Merge pull request 'feat(frontend): Tomogram' (#220) from frontend/tomogram into dev

Reviewed-on: #220

Pantograph/Delate.lean

@@ -63,12 +63,16 @@ def exprProjToApp (env : Environment) (e : Expr) : Expr :=
       (List.range numFields)
     mkAppN callee (typeArgs ++ [motive, major, induct]).toArray
 
-def _root_.Lean.Name.isAuxLemma (n : Lean.Name) : Bool := n matches .num (.str _ "_auxLemma") _
+def isAuxLemma (n : Name) : Bool :=
+  match n with
+  -- `mkAuxLemma` generally allows for arbitrary prefixes but these are the ones produced by core.
+  | .str _ s => "_proof_".isPrefixOf s || "_simp_".isPrefixOf s
+  | _ => false
 
 /-- Unfold all lemmas created by `Lean.Meta.mkAuxLemma`. These end in `_auxLemma.nn` where `nn` is a number. -/
 @[export pantograph_unfold_aux_lemmas_m]
-def unfoldAuxLemmas : Expr → CoreM Expr :=
-  (Meta.deltaExpand · Lean.Name.isAuxLemma)
+def unfoldAuxLemmas (e : Expr) : CoreM Expr := do
+  Meta.deltaExpand e isAuxLemma
 /-- Unfold all matcher applications -/
 @[export pantograph_unfold_matchers_m]
 def unfoldMatchers (expr : Expr) : CoreM Expr :=
@@ -451,7 +455,6 @@ def serializeExpression (options: @&Protocol.Options) (e: Expr): MetaM Protocol.
     dependentMVars?,
   }
 
-
 /-- Adapted from ppGoal -/
 def serializeGoal (options: @&Protocol.Options) (goal: MVarId) (mvarDecl: MetavarDecl) (parentDecl?: Option MetavarDecl := .none)
       : MetaM Protocol.Goal := do
@@ -517,7 +520,6 @@ def serializeGoal (options: @&Protocol.Options) (goal: MVarId) (mvarDecl: Metava
     return {
       name := goal.name.toString,
       userName? := if mvarDecl.userName == .anonymous then .none else .some (ofName mvarDecl.userName),
-      isConversion := isLHSGoal? mvarDecl.type |>.isSome,
       target := (← serializeExpression options (← instantiate mvarDecl.type)),
       vars := vars.reverse.toArray
     }
@@ -527,17 +529,20 @@ def serializeGoal (options: @&Protocol.Options) (goal: MVarId) (mvarDecl: Metava
 
 protected def GoalState.serializeGoals
       (state: GoalState)
-      (parent: Option GoalState := .none)
       (options: @&Protocol.Options := {}):
     MetaM (Array Protocol.Goal):= do
   state.restoreMetaM
   let goals := state.goals.toArray
-  let parentDecl? := parent.bind (λ parentState => parentState.mctx.findDecl? state.parentMVar?.get!)
   goals.mapM fun goal => do
+    let fragment := match state.fragments[goal]? with
+      | .none => .tactic
+      | .some $ .calc .. => .calc
+      | .some $ .conv .. => .conv
+      | .some $ .convSentinel .. => .conv
     match state.mctx.findDecl? goal with
     | .some mvarDecl =>
-      let serializedGoal ← serializeGoal options goal mvarDecl (parentDecl? := parentDecl?)
-      pure serializedGoal
+      let serializedGoal ← serializeGoal options goal mvarDecl (parentDecl? := .none)
+      pure { serializedGoal with fragment }
     | .none => throwError s!"Metavariable does not exist in context {goal.name}"
 
 /-- Print the metavariables in a readable format -/
@@ -603,7 +608,9 @@ protected def GoalState.diag (goalState: GoalState) (parent?: Option GoalState :
     userNameToString : Name → String
       | .anonymous => ""
       | other => s!"[{other}]"
-    parentHasMVar (mvarId: MVarId): Bool := parent?.map (λ state => state.mctx.decls.contains mvarId) |>.getD true
+    parentHasMVar (mvarId: MVarId): Bool := match parent? with
+      | .some state => state.mctx.decls.contains mvarId
+      | .none => true
 
 initialize
   registerTraceClass `Pantograph.Delate

Pantograph/Environment.lean

@@ -14,7 +14,7 @@ namespace Pantograph.Environment
 @[export pantograph_is_name_internal]
 def isNameInternal (n: Name): Bool :=
   -- Returns true if the name is an implementation detail which should not be shown to the user.
-  n.isAuxLemma ∨ n.hasMacroScopes
+  isAuxLemma n ∨ n.hasMacroScopes
 
 /-- Catalog all the non-internal and safe names -/
 @[export pantograph_environment_catalog]

Pantograph/Frontend/InfoTree.lean

@@ -10,7 +10,7 @@ namespace Lean.Elab
 private def elaboratorToString : Name → String
   | .anonymous => ""
   | n => s!"⟨{n}⟩ "
-private def indent (s : String) : String := "\n".intercalate $ s.splitOn "\n" |>.map ("\t" ++ .)
+private def indent (s : String) : String := "\n".intercalate $ s.splitOn "\n" |>.map ("  " ++ .)
 
 /-- The `Syntax` for a `Lean.Elab.Info`, if there is one. -/
 protected def Info.stx? : Info → Option Syntax
@@ -131,16 +131,16 @@ partial def InfoTree.toString (t : InfoTree) (ctx?: Option Elab.ContextInfo := .
   | .node info children =>
     if let some ctx := ctx? then
       let node : String ← match info with
-      | .ofTermInfo    info => pure s!"[term] {(← info.toString ctx)}"
-      | .ofCommandInfo info => pure s!"[command] {(← info.toString ctx)}"
-      | .ofTacticInfo  info => pure s!"[tactic] {(← info.toString ctx)}"
+      | .ofTermInfo    info => pure s!"[term] {info.stx}"
+      | .ofCommandInfo info => pure s!"[command] {info.stx}"
+      | .ofTacticInfo  info => pure s!"[tactic] {info.stx}"
       | .ofMacroExpansionInfo _ => pure "[macro_exp]"
-      | .ofOptionInfo _ => pure "[option]"
+      | .ofOptionInfo info => pure s!"[option] {info.stx}"
       | .ofFieldInfo _ => pure "[field]"
-      | .ofCompletionInfo _ => pure "[completion]"
+      | .ofCompletionInfo info => pure s!"[completion] {info.stx}"
       | .ofUserWidgetInfo _ => pure "[user_widget]"
       | .ofCustomInfo _ => pure "[custom]"
-      | .ofFVarAliasInfo _ => pure "[fvar]"
+      | .ofFVarAliasInfo _ => pure "[fvar_alias]"
       | .ofFieldRedeclInfo _ => pure "[field_redecl]"
       | .ofChoiceInfo _ => pure "[choice]"
       | .ofPartialTermInfo  _ => pure "[partial_term]"

