean b/Pantograph/Goal.lean
index fd24232..3645087 100644
--- a/Pantograph/Goal.lean
+++ b/Pantograph/Goal.lean
@@ -192,7 +192,9 @@ protected def GoalState.resume (state: GoalState) (goals: List MVarId): Except S
 Brings into scope all goals from `branch`
 -/
 protected def GoalState.continue (target: GoalState) (branch: GoalState): Except String GoalState :=
-  if target.root != branch.root then
+  if !target.goals.isEmpty then
+    .error s!"Target state has unresolved goals"
+  else if target.root != branch.root then
     .error s!"Roots of two continued goal states do not match: {target.root.name} != {branch.root.name}"
   else
     target.resume (goals := branch.goals)
diff --git a/Test/Holes.lean b/Test/Holes.lean
index 8692c2a..b6647ef 100644
--- a/Test/Holes.lean
+++ b/Test/Holes.lean
@@ -133,6 +133,7 @@ def test_proposition_generation: TestM Unit := do
       return ()
   addTest $ LSpec.check ":= Eq.refl" ((← state3.serializeGoals (options := ← read)).map (·.target.pp?) =
     #[])
+
   addTest $ LSpec.test "(3 root)" state3.rootExpr?.isSome
   return ()
 
@@ -175,6 +176,10 @@ def test_partial_continuation: TestM Unit := do
   match state0.resume coupled_goals with
   | .error error => addTest $ LSpec.check "(continuation failure message)" (error = "Goals not in scope")
   | .ok _ => addTest $ assertUnreachable "(continuation failure)"
+  -- Continuation should fail if some goals have not been solved
+  match state2.continue state1 with
+  | .error error => addTest $ LSpec.check "(continuation failure message)" (error = "Target state has unresolved goals")
+  | .ok _ => addTest $ assertUnreachable "(continuation failure)"
   return ()
 
 

From 782ce38c872492f293838ea10912d1da940b66bb Mon Sep 17 00:00:00 2001
From: Leni Aniva <v@leni.sh>
Date: Sat, 4 Nov 2023 15:54:28 -0700
Subject: [PATCH 05/12] chore: Version bump to 0.2.8

---
 Pantograph/Version.lean | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Pantograph/Version.lean b/Pantograph/Version.lean
index 29b3613..3fb09e9 100644
--- a/Pantograph/Version.lean
+++ b/Pantograph/Version.lean
@@ -1,5 +1,5 @@
 namespace Pantograph
 
-def version := "0.2.7"
+def version := "0.2.8"
 
 end Pantograph

From dbace9f2d57a4415c61eb9d4895a85bb9f7d54ae Mon Sep 17 00:00:00 2001
From: Leni Aniva <v@leni.sh>
Date: Mon, 6 Nov 2023 10:45:11 -0800
Subject: [PATCH 06/12] fix: Use Lean's built in name parser

The `str_to_name` parser cannot handle numerical names and escapes.
---
 Main.lean              |  4 ++--
 Pantograph.lean        |  6 +++---
 Pantograph/Symbol.lean |  4 ----
 Test/Holes.lean        | 16 +++++++++++++++-
 Test/Proofs.lean       |  2 +-
 Test/Serial.lean       | 20 ++++++++------------
 6 files changed, 29 insertions(+), 23 deletions(-)

diff --git a/Main.lean b/Main.lean
index d7f936e..bed33bb 100644
--- a/Main.lean
+++ b/Main.lean
@@ -46,7 +46,7 @@ namespace Lean
 def setOptionFromString' (opts : Options) (entry : String) : ExceptT String IO Options := do
   let ps := (entry.splitOn "=").map String.trim
   let [key, val] ← pure ps | throw "invalid configuration option entry, it must be of the form '<key> = <value>'"
-  let key := Pantograph.str_to_name key
+  let key := key.toName
   let defValue ← getOptionDefaultValue key
   match defValue with
   | DataValue.ofString _ => pure $ opts.setString key val
@@ -88,7 +88,7 @@ unsafe def main (args: List String): IO Unit := do
   let imports:= args.filter (λ s => ¬ (s.startsWith "--"))
 