Pantograph/Goal.lean

@@ -10,24 +10,72 @@ import Lean
 namespace Pantograph
 open Lean
 
+/-- The acting area of a tactic -/
+inductive Site where
+  -- Dormant all other goals
+  | focus (goal : MVarId)
+  -- Move the goal to the first in the list
+  | prefer (goal : MVarId)
+  -- Execute as-is, no goals go dormant
+  | unfocus
+  deriving BEq, Inhabited
+
+instance : Coe MVarId Site where
+  coe := .focus
+instance : ToString Site where
+  toString
+    | .focus { name } => s!"[{name}]"
+    | .prefer { name } => s!"[{name},...]"
+    | .unfocus => "[*]"
+
+/-- Executes a `TacticM` on a site and return affected goals -/
+protected def Site.runTacticM (site : Site)
+  { m } [Monad m] [MonadLiftT Elab.Tactic.TacticM m] [MonadControlT Elab.Tactic.TacticM m] [MonadMCtx m] [MonadError m]
+  (f : m α) : m (α × List MVarId) :=
+  match site with
+  | .focus goal => do
+    Elab.Tactic.setGoals [goal]
+    let a ← f
+    return (a, [goal])
+  | .prefer goal => do
+    let before ← Elab.Tactic.getUnsolvedGoals
+    let otherGoals := before.filter (· != goal)
+    Elab.Tactic.setGoals (goal :: otherGoals)
+    let a ← f
+    let after ← Elab.Tactic.getUnsolvedGoals
+    let parents := before.filter (¬ after.contains ·)
+    Elab.Tactic.pruneSolvedGoals
+    return (a, parents)
+  | .unfocus => do
+    let before ← Elab.Tactic.getUnsolvedGoals
+    let a ← f
+    let after ← Elab.Tactic.getUnsolvedGoals
+    let parents := before.filter (¬ after.contains ·)
+    Elab.Tactic.pruneSolvedGoals
+    return (a, parents)
+
 /--
-Represents an interconnected set of metavariables, or a state in proof search
+Kernel view of the state of a proof
  -/
 structure GoalState where
+  -- Captured `TacticM` state
   savedState : Elab.Tactic.SavedState
 
-  -- The root hole which is the search target
+  -- The root goal which is the search target
   root: MVarId
 
-  -- Parent state metavariable source
-  parentMVar?: Option MVarId
+  /--
+  Parent goals which became assigned or fragmented to produce this state.
+  Note that due to the existence of tactic fragments, parent goals do not
+  necessarily have an expression assignment.
+  -/
+  parentMVars : List MVarId := []
 
-  -- Existence of this field shows that we are currently in `conv` mode.
-  -- (convRhs, goal, dormant)
-  convMVar?: Option (MVarId × MVarId × List MVarId) := .none
-  -- Previous RHS for calc, so we don't have to repeat it every time
-  -- WARNING: If using `state with` outside of `calc`, this must be set to `.none`
-  calcPrevRhs?: Option (MVarId × Expr) := .none
+  -- Any goal associated with a fragment has a partial tactic which has not
+  -- finished executing.
+  fragments : FragmentMap := .empty
+
+def throwNoGoals { m α } [Monad m] [MonadError m] : m α := throwError "no goals to be solved"
 
 @[export pantograph_goal_state_create_m]
 protected def GoalState.create (expr: Expr): Elab.TermElabM GoalState := do
@@ -42,7 +90,6 @@ protected def GoalState.create (expr: Expr): Elab.TermElabM GoalState := do
   return {
     root := root.mvarId!,
     savedState,
-    parentMVar? := .none,
   }
 @[export pantograph_goal_state_create_from_mvars_m]
 protected def GoalState.createFromMVars (goals: List MVarId) (root: MVarId): MetaM GoalState := do
@@ -51,13 +98,19 @@ protected def GoalState.createFromMVars (goals: List MVarId) (root: MVarId): Met
   return {
     root,
     savedState,
-    parentMVar? := .none,
   }
-@[export pantograph_goal_state_is_conv]
-protected def GoalState.isConv (state: GoalState): Bool :=
-  state.convMVar?.isSome
+@[always_inline]
 protected def GoalState.goals (state: GoalState): List MVarId :=
   state.savedState.tactic.goals
+@[always_inline]
+protected def GoalState.mainGoal? (state : GoalState) : Option MVarId :=
+  state.goals.head?
+@[always_inline]
+protected def GoalState.actingGoal? (state : GoalState) (site : Site) : Option MVarId := do
+  match site with
+  | .focus goal | .prefer goal => return goal
+  | .unfocus => state.mainGoal?
+
 @[export pantograph_goal_state_goals]
 protected def GoalState.goalsArray (state: GoalState): Array MVarId := state.goals.toArray
 protected def GoalState.mctx (state: GoalState): MetavarContext :=
@@ -69,8 +122,10 @@ protected def GoalState.env (state: GoalState): Environment :=
 protected def GoalState.metaContextOfGoal (state: GoalState) (mvarId: MVarId): Option Meta.Context := do
   let mvarDecl ← state.mctx.findDecl? mvarId
   return { lctx := mvarDecl.lctx, localInstances := mvarDecl.localInstances }
+@[always_inline]
 protected def GoalState.metaState (state: GoalState): Meta.State :=
   state.savedState.term.meta.meta
+@[always_inline]
 protected def GoalState.coreState (state: GoalState): Core.SavedState :=
   state.savedState.term.meta.core
 
@@ -78,18 +133,19 @@ protected def GoalState.withContext' (state: GoalState) (mvarId: MVarId) (m: Met
   mvarId.withContext m |>.run' (← read) state.metaState
 protected def GoalState.withContext { m } [MonadControlT MetaM m] [Monad m] (state: GoalState) (mvarId: MVarId) : m α → m α :=
   Meta.mapMetaM <| state.withContext' mvarId
+/-- Uses context of the first parent -/
 protected def GoalState.withParentContext { n } [MonadControlT MetaM n] [Monad n] (state: GoalState): n α → n α :=
-  Meta.mapMetaM <| state.withContext' state.parentMVar?.get!
+  Meta.mapMetaM <| state.withContext' state.parentMVars[0]!
 protected def GoalState.withRootContext { n } [MonadControlT MetaM n] [Monad n] (state: GoalState): n α → n α :=
   Meta.mapMetaM <| state.withContext' state.root
 
-private def GoalState.mvars (state: GoalState): SSet MVarId :=
-  state.mctx.decls.foldl (init := .empty) fun acc k _ => acc.insert k
--- Restore the name generator and macro scopes of the core state
-protected def GoalState.restoreCoreMExtra (state: GoalState): CoreM Unit := do
-  let savedCore := state.coreState
+private def restoreCoreMExtra (state : Core.SavedState) : CoreM Unit :=
+  let { nextMacroScope, ngen, .. } := state
   modifyGetThe Core.State (fun st => ((),
-    { st with nextMacroScope := savedCore.nextMacroScope, ngen := savedCore.ngen }))
+    { st with nextMacroScope, ngen }))
+-- Restore the name generator and macro scopes of the core state
+protected def GoalState.restoreCoreMExtra (state: GoalState): CoreM Unit :=
+  restoreCoreMExtra state.coreState
 protected def GoalState.restoreMetaM (state: GoalState): MetaM Unit := do
   state.restoreCoreMExtra
   state.savedState.term.meta.restore
@@ -100,42 +156,13 @@ private def GoalState.restoreTacticM (state: GoalState) (goal: MVarId): Elab.Tac
   state.restoreElabM
   Elab.Tactic.setGoals [goal]
 