   let env ← Lean.importModules
-    (imports := imports.toArray.map (λ str => { module := str_to_name str, runtimeOnly := false }))
+    (imports := imports.toArray.map (λ str => { module := str.toName, runtimeOnly := false }))
     (opts := {})
     (trustLevel := 1)
   let context: Context := {
diff --git a/Pantograph.lean b/Pantograph.lean
index 0984db8..fb4cc41 100644
--- a/Pantograph.lean
+++ b/Pantograph.lean
@@ -69,7 +69,7 @@ def execute (command: Protocol.Command): MainM Lean.Json := do
   lib_inspect (args: Protocol.LibInspect): MainM (CR Protocol.LibInspectResult) := do
     let state ← get
     let env ← Lean.MonadEnv.getEnv
-    let name := str_to_name args.name
+    let name :=  args.name.toName
     let info? := env.find? name
     match info? with
     | none => return .error $ errorIndex s!"Symbol not found {args.name}"
@@ -132,7 +132,7 @@ def execute (command: Protocol.Command): MainM Lean.Json := do
           | .error str => return .error <| errorI "elab" str
           | .ok expr => return .ok expr))
       | .none, .some copyFrom =>
-        (match env.find? <| str_to_name copyFrom with
+        (match env.find? <| copyFrom.toName with
         | .none => return .error <| errorIndex s!"Symbol not found: {copyFrom}"
         | .some cInfo => return .ok cInfo.type)
       | _, _ =>
@@ -182,7 +182,7 @@ def execute (command: Protocol.Command): MainM Lean.Json := do
           | .none => return .error $ errorIndex s!"Invalid state index {branchId}"
           | .some branch => pure $ target.continue branch
         | .none, .some goals =>
-          let goals := goals.map (λ name => { name := str_to_name name })
+          let goals := goals.map (λ name => { name := name.toName })
           pure $ target.resume goals
         | _, _ => return .error <| errorI "arguments" "Exactly one of {branch, goals} must be supplied"
       match nextState? with
diff --git a/Pantograph/Symbol.lean b/Pantograph/Symbol.lean
index 81d7deb..fb0ea1d 100644
--- a/Pantograph/Symbol.lean
+++ b/Pantograph/Symbol.lean
@@ -2,10 +2,6 @@ import Lean.Declaration
 
 namespace Pantograph
 
-/-- Converts a symbol of the form `aa.bb.cc` to a name -/
-def str_to_name (s: String): Lean.Name :=
-  (s.splitOn ".").foldl Lean.Name.str Lean.Name.anonymous
-
 def is_symbol_unsafe_or_internal (n: Lean.Name) (info: Lean.ConstantInfo): Bool :=
   let nameDeduce: Bool := match n.getRoot with
   | .str _ name => name.startsWith "_" ∨ name == "Lean"
diff --git a/Test/Holes.lean b/Test/Holes.lean
index b6647ef..afad4e8 100644
--- a/Test/Holes.lean
+++ b/Test/Holes.lean
@@ -172,6 +172,20 @@ def test_partial_continuation: TestM Unit := do
     #[.some "2 ≤ Nat.succ ?m", .some "Nat.succ ?m ≤ 5", .some "Nat"])
   addTest $ LSpec.test "(2 root)" state1b.rootExpr?.isNone
 
+  -- Roundtrip
+  --let coupled_goals := coupled_goals.map (λ g =>
+  --  { name := str_to_name $ name_to_ast g.name (sanitize := false)})
+  let coupled_goals := coupled_goals.map (λ g => name_to_ast g.name (sanitize := false))
+  let coupled_goals := coupled_goals.map (λ g => { name := g.toName })
+  let state1b ← match state2.resume (goals := coupled_goals) with
+    | .error msg => do
+      addTest $ assertUnreachable $ msg
+      return ()
+    | .ok state => pure state
+  addTest $ LSpec.check "(continue)" ((← state1b.serializeGoals (options := ← read)).map (·.target.pp?) =
+    #[.some "2 ≤ Nat.succ ?m", .some "Nat.succ ?m ≤ 5", .some "Nat"])
+  addTest $ LSpec.test "(2 root)" state1b.rootExpr?.isNone
+
   -- Continuation should fail if the state does not exist:
   match state0.resume coupled_goals with
   | .error error => addTest $ LSpec.check "(continuation failure message)" (error = "Goals not in scope")
@@ -185,7 +199,7 @@ def test_partial_continuation: TestM Unit := do
 
 def suite: IO LSpec.TestSeq := do
   let env: Lean.Environment ← Lean.importModules
-    (imports := #["Init"].map (λ str => { module := str_to_name str, runtimeOnly := false }))
+    (imports := #["Init"].map (λ str => { module := str.toName, runtimeOnly := false }))
     (opts := {})
     (trustLevel := 1)
   let tests := [
diff --git a/Test/Proofs.lean b/Test/Proofs.lean
index 0d5fb4e..8992697 100644
--- a/Test/Proofs.lean
+++ b/Test/Proofs.lean
@@ -23,7 +23,7 @@ def startProof (start: Start): TestM (Option GoalState) := do
   let env ← Lean.MonadEnv.getEnv
   match start with
   | .copy name =>
-    let cInfo? := str_to_name name |> env.find?
+    let cInfo? := name.toName |> env.find?
     addTest $ LSpec.check s!"Symbol exists {name}" cInfo?.isSome
     match cInfo? with
     | .some cInfo =>
diff --git a/Test/Serial.lean b/Test/Serial.lean
index dfa3890..c057bfb 100644
--- a/Test/Serial.lean
+++ b/Test/Serial.lean
@@ -9,9 +9,6 @@ open Lean
 
 deriving instance Repr, DecidableEq for Protocol.BoundExpression
 
-def test_str_to_name: LSpec.TestSeq :=
-  LSpec.test "Symbol parsing" (Name.str (.str (.str .anonymous "Lean") "Meta") "run" = Pantograph.str_to_name "Lean.Meta.run")
-
 def test_name_to_ast: LSpec.TestSeq :=
   let quote := "\""
   let escape := "\\"
@@ -21,14 +18,14 @@ def test_name_to_ast: LSpec.TestSeq :=
   LSpec.test s!"«̈{escape}{quote}»" (name_to_ast (Name.str .anonymous s!"{escape}{quote}") = s!"{quote}«{escape}{quote}»{quote}")
 
 def test_expr_to_binder (env: Environment): IO LSpec.TestSeq := do
-  let entries: List (String × Protocol.BoundExpression) := [
-    ("Nat.add_comm", { binders := #[("n", "Nat"), ("m", "Nat")], target := "n + m = m + n" }),
-    ("Nat.le_of_succ_le", { binders := #[("n", "Nat"), ("m", "Nat"), ("h", "Nat.succ n ≤ m")], target := "n ≤ m" })
+  let entries: List (Name × Protocol.BoundExpression) := [
+    ("Nat.add_comm".toName, { binders := #[("n", "Nat"), ("m", "Nat")], target := "n + m = m + n" }),
+    ("Nat.le_of_succ_le".toName, { binders := #[("n", "Nat"), ("m", "Nat"), ("h", "Nat.succ n ≤ m")], target := "n ≤ m" })
   ]
-  let coreM := entries.foldlM (λ suites (symbol, target) => do
+  let coreM: CoreM LSpec.TestSeq := entries.foldlM (λ suites (symbol, target) => do
     let env ← MonadEnv.getEnv
-    let expr := str_to_name symbol |> env.find? |>.get! |>.type
-    let test := LSpec.check symbol ((← type_expr_to_bound expr) = target)
+    let expr := env.find? symbol |>.get! |>.type
+    let test := LSpec.check symbol.toString ((← type_expr_to_bound expr) = target)
     return LSpec.TestSeq.append suites test) LSpec.TestSeq.done |>.run'
   let coreContext: Core.Context := {
     currNamespace := Lean.Name.str .anonymous "Aniva"
@@ -54,7 +51,7 @@ def test_sexp_of_symbol (env: Environment): IO LSpec.TestSeq := do
   ]
   let metaM: MetaM LSpec.TestSeq := entries.foldlM (λ suites (symbol, target) => do
     let env ← MonadEnv.getEnv
-    let expr := str_to_name symbol |> env.find? |>.get! |>.type
+    let expr := env.find? symbol.toName |>.get! |>.type
     let test := LSpec.check symbol ((serialize_expression_ast expr) = target)
     return LSpec.TestSeq.append suites test) LSpec.TestSeq.done
   let coreM := metaM.run'
@@ -72,12 +69,11 @@ def test_sexp_of_symbol (env: Environment): IO LSpec.TestSeq := do
 
 def suite: IO LSpec.TestSeq := do
   let env: Environment ← importModules
-    (imports := #["Init"].map (λ str => { module := str_to_name str, runtimeOnly := false }))
+    (imports := #["Init"].map (λ str => { module := str.toName, runtimeOnly := false }))
     (opts := {})
     (trustLevel := 1)
 
   return LSpec.group "Serialization" $
-    (LSpec.group "str_to_name" test_str_to_name) ++
     (LSpec.group "name_to_ast" test_name_to_ast) ++
     (LSpec.group "Expression binder" (← test_expr_to_binder env)) ++
     (LSpec.group "Sexp from symbol" (← test_sexp_of_symbol env))

From a7aeb03b43cad5b4c30610c83ad510cca59f383f Mon Sep 17 00:00:00 2001
From: Leni Aniva <v@leni.sh>
Date: Mon, 6 Nov 2023 11:04:28 -0800
Subject: [PATCH 07/12] chore: Update documentation