-@[export pantograph_goal_state_focus]
-protected def GoalState.focus (state: GoalState) (goalId: Nat): Option GoalState := do
-  let goal ← state.savedState.tactic.goals[goalId]?
-  return {
-    state with
-    savedState := {
-      state.savedState with
-      tactic := { goals := [goal] },
-    },
-    calcPrevRhs? := .none,
-  }
-
-/-- Immediately bring all parent goals back into scope. Used in automatic mode -/
-@[export pantograph_goal_state_immediate_resume]
-protected def GoalState.immediateResume (state: GoalState) (parent: GoalState): GoalState :=
-  -- Prune parents solved goals
-  let mctx := state.mctx
-  let parentGoals := parent.goals.filter λ goal =>
-    let isDuplicate := state.goals.contains goal
-    let isSolved := mctx.eAssignment.contains goal || mctx.dAssignment.contains goal
-    (¬ isDuplicate) && (¬ isSolved)
-  {
-    state with
-    savedState := {
-      state.savedState with
-      tactic := { goals := state.goals ++ parentGoals },
-    },
-  }
-
 /--
-Brings into scope a list of goals. User must ensure `goals` is distinct.
+Brings into scope a list of goals. User must ensure `goals` are distinct.
 -/
 @[export pantograph_goal_state_resume]
 protected def GoalState.resume (state : GoalState) (goals : List MVarId) : Except String GoalState := do
-  if ¬ (goals.all (λ goal => state.mvars.contains goal)) then
-    let invalid_goals := goals.filter (λ goal => ¬ state.mvars.contains goal) |>.map (·.name.toString)
+  if ¬ (goals.all (state.mctx.decls.contains ·)) then
+    let invalid_goals := goals.filter (λ goal => ¬ state.mctx.decls.contains goal) |>.map (·.name.toString)
     .error s!"Goals {invalid_goals} are not in scope"
   -- Set goals to the goals that have not been assigned yet, similar to the `focus` tactic.
   let unassigned := goals.filter λ goal =>
@@ -173,27 +200,227 @@ protected def GoalState.isSolved (goalState : GoalState) : Bool :=
     | .some e => ¬ e.hasExprMVar
     | .none => true
   goalState.goals.isEmpty && solvedRoot
-@[export pantograph_goal_state_parent_expr]
-protected def GoalState.parentExpr? (goalState: GoalState): Option Expr := do
-  let parent ← goalState.parentMVar?
-  let expr := goalState.mctx.eAssignment.find! parent
-  let (expr, _) := instantiateMVarsCore (mctx := goalState.mctx) (e := expr)
-  return expr
 @[export pantograph_goal_state_get_mvar_e_assignment]
 protected def GoalState.getMVarEAssignment (goalState: GoalState) (mvarId: MVarId): Option Expr := do
   let expr ← goalState.mctx.eAssignment.find? mvarId
   let (expr, _) := instantiateMVarsCore (mctx := goalState.mctx) (e := expr)
   return expr
+@[export pantograph_goal_state_parent_exprs]
+protected def GoalState.parentExprs (state : GoalState) : List (Except Fragment Expr) :=
+  state.parentMVars.map λ goal => match state.getMVarEAssignment goal with
+    | .some e => .ok e
+    -- A parent goal which is not assigned must have a fragment
+    | .none => .error state.fragments[goal]!
+@[always_inline]
+protected def GoalState.hasUniqueParent (state : GoalState) : Bool :=
+  state.parentMVars.length == 1
+@[always_inline]
+protected def GoalState.parentExpr! (state : GoalState) : Expr :=
+  assert! state.parentMVars.length == 1
+  (state.getMVarEAssignment state.parentMVars[0]!).get!
+
+deriving instance BEq for DelayedMetavarAssignment
+
+/-- Given states `dst`, `src`, and `src'`, where `dst` and `src'` are
+descendants of `src`, replay the differential `src' - src` in `dst`. Colliding
+metavariable and lemma names will be automatically renamed to ensure there is no
+collision. This implements branch unification. Unification might be impossible
+if conflicting assignments exist. We also assume the monotonicity property: In a
+chain of descending goal states, a mvar cannot be unassigned, and once assigned
+its assignment cannot change. -/
+@[export pantograph_goal_state_replay_m]
+protected def GoalState.replay (dst : GoalState) (src src' : GoalState) : CoreM GoalState :=
+  withTraceNode `Pantograph.GoalState.replay (fun _ => return m!"replay") do
+  let srcNGen := src.coreState.ngen
+  let srcNGen' := src'.coreState.ngen
+  let dstNGen := dst.coreState.ngen
+  assert! srcNGen.namePrefix == srcNGen'.namePrefix
+  assert! srcNGen.namePrefix == dstNGen.namePrefix
+  assert! src.mctx.depth == src'.mctx.depth
+  assert! src.mctx.depth == dst.mctx.depth
+
+  let diffNGenIdx := dst.coreState.ngen.idx - srcNGen.idx
+
+  let env ← dst.coreState.env.replayConsts src.env src'.env (skipExisting := true)
+
+  trace[Pantograph.GoalState.replay] "Merging ngen {srcNGen.idx} -> ({srcNGen'.idx}, {dstNGen.idx})"
+  -- True if the name is generated after `src`
+  let isNewName : Name → Bool
+    | .num pref n =>
+      pref == srcNGen.namePrefix ∧ n ≥ srcNGen.idx
+    | _ => false
+  let mapId : Name → Name
+    | id@(.num pref n) =>
+      if isNewName id then
+        .num pref (n + diffNGenIdx)
+      else
+        id
+    | id => id
+  let mapMVar : MVarId → MVarId
+    | { name } => ⟨mapId name⟩
+  let rec mapLevel : Level → Level
+    | .succ x => .succ (mapLevel x)
+    | .max l1 l2 => .max (mapLevel l1) (mapLevel l2)
+    | .imax l1 l2 => .imax (mapLevel l1) (mapLevel l2)
+    | .mvar { name } => .mvar ⟨mapId name⟩
+    | l => l
+  let mapExpr (e : Expr) : CoreM Expr := Core.transform e λ
+    | .sort level => pure $ .done $ .sort (mapLevel level)
+    | .mvar { name } => pure $ .done $ .mvar ⟨mapId name⟩
+    | _ => pure .continue
+  let mapDelayedAssignment (d : DelayedMetavarAssignment) : CoreM DelayedMetavarAssignment := do
+    let { mvarIdPending, fvars } := d
+    return {
+      mvarIdPending := mapMVar mvarIdPending,
+      fvars := ← fvars.mapM mapExpr,
+    }
+  let mapLocalDecl (ldecl : LocalDecl) : CoreM LocalDecl := do
+    let ldecl := ldecl.setType (← mapExpr ldecl.type)
+    if let .some value := ldecl.value? then
+      return ldecl.setValue (← mapExpr value)
+    else
+      return ldecl
+
+  let { term := savedTerm@{ meta := savedMeta@{ core, meta := meta@{ mctx, .. } }, .. }, .. } := dst.savedState
+  trace[Pantograph.GoalState.replay] "Merging mvars {src.mctx.mvarCounter} -> ({src'.mctx.mvarCounter}, {dst.mctx.mvarCounter})"
+  let mctx := {
+    mctx with
+    mvarCounter := mctx.mvarCounter + (src'.mctx.mvarCounter - src.mctx.mvarCounter),
+    lDepth := src'.mctx.lDepth.foldl (init := mctx.lDepth) λ acc lmvarId@{ name } depth =>
+      if src.mctx.lDepth.contains lmvarId then
+        acc
+      else
+        acc.insert ⟨mapId name⟩ depth
+    decls := ← src'.mctx.decls.foldlM (init := mctx.decls) λ acc _mvarId@{ name } decl => do
+      if decl.index < src.mctx.mvarCounter then
+        return acc
+      let mvarId := ⟨mapId name⟩
+      let decl := {
+        decl with
+        lctx := ← decl.lctx.foldlM (init := .empty) λ acc decl => do
+          let decl ← mapLocalDecl decl
+          return acc.addDecl decl,
+        type := ← mapExpr decl.type,
+      }
+      return acc.insert mvarId decl
+
+    -- Merge mvar assignments
+    userNames := src'.mctx.userNames.foldl (init := mctx.userNames) λ acc userName mvarId =>
+      if acc.contains userName then
+        acc
+      else
+        acc.insert userName mvarId,
+    lAssignment := src'.mctx.lAssignment.foldl (init := mctx.lAssignment) λ acc lmvarId' l =>
+      let lmvarId := ⟨mapId lmvarId'.name⟩
+      if mctx.lAssignment.contains lmvarId then
+        -- Skip the intersecting assignments for now
+        acc
+      else
+        let l := mapLevel l
+        acc.insert lmvarId l,
+    eAssignment := ← src'.mctx.eAssignment.foldlM (init := mctx.eAssignment) λ acc mvarId' e => do
+      let mvarId := ⟨mapId mvarId'.name⟩
+      if mctx.eAssignment.contains mvarId then
+        -- Skip the intersecting assignments for now
+        return acc
+      else
+        let e ← mapExpr e
+        return acc.insert mvarId e,
+    dAssignment := ← src'.mctx.dAssignment.foldlM (init := mctx.dAssignment) λ acc mvarId' d => do
+      let mvarId := ⟨mapId mvarId'.name⟩
+      if mctx.dAssignment.contains mvarId then
+        return acc
+      else
+        let d ← mapDelayedAssignment d
+        return acc.insert mvarId d
+  }
+  let ngen := {
+    core.ngen with
+    idx := core.ngen.idx + (srcNGen'.idx - srcNGen.idx)
+  }
+  -- Merge conflicting lmvar and mvar assignments using `isDefEq`
+
+  let savedMeta := {
+    savedMeta with
+    core := {
+      core with
+      ngen,
+      env,
+      -- Reset the message log when declaration uses `sorry`
+      messages := {}
+    }
+    meta := {
+      meta with
+      mctx,
+    }
+  }
+  let m : MetaM Meta.SavedState := Meta.withMCtx mctx do
+    restoreCoreMExtra savedMeta.core
+    savedMeta.restore
+
+    for (lmvarId, l') in src'.mctx.lAssignment do
+      if isNewName lmvarId.name then
+        continue
+      let .some l ← getLevelMVarAssignment? lmvarId | continue
+      let l' := mapLevel l'
+      trace[Pantograph.GoalState.replay] "Merging level assignments on {lmvarId.name}"
+      unless ← Meta.isLevelDefEq l l' do
+        throwError "Conflicting assignment of level metavariable {lmvarId.name}"
+    for (mvarId, e') in src'.mctx.eAssignment do
+      if isNewName mvarId.name then
+        continue
+      if ← mvarId.isDelayedAssigned then
+        throwError "Conflicting assignment of expr metavariable (e != d) {mvarId.name}"
+      let .some e ← getExprMVarAssignment? mvarId | continue
+      let e' ← mapExpr e'
+      trace[Pantograph.GoalState.replay] "Merging expr assignments on {mvarId.name}"
+      unless ← Meta.isDefEq e e' do
+        throwError "Conflicting assignment of expr metavariable (e != e) {mvarId.name}"
+    for (mvarId, d') in src'.mctx.dAssignment do
+      if isNewName mvarId.name then
+        continue
+      if ← mvarId.isAssigned then
+        throwError "Conflicting assignment of expr metavariable (d != e) {mvarId.name}"
+      let .some d ← getDelayedMVarAssignment? mvarId | continue
+      trace[Pantograph.GoalState.replay] "Merging expr (delayed) assignments on {mvarId.name}"
+      unless d == d' do
+        throwError "Conflicting assignment of expr metavariable (d != d) {mvarId.name}"
+
+    Meta.saveState
+  let goals := dst.savedState.tactic.goals ++
+    src'.savedState.tactic.goals.map (⟨mapId ·.name⟩)
+  let fragments ← src'.fragments.foldM (init := dst.fragments) λ acc mvarId' fragment' => do
+    let mvarId := ⟨mapId mvarId'.name⟩
+    let fragment ← fragment'.map mapExpr
+    if let .some _fragment0 := acc[mvarId]? then
+      throwError "Conflicting fragments on {mvarId.name}"
+    return acc.insert mvarId fragment
+  return {
+    dst with
+    savedState := {
+      tactic := {
+        goals
+      },
+      term := {
+        savedTerm with
+        meta := ← m.run',
+      },
+    },
+    parentMVars := dst.parentMVars ++ src.parentMVars.map mapMVar,
+    fragments,
+  }
 