---
 README.md | 15 ++++++++-------
 1 file changed, 8 insertions(+), 7 deletions(-)

diff --git a/README.md b/README.md
index 0c19a3a..2b8425c 100644
--- a/README.md
+++ b/README.md
@@ -33,7 +33,7 @@ result of a command execution.  The command can be passed in one of two formats
 command { ... }
 { "cmd": command, "payload": ... }
 ```
-The list of available commands can be found in `Pantograph/Commands.lean` and below. An
+The list of available commands can be found in `Pantograph/Protocol.lean` and below. An
 empty command aborts the REPL.
 
 The `pantograph` executable must be run with a list of modules to import. It can
@@ -54,18 +54,18 @@ Example proving a theorem: (alternatively use `goal.start {"copyFrom": "Nat.add_
 ```
 $ pantograph Init
 goal.start {"expr": "∀ (n m : Nat), n + m = m + n"}
-goal.tactic {"goalId": 0, "tactic": "intro n m"}
-goal.tactic {"goalId": 1, "tactic": "assumption"}
-goal.delete {"goalIds": [0]}
+goal.tactic {"stateId": 0, "goalId": 0, "tactic": "intro n m"}
+goal.tactic {"stateId": 1, "goalId": 0, "tactic": "assumption"}
+goal.delete {"stateIds": [0]}
 stat {}
-goal.tactic {"goalId": 1, "tactic": "rw [Nat.add_comm]"}
+goal.tactic {"stateId": 1, "goalId": 0, "tactic": "rw [Nat.add_comm]"}
 stat
 ```
 where the application of `assumption` should lead to a failure.
 
 ## Commands
 
-See `Pantograph/Commands.lean` for a description of the parameters and return values in JSON.
+See `Pantograph/Protocol.lean` for a description of the parameters and return values in JSON.
 - `reset`: Delete all cached expressions and proof trees
 - `expr.echo {"expr": <expr>}`: Determine the type of an expression and round-trip it
 - `lib.catalog`: Display a list of all safe Lean symbols in the current context
@@ -73,10 +73,11 @@ See `Pantograph/Commands.lean` for a description of the parameters and return va
   given symbol; If value flag is set, the value is printed or hidden. By default
   only the values of definitions are printed.
 - `options.set { key: value, ... }`: Set one or more options (not Lean options; those
-  have to be set via command line arguments.), for options, see `Pantograph/Commands.lean`
+  have to be set via command line arguments.), for options, see `Pantograph/Protocol.lean`
 - `options.print`: Display the current set of options
 - `goal.start {["name": <name>], ["expr": <expr>], ["copyFrom": <symbol>]}`: Start a new goal from a given expression or symbol
 - `goal.tactic {"stateId": <id>, "goalId": <id>, ["tactic": <tactic>], ["expr": <expr>]}`: Execute a tactic string on a given goal
+- `goal.continue {"stateId": <id>, ["branch": <id>], ["goals": <names>]}`: Continue from a proof state
 - `goal.remove {"stateIds": [<id>]}"`: Remove a bunch of stored goals.
 - `goal.print {"stateId": <id>}"`: Print a goal state
 - `stat`: Display resource usage

From 245e76b2f1b5f0938989850e9a979250133ef651 Mon Sep 17 00:00:00 2001
From: Leni Aniva <v@leni.sh>
Date: Mon, 6 Nov 2023 11:51:31 -0800
Subject: [PATCH 08/12] feat: Print the root mvar name

---
 Pantograph.lean          | 2 +-
 Pantograph/Protocol.lean | 2 ++
 Test/Integration.lean    | 2 +-
 3 files changed, 4 insertions(+), 2 deletions(-)

diff --git a/Pantograph.lean b/Pantograph.lean
index fb4cc41..6ec4ac1 100644
--- a/Pantograph.lean
+++ b/Pantograph.lean
@@ -143,7 +143,7 @@ def execute (command: Protocol.Command): MainM Lean.Json := do
       let goalState ← GoalState.create expr
       let (goalStates, stateId) := state.goalStates.insert goalState
       set { state with goalStates }
-      return .ok { stateId }
+      return .ok { stateId, root := goalState.root.name.toString }
   goal_tactic (args: Protocol.GoalTactic): MainM (CR Protocol.GoalTacticResult) := do
     let state ← get
     match state.goalStates.get? args.stateId with
diff --git a/Pantograph/Protocol.lean b/Pantograph/Protocol.lean
index 2469a6c..ce42d9d 100644
--- a/Pantograph/Protocol.lean
+++ b/Pantograph/Protocol.lean
@@ -142,6 +142,8 @@ structure GoalStart where
   deriving Lean.FromJson
 structure GoalStartResult where
   stateId: Nat := 0