 --- Tactic execution functions ---
 
--- Mimics `Elab.Term.logUnassignedUsingErrorInfos`
+/--
+These descendants serve as "seed" mvars. If a MVarError's mvar is related to one
+of these seed mvars, it means an error has occurred when a tactic was executing
+on `src`. `evalTactic`, will not capture these mvars, so we need to manually
+find them and save them into the goal list. See the rationales document for the
+inspiration of this function.
+-/
 private def collectAllErroredMVars (src : MVarId) : Elab.TermElabM (List MVarId) := do
-  -- These descendants serve as "seed" mvars. If a MVarError's mvar is related
-  -- to one of these seed mvars, it means an error has occurred when a tactic
-  -- was executing on `src`. `evalTactic`, will not capture these mvars, so we
-  -- need to manually find them and save them into the goal list.
-
+  -- Mimics `Elab.Term.logUnassignedUsingErrorInfos`
   let descendants ←  Meta.getMVars (.mvar src)
   --let _ ← Elab.Term.logUnassignedUsingErrorInfos descendants
   let mut alreadyVisited : MVarIdSet := {}
@@ -208,6 +435,7 @@ private def collectAllErroredMVars (src : MVarId) : Elab.TermElabM (List MVarId)
         result := mvarDeps.foldl (·.insert ·) result
   return result.toList
 