+  -- Name of the root metavariable
+  root: String
   deriving Lean.ToJson
 structure GoalTactic where
   -- Identifiers for tree, state, and goal
diff --git a/Test/Integration.lean b/Test/Integration.lean
index 0420a29..d8570b0 100644
--- a/Test/Integration.lean
+++ b/Test/Integration.lean
@@ -91,7 +91,7 @@ def test_tactic : IO LSpec.TestSeq :=
   subroutine_runner [
     subroutine_step "goal.start"
       [("expr", .str "∀ (p q: Prop), p ∨ q → q ∨ p")]
-     (Lean.toJson ({stateId := 0}:
+     (Lean.toJson ({stateId := 0, root := "_uniq.8"}:
       Protocol.GoalStartResult)),
     subroutine_step "goal.tactic"
       [("stateId", .num 0), ("goalId", .num 0), ("tactic", .str "intro x")]

From 7076669c3de25ab637d3465c153ff32622d025a6 Mon Sep 17 00:00:00 2001
From: Leni Aniva <v@leni.sh>
Date: Mon, 6 Nov 2023 12:20:08 -0800
Subject: [PATCH 09/12] chore: Code formatting

---
 Pantograph.lean | 22 +++++++++++-----------
 1 file changed, 11 insertions(+), 11 deletions(-)

diff --git a/Pantograph.lean b/Pantograph.lean
index 6ec4ac1..a1f2602 100644
--- a/Pantograph.lean
+++ b/Pantograph.lean
@@ -29,17 +29,17 @@ def execute (command: Protocol.Command): MainM Lean.Json := do
       | .error ierror => return Lean.toJson ierror
     | .error error => return Lean.toJson $ errorCommand s!"Unable to parse json: {error}"
   match command.cmd with
-  | "reset"          => run reset
-  | "stat"           => run stat
-  | "expr.echo"      => run expr_echo
-  | "lib.catalog"    => run lib_catalog
-  | "lib.inspect"    => run lib_inspect
-  | "options.set"    => run options_set
-  | "options.print"  => run options_print
-  | "goal.start"     => run goal_start
-  | "goal.tactic"    => run goal_tactic
-  | "goal.continue"  => run goal_continue
-  | "goal.delete"    => run goal_delete
+  | "reset"         => run reset
+  | "stat"          => run stat
+  | "expr.echo"     => run expr_echo
+  | "lib.catalog"   => run lib_catalog
+  | "lib.inspect"   => run lib_inspect
+  | "options.set"   => run options_set
+  | "options.print" => run options_print
+  | "goal.start"    => run goal_start
+  | "goal.tactic"   => run goal_tactic
+  | "goal.continue" => run goal_continue
+  | "goal.delete"   => run goal_delete
   | "goal.print"    => run goal_print
   | cmd =>
     let error: Protocol.InteractionError :=

From 764be6d14b5e77771e8233e12c83b1c40125f861 Mon Sep 17 00:00:00 2001
From: Leni Aniva <v@leni.sh>
Date: Tue, 7 Nov 2023 12:09:54 -0800
Subject: [PATCH 10/12] fix: Remove the error prone SemihashMap

---
 Pantograph.lean             |  36 +++++----
 Pantograph/SemihashMap.lean | 149 ------------------------------------
 2 files changed, 22 insertions(+), 163 deletions(-)
 delete mode 100644 Pantograph/SemihashMap.lean

diff --git a/Pantograph.lean b/Pantograph.lean
index a1f2602..0ae8192 100644
--- a/Pantograph.lean
+++ b/Pantograph.lean
@@ -1,8 +1,8 @@
 import Pantograph.Goal
 import Pantograph.Protocol
-import Pantograph.SemihashMap
 import Pantograph.Serial
 import Pantograph.Symbol
+import Lean.Data.HashMap
 
 namespace Pantograph
 
@@ -12,7 +12,8 @@ structure Context where
 /-- Stores state of the REPL -/
 structure State where
   options: Protocol.Options := {}
-  goalStates: SemihashMap GoalState := SemihashMap.empty
+  nextId: Nat := 0
+  goalStates: Lean.HashMap Nat GoalState := Lean.HashMap.empty
 
 /-- Main state monad for executing commands -/
 abbrev MainM := ReaderT Context (StateT State Lean.Elab.TermElabM)
@@ -53,7 +54,7 @@ def execute (command: Protocol.Command): MainM Lean.Json := do
   reset (_: Protocol.Reset): MainM (CR Protocol.StatResult) := do
     let state ← get
     let nGoals := state.goalStates.size
-    set { state with goalStates := SemihashMap.empty }
+    set { state with goalStates := Lean.HashMap.empty }
     return .ok { nGoals }
   stat (_: Protocol.Stat): MainM (CR Protocol.StatResult) := do
     let state ← get
@@ -141,12 +142,15 @@ def execute (command: Protocol.Command): MainM Lean.Json := do
     | .error error => return .error error
     | .ok expr =>
       let goalState ← GoalState.create expr