+/-- Merger of two unique lists -/
 private def mergeMVarLists (li1 li2 : List MVarId) : List MVarId :=
   let li2' := li2.filter (¬ li1.contains ·)
   li1 ++ li2'
@@ -217,25 +445,29 @@ Set `guardMVarErrors` to true to capture mvar errors. Lean will not
 automatically collect mvars from text tactics (vide
 `test_tactic_failure_synthesize_placeholder`)
 -/
-protected def GoalState.step (state: GoalState) (goal: MVarId) (tacticM: Elab.Tactic.TacticM Unit) (guardMVarErrors : Bool := false)
-  : Elab.TermElabM GoalState := do
-  unless (← getMCtx).decls.contains goal do
-    throwError s!"Goal is not in context: {goal.name}"
-  goal.checkNotAssigned `GoalState.step
-  let (_, { goals }) ← tacticM { elaborator := .anonymous } |>.run { goals := [goal] }
+protected def GoalState.step' { α } (state : GoalState) (site : Site) (tacticM : Elab.Tactic.TacticM α) (guardMVarErrors : Bool := false)
+  : Elab.TermElabM (α × GoalState) := do
+  let ((a, parentMVars), { goals }) ← site.runTacticM tacticM
+    |>.run { elaborator := .anonymous }
+    |>.run state.savedState.tactic
   let nextElabState ← MonadBacktrack.saveState
   --Elab.Term.synthesizeSyntheticMVarsNoPostponing
 
   let goals ← if guardMVarErrors then
-      pure $ mergeMVarLists goals (← collectAllErroredMVars goal)
+      parentMVars.foldlM (init := goals) λ goals parent => do
+        let errors ← collectAllErroredMVars parent
+        return mergeMVarLists goals errors
     else
       pure goals
-  return {
+  let state' := {
     state with
     savedState := { term := nextElabState, tactic := { goals }, },
-    parentMVar? := .some goal,
-    calcPrevRhs? := .none,
+    parentMVars,
   }
+  return (a, state')
+protected def GoalState.step (state : GoalState) (site : Site) (tacticM : Elab.Tactic.TacticM Unit) (guardMVarErrors : Bool := false)
+  : Elab.TermElabM GoalState :=
+  Prod.snd <$> GoalState.step' state site tacticM guardMVarErrors
 
 /-- Response for executing a tactic -/
 inductive TacticResult where
@@ -248,66 +480,84 @@ inductive TacticResult where
   -- The given action cannot be executed in the state
   | invalidAction (message : String)
 
-private def dumpMessageLog (prevMessageLength : Nat) : CoreM (Bool × Array String) := do
+private def dumpMessageLog (prevMessageLength : Nat := 0) : CoreM (Bool × Array String) := do
   let newMessages := (← Core.getMessageLog).toList.drop prevMessageLength
   let hasErrors := newMessages.any (·.severity == .error)
   let newMessages ← newMessages.mapM λ m => m.toString
   Core.resetMessageLog
   return (hasErrors, newMessages.toArray)
 
-/-- Executes a `TacticM` monad on this `GoalState`, collecting the errors as necessary -/
-protected def GoalState.tryTacticM
-    (state: GoalState) (goal: MVarId) (tacticM: Elab.Tactic.TacticM Unit)
-    (guardMVarErrors : Bool := false)
-    : Elab.TermElabM TacticResult := do
-  assert! ¬ (← goal.isAssigned)
-  let prevMessageLength := state.coreState.messages.toList.length
+/-- Execute a `TermElabM` producing a goal state, capturing the error and turn it into a `TacticResult` -/
+def withCapturingError (elabM : Elab.Term.TermElabM GoalState) : Elab.TermElabM TacticResult := do
+  let messageLog ← Core.getMessageLog
+  unless messageLog.toList.isEmpty do
+    IO.eprintln s!"{← messageLog.toList.mapM (·.toString)}"
+    assert! messageLog.toList.isEmpty
   try
-    let nextState ← state.step goal tacticM guardMVarErrors
+    let state ← elabM
 
     -- Check if error messages have been generated in the core.
-    let (hasError, newMessages) ← dumpMessageLog prevMessageLength
+    let (hasError, newMessages) ← dumpMessageLog
     if hasError then
       return .failure newMessages
     else
-      return .success nextState newMessages
+      return .success state newMessages
   catch exception =>
     match exception with
     | .internal _ =>
-      let (_, messages) ← dumpMessageLog prevMessageLength
+      let (_, messages) ← dumpMessageLog
       return .failure messages
     | _ => return .failure #[← exception.toMessageData.toString]
 
+/-- Executes a `TacticM` monad on this `GoalState`, collecting the errors as necessary -/
+protected def GoalState.tryTacticM
+    (state: GoalState) (site : Site)
+    (tacticM: Elab.Tactic.TacticM Unit)
+    (guardMVarErrors : Bool := false)
+    : Elab.TermElabM TacticResult := do
+  state.restoreElabM
+  withCapturingError do
+    state.step site tacticM guardMVarErrors
+
 /-- Execute a string tactic on given state. Restores TermElabM -/
 @[export pantograph_goal_state_try_tactic_m]
-protected def GoalState.tryTactic (state: GoalState) (goal: MVarId) (tactic: String):
+protected def GoalState.tryTactic (state: GoalState) (site : Site) (tactic: String):
     Elab.TermElabM TacticResult := do
   state.restoreElabM
+  let .some goal := state.actingGoal? site | throwNoGoals
+  if let .some fragment := state.fragments[goal]? then
+    return ← withCapturingError do
+      let (fragments, state') ← state.step' site do
+        fragment.step goal tactic $ state.fragments.erase goal
+      return { state' with fragments }
+  -- Normal tactic without fragment
   let tactic ← match Parser.runParserCategory
-    (env := ← MonadEnv.getEnv)
-    (catName := if state.isConv then `conv else `tactic)
+    (env := ← getEnv)
+    (catName := `tactic)
     (input := tactic)
     (fileName := ← getFileName) with
     | .ok stx => pure $ stx
     | .error error => return .parseError error
-  state.tryTacticM goal (Elab.Tactic.evalTactic tactic) true
+  let tacticM := Elab.Tactic.evalTactic tactic
+  withCapturingError do
+    state.step site tacticM (guardMVarErrors := true)
 
-protected def GoalState.tryAssign (state: GoalState) (goal: MVarId) (expr: String):
-      Elab.TermElabM TacticResult := do
+-- Specialized Tactics
+
+protected def GoalState.tryAssign (state : GoalState) (site : Site) (expr : String)
+    : Elab.TermElabM TacticResult := do
   state.restoreElabM
   let expr ← match Parser.runParserCategory
-    (env := ← MonadEnv.getEnv)
+    (env := ← getEnv)
     (catName := `term)
     (input := expr)
     (fileName := ← getFileName) with
     | .ok syn => pure syn
     | .error error => return .parseError error
-  state.tryTacticM goal $ Tactic.evalAssign expr
+  state.tryTacticM site $ Tactic.evalAssign expr
 
--- Specialized Tactics
-
-protected def GoalState.tryLet (state: GoalState) (goal: MVarId) (binderName: String) (type: String):
-      Elab.TermElabM TacticResult := do
+protected def GoalState.tryLet (state : GoalState) (site : Site) (binderName : String) (type : String)
+    : Elab.TermElabM TacticResult := do
   state.restoreElabM
   let type ← match Parser.runParserCategory
     (env := ← MonadEnv.getEnv)
@@ -316,150 +566,59 @@ protected def GoalState.tryLet (state: GoalState) (goal: MVarId) (binderName: St
     (fileName := ← getFileName) with
     | .ok syn => pure syn
     | .error error => return .parseError error
-  state.tryTacticM goal $ Tactic.evalLet binderName.toName type
+  state.tryTacticM site $ Tactic.evalLet binderName.toName type
 
 /-- Enter conv tactic mode -/
-protected def GoalState.conv (state: GoalState) (goal: MVarId):
+@[export pantograph_goal_state_conv_enter_m]
+protected def GoalState.convEnter (state : GoalState) (site : Site) :
       Elab.TermElabM TacticResult := do
-  if state.convMVar?.isSome then
+  let .some goal := state.actingGoal? site | throwNoGoals
+  if let .some (.conv ..) := state.fragments[goal]? then
     return .invalidAction "Already in conv state"
-  goal.checkNotAssigned `GoalState.conv
-  let tacticM :  Elab.Tactic.TacticM (Elab.Tactic.SavedState × MVarId) := do
-    state.restoreTacticM goal
+  state.restoreElabM
+  withCapturingError do
+    let (fragments, state') ← state.step' site Fragment.enterConv
+    return {
+      state' with
+      fragments := fragments.fold (init := state'.fragments) λ acc goal fragment =>
+        acc.insert goal fragment
+    }
 
-    -- See Lean.Elab.Tactic.Conv.convTarget
-    let convMVar ← Elab.Tactic.withMainContext do
-      let (rhs, newGoal) ← Elab.Tactic.Conv.mkConvGoalFor (← Elab.Tactic.getMainTarget)
-      Elab.Tactic.replaceMainGoal [newGoal.mvarId!]
-      pure rhs.mvarId!
-    return (← MonadBacktrack.saveState, convMVar)
-  try
-    let (nextSavedState, convRhs) ← tacticM { elaborator := .anonymous } |>.run' state.savedState.tactic
-    -- Other goals are now dormant
-    let otherGoals := state.goals.filter $ λ g => g != goal
-    return .success {
-      root := state.root,
-      savedState := nextSavedState
-      parentMVar? := .some goal,
-      convMVar? := .some (convRhs, goal, otherGoals),
-      calcPrevRhs? := .none
-    } #[]
-  catch exception =>
-    return .failure #[← exception.toMessageData.toString]
-
-/-- Exit from `conv` mode. Resumes all goals before the mode starts and applys the conv -/
-@[export pantograph_goal_state_conv_exit_m]
-protected def GoalState.convExit (state: GoalState):
+/-- Exit from a tactic fragment. -/
+@[export pantograph_goal_state_fragment_exit_m]
+protected def GoalState.fragmentExit (state : GoalState) (site : Site):
       Elab.TermElabM TacticResult := do
-  let (convRhs, convGoal, _) ← match state.convMVar? with
-    | .some mvar => pure mvar
-    | .none => return .invalidAction "Not in conv state"
-  let tacticM :  Elab.Tactic.TacticM Elab.Tactic.SavedState:= do
-    -- Vide `Lean.Elab.Tactic.Conv.convert`
-    state.savedState.restore
-
-    -- Close all existing goals with `refl`
-    for mvarId in (← Elab.Tactic.getGoals) do
-      liftM <| mvarId.refl <|> mvarId.inferInstance <|> pure ()
-    Elab.Tactic.pruneSolvedGoals
-    unless (← Elab.Tactic.getGoals).isEmpty do
-      throwError "convert tactic failed, there are unsolved goals\n{Elab.goalsToMessageData (← Elab.Tactic.getGoals)}"
-
-    Elab.Tactic.setGoals [convGoal]
-
-    let targetNew ← instantiateMVars (.mvar convRhs)
-    let proof ← instantiateMVars (.mvar convGoal)
-
-    Elab.Tactic.liftMetaTactic1 fun mvarId => mvarId.replaceTargetEq targetNew proof
-    MonadBacktrack.saveState
-  try
-    let nextSavedState ← tacticM { elaborator := .anonymous } |>.run' state.savedState.tactic
-    return .success {
-      root := state.root,
-      savedState := nextSavedState
-      parentMVar? := .some convGoal,
-      convMVar? := .none
-      calcPrevRhs? := .none
-    } #[]
-  catch exception =>
-    return .failure #[← exception.toMessageData.toString]
+  let .some goal := state.actingGoal? site | throwNoGoals
+  let .some fragment := state.fragments[goal]? |
+    return .invalidAction "Goal does not have a fragment"
+  state.restoreElabM
+  withCapturingError do
+    let (fragments, state') ← state.step' goal (fragment.exit goal state.fragments)
+    return {
+      state' with
+      fragments,
+    }
 
 protected def GoalState.calcPrevRhsOf? (state : GoalState) (goal : MVarId) : Option Expr := do
-  let (mvarId, rhs) ← state.calcPrevRhs?
-  if mvarId == goal then
-    .some rhs
-  else
-    .none
-@[export pantograph_goal_state_try_calc_m]
-protected def GoalState.tryCalc (state: GoalState) (goal: MVarId) (pred: String):
-      Elab.TermElabM TacticResult := do
+  let .some (.calc prevRhs?) := state.fragments[goal]? | .none
+  prevRhs?
+
+@[export pantograph_goal_state_calc_enter_m]
+protected def GoalState.calcEnter (state : GoalState) (site : Site)
+  : Elab.TermElabM TacticResult := do
+  let .some goal := state.actingGoal? site | throwNoGoals
+  if let .some _ := state.fragments[goal]? then
+    return .invalidAction "Goal already has a fragment"
   state.restoreElabM
-  if state.convMVar?.isSome then
-    return .invalidAction "Cannot initiate `calc` while in `conv` state"
-  let `(term|$pred) ← match Parser.runParserCategory
-    (env := state.env)
-    (catName := `term)
-    (input := pred)
-    (fileName := ← getFileName) with
-    | .ok syn => pure syn
-    | .error error => return .parseError error
-  goal.checkNotAssigned `GoalState.tryCalc
-  let calcPrevRhs? := state.calcPrevRhsOf? goal
-  let decl ← goal.getDecl
-  let target ← instantiateMVars decl.type
-  let tag := decl.userName
-  try
-    goal.withContext do
+  withCapturingError do
+    let fragment := Fragment.enterCalc
+    let fragments := state.fragments.insert goal fragment
+    return {
+      state with
+      fragments,
+    }
 
-    let mut step ← Elab.Term.elabType <| ← do
-      if let some prevRhs := calcPrevRhs? then
-        Elab.Term.annotateFirstHoleWithType pred (← Meta.inferType prevRhs)
-      else
-        pure pred
-
-    let some (_, lhs, rhs) ← Elab.Term.getCalcRelation? step |
-      throwErrorAt pred "invalid 'calc' step, relation expected{indentExpr step}"
-    if let some prevRhs := calcPrevRhs? then
-      unless ← Meta.isDefEqGuarded lhs prevRhs do
-        throwErrorAt pred "invalid 'calc' step, left-hand-side is{indentD m!"{lhs} : {← Meta.inferType lhs}"}\nprevious right-hand-side is{indentD m!"{prevRhs} : {← Meta.inferType prevRhs}"}"
-
-    -- Creates a mvar to represent the proof that the calc tactic solves the
-    -- current branch
-    -- In the Lean `calc` tactic this is gobbled up by
-    -- `withCollectingNewGoalsFrom`
-    let mut proof ← Meta.mkFreshExprMVarAt (← getLCtx) (← Meta.getLocalInstances) step
-      (userName := tag ++ `calc)
-    let mvarBranch := proof.mvarId!
-
-    let mut proofType ← Meta.inferType proof
-    let mut remainder? := Option.none
-
-    -- The calc tactic either solves the main goal or leaves another relation.
-    -- Replace the main goal, and save the new goal if necessary
-    unless ← Meta.isDefEq proofType target do
-      let rec throwFailed :=
-        throwError "'calc' tactic failed, has type{indentExpr proofType}\nbut it is expected to have type{indentExpr target}"
-      let some (_, _, rhs) ← Elab.Term.getCalcRelation? proofType | throwFailed
-      let some (r, _, rhs') ← Elab.Term.getCalcRelation? target | throwFailed
-      let lastStep := mkApp2 r rhs rhs'
-      let lastStepGoal ← Meta.mkFreshExprSyntheticOpaqueMVar lastStep tag
-      (proof, proofType) ← Elab.Term.mkCalcTrans proof proofType lastStepGoal lastStep
-      unless ← Meta.isDefEq proofType target do throwFailed
-      remainder? := .some lastStepGoal.mvarId!
-    goal.assign proof
-
-    let goals := [ mvarBranch ] ++ remainder?.toList
-    let calcPrevRhs? := remainder?.map $ λ g => (g, rhs)
-    return .success {
-      root := state.root,
-      savedState := {
-        term := ← MonadBacktrack.saveState,
-        tactic := { goals },
-      },
-      parentMVar? := .some goal,
-      calcPrevRhs?
-    } #[]
-  catch exception =>
-    return .failure #[← exception.toMessageData.toString]
+initialize
+  registerTraceClass `Pantograph.GoalState.replay
 