-      let (goalStates, stateId) := state.goalStates.insert goalState
-      set { state with goalStates }
+      let stateId := state.nextId
+      set { state with
+        goalStates := state.goalStates.insert stateId goalState,
+        nextId := state.nextId + 1
+      }
       return .ok { stateId, root := goalState.root.name.toString }
   goal_tactic (args: Protocol.GoalTactic): MainM (CR Protocol.GoalTacticResult) := do
     let state ← get
-    match state.goalStates.get? args.stateId with
+    match state.goalStates.find? args.stateId with
     | .none => return .error $ errorIndex s!"Invalid state index {args.stateId}"
     | .some goalState => do
       let nextGoalState?: Except _ GoalState ← match args.tactic?, args.expr? with
@@ -158,8 +162,9 @@ def execute (command: Protocol.Command): MainM Lean.Json := do
       match nextGoalState? with
       | .error error => return .error error
       | .ok (.success nextGoalState) =>
-        let (goalStates, nextStateId) := state.goalStates.insert nextGoalState
-        set { state with goalStates }
+        let nextStateId := state.nextId
+        let goalStates := state.goalStates.insert state.nextId goalState
+        set { state with goalStates, nextId := state.nextId + 1 }
         let goals ← nextGoalState.serializeGoals (parent := .some goalState) (options := state.options)
         return .ok {
           nextStateId? := .some nextStateId,
@@ -173,12 +178,12 @@ def execute (command: Protocol.Command): MainM Lean.Json := do
         return .ok { tacticErrors? := .some messages }
   goal_continue (args: Protocol.GoalContinue): MainM (CR Protocol.GoalContinueResult) := do
     let state ← get
-    match state.goalStates.get? args.target with
+    match state.goalStates.find? args.target with
     | .none => return .error $ errorIndex s!"Invalid state index {args.target}"
     | .some target => do
       let nextState? ← match args.branch?, args.goals? with
         | .some branchId, .none => do
-          match state.goalStates.get? branchId with
+          match state.goalStates.find? branchId with
           | .none => return .error $ errorIndex s!"Invalid state index {branchId}"
           | .some branch => pure $ target.continue branch
         | .none, .some goals =>
@@ -188,8 +193,11 @@ def execute (command: Protocol.Command): MainM Lean.Json := do
       match nextState? with
       | .error error => return .ok { error? := .some error }
       | .ok nextGoalState =>
-        let (goalStates, nextStateId) := state.goalStates.insert nextGoalState
-        set { state with goalStates }
+        let nextStateId := state.nextId
+        set { state with
+          goalStates := state.goalStates.insert nextStateId nextGoalState,
+          nextId := state.nextId + 1
+        }
         let goals ← nextGoalState.serializeGoals (parent := .some target) (options := state.options)
         return .ok {
           nextStateId? := .some nextStateId,
@@ -197,12 +205,12 @@ def execute (command: Protocol.Command): MainM Lean.Json := do
         }
   goal_delete (args: Protocol.GoalDelete): MainM (CR Protocol.GoalDeleteResult) := do
     let state ← get
-    let goalStates := args.stateIds.foldl (λ map id => map.remove id) state.goalStates
+    let goalStates := args.stateIds.foldl (λ map id => map.erase id) state.goalStates
     set { state with goalStates }
     return .ok {}
   goal_print (args: Protocol.GoalPrint): MainM (CR Protocol.GoalPrintResult) := do
     let state ← get
-    match state.goalStates.get? args.stateId with
+    match state.goalStates.find? args.stateId with
     | .none => return .error $ errorIndex s!"Invalid state index {args.stateId}"
     | .some goalState => do
       let root? ← goalState.rootExpr?.mapM (λ expr => serialize_expression state.options expr)
diff --git a/Pantograph/SemihashMap.lean b/Pantograph/SemihashMap.lean
deleted file mode 100644
index 1d9ebae..0000000
--- a/Pantograph/SemihashMap.lean
+++ /dev/null
@@ -1,149 +0,0 @@
-
-namespace Pantograph.SemihashMap
-
-structure Imp (β: Type u) where
-  data: Array (Option β)