 end Pantograph

Pantograph/Library.lean

@@ -117,10 +117,10 @@ def goalStartExpr (expr: String) : Protocol.FallibleT Elab.TermElabM GoalState :
 
 @[export pantograph_goal_serialize_m]
 def goalSerialize (state: GoalState) (options: @&Protocol.Options): CoreM (Array Protocol.Goal) :=
-  runMetaM <| state.serializeGoals (parent := .none) options
+  runMetaM <| state.serializeGoals options
 
 @[export pantograph_goal_print_m]
-def goalPrint (state: GoalState) (rootExpr: Bool) (parentExpr: Bool) (goals: Bool) (extraMVars : Array String) (options: @&Protocol.Options)
+def goalPrint (state: GoalState) (rootExpr: Bool) (parentExprs: Bool) (goals: Bool) (extraMVars : Array String) (options: @&Protocol.Options)
   : CoreM Protocol.GoalPrintResult := runMetaM do
   state.restoreMetaM
 
@@ -130,9 +130,11 @@ def goalPrint (state: GoalState) (rootExpr: Bool) (parentExpr: Bool) (goals: Boo
         serializeExpression options (← instantiateAll expr)
     else
       pure .none
-  let parent? ← if parentExpr then
-      state.parentExpr?.mapM λ expr => state.withParentContext do
-        serializeExpression options (← instantiateAll expr)
+  let parentExprs? ← if parentExprs then
+      .some <$> state.parentMVars.mapM λ parent => parent.withContext do
+        let val? := state.getMVarEAssignment parent
+        val?.mapM λ val => do
+          serializeExpression options (← instantiateAll val)
     else
       pure .none
   let goals ← if goals then
@@ -148,7 +150,7 @@ def goalPrint (state: GoalState) (rootExpr: Bool) (parentExpr: Bool) (goals: Boo
   let env ← getEnv
   return {
     root?,
-    parent?,
+    parentExprs?,
     goals,
     extraMVars,
     rootHasSorry := rootExpr?.map (·.hasSorry) |>.getD false,
@@ -157,26 +159,26 @@ def goalPrint (state: GoalState) (rootExpr: Bool) (parentExpr: Bool) (goals: Boo
   }
 
 @[export pantograph_goal_have_m]
-protected def GoalState.tryHave (state: GoalState) (goal: MVarId) (binderName: String) (type: String): Elab.TermElabM TacticResult := do
+protected def GoalState.tryHave (state: GoalState) (site : Site) (binderName: String) (type: String): Elab.TermElabM TacticResult := do
   let type ← match (← parseTermM type) with
     | .ok syn => pure syn
     | .error error => return .parseError error
   state.restoreElabM
-  state.tryTacticM goal $ Tactic.evalHave binderName.toName type
+  state.tryTacticM site $ Tactic.evalHave binderName.toName type
 @[export pantograph_goal_try_define_m]
-protected def GoalState.tryDefine (state: GoalState) (goal: MVarId) (binderName: String) (expr: String): Elab.TermElabM TacticResult := do
+protected def GoalState.tryDefine (state: GoalState) (site : Site) (binderName: String) (expr: String): Elab.TermElabM TacticResult := do
   let expr ← match (← parseTermM expr) with
     | .ok syn => pure syn
     | .error error => return .parseError error
   state.restoreElabM
-  state.tryTacticM goal (Tactic.evalDefine binderName.toName expr)
+  state.tryTacticM site $ Tactic.evalDefine binderName.toName expr
 @[export pantograph_goal_try_draft_m]
-protected def GoalState.tryDraft (state: GoalState) (goal: MVarId) (expr: String): Elab.TermElabM TacticResult := do
+protected def GoalState.tryDraft (state: GoalState) (site : Site) (expr: String): Elab.TermElabM TacticResult := do
   let expr ← match (← parseTermM expr) with
     | .ok syn => pure syn
     | .error error => return .parseError error
   state.restoreElabM
-  state.tryTacticM goal (Tactic.evalDraft expr)
+  state.tryTacticM site $ Tactic.evalDraft expr
 
 -- Cancel the token after a timeout.
 @[export pantograph_run_cancel_token_with_timeout_m]

Pantograph/Protocol.lean

@@ -60,12 +60,17 @@ structure Variable where
   type?: Option Expression  := .none
   value?: Option Expression := .none
   deriving Lean.ToJson
+inductive Fragment where
+  | tactic
+  | conv
+  | calc
+  deriving BEq, DecidableEq, Repr, Lean.ToJson
 structure Goal where
-  name: String := ""
   /-- Name of the metavariable -/
+  name : String := ""
+  /-- User-facing name -/
   userName? : Option String  := .none
-  /-- Is the goal in conversion mode -/
-  isConversion: Bool        := false
+  fragment : Fragment := .tactic
   /-- target expression type -/
   target : Expression
   /-- Variables -/
@@ -87,6 +92,7 @@ structure InteractionError where
   deriving Lean.ToJson
 
 def errorIndex (desc: String): InteractionError := { error := "index", desc }
+def errorOperation (desc: String): InteractionError := { error := "operation", desc }
 def errorExpr (desc: String): InteractionError := { error := "expr", desc }
 
 
@@ -248,17 +254,17 @@ structure GoalStartResult where
   root: String
   deriving Lean.ToJson
 structure GoalTactic where
-  -- Identifiers for tree, state, and goal
   stateId: Nat
-  goalId: Nat := 0
+  -- If omitted, act on the first goal
+  goalId?: Option Nat := .none
+  -- If set to true, goal will not go dormant. Defaults to `automaticMode`
+  autoResume?: Option Bool := .none
   -- One of the fields here must be filled
   tactic?: Option String := .none
+  mode?: Option String := .none -- Changes the current category to {"tactic", "calc", "conv"}
   expr?: Option String := .none
   have?: Option String := .none
   let?: Option String := .none
-  calc?: Option String := .none
-  -- true to enter `conv`, `false` to exit. In case of exit the `goalId` is ignored.
-  conv?: Option Bool := .none
   draft?: Option String := .none
 
   -- In case of the `have` tactic, the new free variable name is provided here
@@ -308,8 +314,8 @@ structure GoalPrint where
 