-
-  -- Number of elements currently in use
-  size: Nat
-
-  -- Next index that has never been touched
-  allocFront: Nat
-
-  -- Deallocated indices
-  deallocs: Array Nat
-
-  -- Number of valid entries in `deallocs` array
-  lastDealloc: Nat
-
-namespace Imp
-
-structure WF (m: Imp β): Prop where
-  capacity: m.data.size = m.deallocs.size
-  front_dealloc: ∀ i: Fin m.deallocs.size, (i < m.allocFront) → (m.deallocs.get i) < m.allocFront
-  front_data: ∀ i: Fin m.data.size, (i ≥ m.allocFront) → (m.data.get i).isNone
-
-def empty (capacity := 16): Imp β :=
-  {
-    data := mkArray capacity .none,
-    size := 0,
-    allocFront := 0,
-    deallocs := mkArray capacity 0,
-    lastDealloc := 0,
-  }
-
-private theorem list_get_replicate (x: α) (i: Fin (List.replicate n x).length):
-    List.get (List.replicate n x) i = x := by
-  sorry
-
-theorem empty_wf : WF (empty n: Imp β) := by
-  unfold empty
-  apply WF.mk
-  case capacity =>
-    conv =>
-      lhs
-      congr
-      simp
-    conv =>
-      rhs
-      congr
-      simp
-    simp
-  case front_dealloc =>
-    simp_all
-    intro i
-    intro a
-    contradiction
-  case front_data =>
-    simp_all
-    intro i
-    unfold Imp.data at i
-    simp at i
-    conv =>
-      lhs
-      unfold Array.get
-      unfold mkArray
-      simp [List.replicate]
-      rewrite [list_get_replicate]
-
--- FIXME: Merge this with the well-formed versions below so proof and code can
--- mesh seamlessly.
-@[inline] def insert (map: Imp β) (v: β): (Imp β × Nat) :=
-  match map.lastDealloc with
-  | 0 => -- Capacity is full, buffer expansion is required
-    if map.size == map.data.size then
-      let nextIndex := map.data.size
-      let extendCapacity := map.size
-      let result: Imp β := {
-        data := (map.data.append #[Option.some v]).append (mkArray extendCapacity .none),
-        size := map.size + 1,
-        allocFront := map.size + 1,
-        deallocs := mkArray (map.data.size + 1 + extendCapacity) 0,
-        lastDealloc := 0,
-      }
-      (result, nextIndex)
-    else
-      let nextIndex := map.size
-      let result: Imp β := {
-        map
-        with
-        data := map.data.set ⟨nextIndex, sorry⟩ (Option.some v),
-        size := map.size + 1,
-        allocFront := map.allocFront + 1,
-      }
-      (result, nextIndex)
-  | (.succ k) => -- Allocation list has space
-    let nextIndex := map.deallocs.get! k
-    let result: Imp β := {
-      map with
-      data := map.data.set ⟨nextIndex, sorry⟩ (Option.some v),
-      size := map.size + 1,
-      lastDealloc := map.lastDealloc - 1
-    }
-    (result, nextIndex)
-
-@[inline] def remove (map: Imp β) (index: Fin (map.size)): Imp β :=
-  have h: index.val < map.data.size := by sorry
-  match map.data.get ⟨index.val, h⟩ with
-  | .none => map
-  | .some _ =>
-    {
-      map with
-      data := map.data.set ⟨index, sorry⟩ .none,
-      size := map.size - 1,
-      deallocs := map.deallocs.set ⟨map.lastDealloc, sorry⟩ index,
-      lastDealloc := map.lastDealloc + 1,
-    }
-
-/-- Retrieval is efficient -/
-@[inline] def get? (map: Imp β) (index: Fin (map.size)): Option β :=
-  have h: index.val < map.data.size := by sorry
-  map.data.get ⟨index.val, h⟩
-@[inline] def capacity (map: Imp β): Nat := map.data.size
-
-end Imp
-
-
-/--
-This is like a hashmap but you cannot control the keys.
--/
-def _root_.Pantograph.SemihashMap β := {m: Imp β // m.WF}
-
-@[inline] def empty (capacity := 16): SemihashMap β :=
-  ⟨ Imp.empty capacity, Imp.empty_wf ⟩
-@[inline] def insert (map: SemihashMap β) (v: β): (SemihashMap β × Nat) :=
-  let ⟨imp, pre⟩ := map
-  let ⟨result, id⟩ := imp.insert v
-  ( ⟨ result, sorry ⟩, id)
-@[inline] def remove (map: SemihashMap β) (index: Nat): SemihashMap β :=
-  let ⟨imp, pre⟩ := map
-  let result := imp.remove ⟨index, sorry⟩
-  ⟨ result, sorry ⟩
-@[inline] def get? (map: SemihashMap β) (index: Nat): Option β :=
-  let ⟨imp, _⟩ := map
-  imp.get? ⟨index, sorry⟩
-@[inline] def size (map: SemihashMap β): Nat :=
-  let ⟨imp, _⟩ := map
-  imp.size
-
-end Pantograph.SemihashMap

From 736e68639fed25fea192575f2661acf1e9e126f2 Mon Sep 17 00:00:00 2001
From: Leni Aniva <v@leni.sh>
Date: Tue, 7 Nov 2023 13:07:50 -0800
Subject: [PATCH 11/12] fix: New goal state not inserted correctly

---
 Pantograph.lean       |  8 +++++---
 Test/Integration.lean | 19 +++++++++++++++++--
 2 files changed, 22 insertions(+), 5 deletions(-)

diff --git a/Pantograph.lean b/Pantograph.lean
index 0ae8192..2532d75 100644
--- a/Pantograph.lean
+++ b/Pantograph.lean
@@ -54,7 +54,7 @@ def execute (command: Protocol.Command): MainM Lean.Json := do
   reset (_: Protocol.Reset): MainM (CR Protocol.StatResult) := do
     let state ← get
     let nGoals := state.goalStates.size
-    set { state with goalStates := Lean.HashMap.empty }
+    set { state with nextId := 0, goalStates := Lean.HashMap.empty }
     return .ok { nGoals }
   stat (_: Protocol.Stat): MainM (CR Protocol.StatResult) := do
     let state ← get
@@ -163,8 +163,10 @@ def execute (command: Protocol.Command): MainM Lean.Json := do
       | .error error => return .error error
       | .ok (.success nextGoalState) =>
         let nextStateId := state.nextId
-        let goalStates := state.goalStates.insert state.nextId goalState
-        set { state with goalStates, nextId := state.nextId + 1 }
+        set { state with
+          goalStates := state.goalStates.insert state.nextId nextGoalState,
+          nextId := state.nextId + 1,
+        }
         let goals ← nextGoalState.serializeGoals (parent := .some goalState) (options := state.options)
         return .ok {
           nextStateId? := .some nextStateId,
diff --git a/Test/Integration.lean b/Test/Integration.lean
index d8570b0..65c2da6 100644
--- a/Test/Integration.lean
+++ b/Test/Integration.lean
@@ -83,11 +83,19 @@ def test_malformed_command : IO LSpec.TestSeq :=
       Protocol.InteractionError))
   ]
 def test_tactic : IO LSpec.TestSeq :=
-  let goal: Protocol.Goal := {
+  let goal1: Protocol.Goal := {
     name := "_uniq.10",
     target := { pp? := .some "∀ (q : Prop), x ∨ q → q ∨ x" },
     vars := #[{ name := "_uniq.9", userName := "x", isInaccessible? := .some false, type? := .some { pp? := .some "Prop" }}],
   }
+  let goal2: Protocol.Goal := {
+    name := "_uniq.13",
+    target := { pp? := .some "x ∨ y → y ∨ x" },
+    vars := #[
+      { name := "_uniq.9", userName := "x", isInaccessible? := .some false, type? := .some { pp? := .some "Prop" }},
+      { name := "_uniq.12", userName := "y", isInaccessible? := .some false, type? := .some { pp? := .some "Prop" }}
+    ],
+  }
   subroutine_runner [
     subroutine_step "goal.start"
       [("expr", .str "∀ (p q: Prop), p ∨ q → q ∨ p")]
@@ -97,7 +105,14 @@ def test_tactic : IO LSpec.TestSeq :=
       [("stateId", .num 0), ("goalId", .num 0), ("tactic", .str "intro x")]
      (Lean.toJson ({
        nextStateId? := .some 1,
-       goals? := #[goal],
+       goals? := #[goal1],
+     }:
+      Protocol.GoalTacticResult)),
+    subroutine_step "goal.tactic"
+      [("stateId", .num 1), ("goalId", .num 0), ("tactic", .str "intro y")]
+     (Lean.toJson ({
+       nextStateId? := .some 2,
+       goals? := #[goal2],
      }:
       Protocol.GoalTacticResult))
   ]

From 8218d3f004726e4758612a4fa0951e89ac4c9a74 Mon Sep 17 00:00:00 2001
From: Leni Aniva <v@leni.sh>
Date: Tue, 7 Nov 2023 13:10:14 -0800
Subject: [PATCH 12/12] fix: Do not show parent state in continue

---
 Pantograph.lean | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Pantograph.lean b/Pantograph.lean
index 2532d75..f9f8cc6 100644
--- a/Pantograph.lean
+++ b/Pantograph.lean
@@ -200,7 +200,7 @@ def execute (command: Protocol.Command): MainM Lean.Json := do
           goalStates := state.goalStates.insert nextStateId nextGoalState,
           nextId := state.nextId + 1
         }
-        let goals ← nextGoalState.serializeGoals (parent := .some target) (options := state.options)
+        let goals ← nextGoalState.serializeGoals (parent := .none) (options := state.options)
         return .ok {
           nextStateId? := .some nextStateId,
           goals? := .some goals,