   -- Print root?
   rootExpr?: Option Bool := .some False
-  -- Print the parent expr?
-  parentExpr?: Option Bool := .some False
+  -- Print the parent expressions
+  parentExprs?: Option Bool := .some False
   -- Print goals?
   goals?: Option Bool := .some False
   -- Print values of extra mvars?
@@ -319,7 +325,7 @@ structure GoalPrintResult where
   -- The root expression
   root?: Option Expression := .none
   -- The filling expression of the parent goal
-  parent?: Option Expression := .none
+  parentExprs?: Option (List (Option Expression)) := .none
   goals: Array Goal := #[]
   extraMVars: Array Expression := #[]
 

Pantograph/Serial.lean

@@ -1,19 +1,19 @@
-import Lean.Environment
-import Lean.Replay
-import Init.System.IOError
-import Std.Data.HashMap
 import Pantograph.Goal
 
+import Lean.Environment
+import Lean.Replay
+import Std.Data.HashMap
+
+open Lean
+
 /-!
-Input/Output functions
+Input/Output functions borrowed from REPL
 
 # Pickling and unpickling objects
 
 By abusing `saveModuleData` and `readModuleData` we can pickle and unpickle objects to disk.
 -/
 
-open Lean
-
 namespace Pantograph
 
 /--
@@ -46,6 +46,21 @@ unsafe def withUnpickle [Monad m] [MonadLiftT IO m] {α β : Type}
   region.free
   pure r
 
+abbrev ConstArray := Array (Name × ConstantInfo)
+abbrev DistilledEnvironment := Array Import × ConstArray
+
+/-- Boil an environment down to minimal components -/
+def distillEnvironment (env : Environment) (background? : Option Environment := .none)
+  : DistilledEnvironment :=
+  let filter : Name → Bool := match background? with
+    | .some env => (¬ env.contains ·)
+    | .none => λ _ => true
+  let constants : ConstArray := env.constants.map₂.foldl (init := #[]) λ acc name info =>
+    if filter name then
+      acc.push (name, info)
+    else
+      acc
+  (env.header.imports, constants)
 /--
 Pickle an `Environment` to disk.
 
@@ -56,15 +71,23 @@ and when unpickling, we build a fresh `Environment` from the imports,
 and then add the new constants.
 -/
 @[export pantograph_env_pickle_m]
-def environmentPickle (env : Environment) (path : System.FilePath) : IO Unit :=
-  Pantograph.pickle path (env.header.imports, env.constants.map₂)
+def environmentPickle (env : Environment) (path : System.FilePath) (background? : Option Environment := .none)
+  : IO Unit :=
+  pickle path $ distillEnvironment env background?
+
+deriving instance BEq for Import
 
 def resurrectEnvironment
-  (imports : Array Import)
-  (map₂ : PHashMap Name ConstantInfo)
+  (distilled : DistilledEnvironment)
+  (background? : Option Environment := .none)
   : IO Environment := do
-  let env ← importModules imports {} 0 (loadExts := true)
-  env.replay (Std.HashMap.ofList map₂.toList)
+  let (imports, constArray) := distilled
+  let env ← match background? with
+    | .none => importModules imports {} 0 (loadExts := true)
+    | .some env =>
+      assert! env.imports == imports
+      pure env
+  env.replay (Std.HashMap.ofList constArray.toList)
 /--
 Unpickle an `Environment` from disk.
 
@@ -72,9 +95,10 @@ We construct a fresh `Environment` with the relevant imports,
 and then replace the new constants.
 -/
 @[export pantograph_env_unpickle_m]
-def environmentUnpickle (path : System.FilePath) : IO (Environment × CompactedRegion) := unsafe do
-  let ((imports, map₂), region) ← Pantograph.unpickle (Array Import × PHashMap Name ConstantInfo) path
-  return (← resurrectEnvironment imports map₂, region)
+def environmentUnpickle (path : System.FilePath) (background? : Option Environment := .none)
+  : IO (Environment × CompactedRegion) := unsafe do
+  let (distilled, region) ← unpickle (Array Import × ConstArray) path
+  return (← resurrectEnvironment distilled background?, region)
 
 
 open Lean.Core in
@@ -88,7 +112,8 @@ structure CompactCoreState where
   -- infoState       : Elab.InfoState := {}
 
 @[export pantograph_goal_state_pickle_m]
-def goalStatePickle (goalState : GoalState) (path : System.FilePath) : IO Unit :=
+def goalStatePickle (goalState : GoalState) (path : System.FilePath) (background? : Option Environment := .none)
+  : IO Unit :=
   let {
     savedState := {
       term := {
@@ -103,12 +128,11 @@ def goalStatePickle (goalState : GoalState) (path : System.FilePath) : IO Unit :
       tactic
     }
     root,
-    parentMVar?,
-    convMVar?,
-    calcPrevRhs?,
+    parentMVars,
+    fragments,
   } := goalState
-  Pantograph.pickle path (
-    env.constants.map₂,
+  pickle path (
+    distillEnvironment env background?,
 
     ({ nextMacroScope, ngen } : CompactCoreState),
     meta,
@@ -116,16 +140,15 @@ def goalStatePickle (goalState : GoalState) (path : System.FilePath) : IO Unit :
     tactic,
 
     root,
-    parentMVar?,
-    convMVar?,
-    calcPrevRhs?,
+    parentMVars,
+    fragments,
   )
 
 @[export pantograph_goal_state_unpickle_m]
-def goalStateUnpickle (path : System.FilePath) (env : Environment)
+def goalStateUnpickle (path : System.FilePath) (background? : Option Environment := .none)
     : IO (GoalState × CompactedRegion) := unsafe do
   let ((
-    map₂,
+    distilledEnv,
 
     compactCore,
     meta,
@@ -133,11 +156,10 @@ def goalStateUnpickle (path : System.FilePath) (env : Environment)
     tactic,
 
     root,
-    parentMVar?,
-    convMVar?,
-    calcPrevRhs?,
+    parentMVars,
+    fragments,
   ), region) ← Pantograph.unpickle (
-    PHashMap Name ConstantInfo ×
+    DistilledEnvironment ×
 
     CompactCoreState ×
     Meta.State ×
@@ -145,11 +167,10 @@ def goalStateUnpickle (path : System.FilePath) (env : Environment)
     Elab.Tactic.State ×
 
     MVarId ×
-    Option MVarId ×
-    Option (MVarId × MVarId × List MVarId) ×
-    Option (MVarId × Expr)
+    List MVarId ×
+    FragmentMap
   ) path
-  let env ← env.replay (Std.HashMap.ofList map₂.toList)
+  let env ← resurrectEnvironment distilledEnv background?
   let goalState := {
     savedState := {
       term := {
@@ -166,9 +187,8 @@ def goalStateUnpickle (path : System.FilePath) (env : Environment)
       tactic,
     },
     root,
-    parentMVar?,
-    convMVar?,
-    calcPrevRhs?,
+    parentMVars,
+    fragments,
   }
   return (goalState, region)
 

Pantograph/Tactic.lean

@@ -1,2 +1,3 @@
 import Pantograph.Tactic.Assign
+import Pantograph.Tactic.Fragment
 import Pantograph.Tactic.Prograde

Pantograph/Tactic/Fragment.lean

@@ -0,0 +1,188 @@
+/- Fragmented tactics are the tactics which can give incremental feedback and
+whose integrity as a block is crucial to its operation. e.g. `calc` or `conv`.
+Here, a unified system handles all fragments.
+
+Inside a tactic fragment, the parser category may be different. An incomplete
+fragmented tactic may not be elaboratable..
+
+In line with continuation/resumption paradigms, the exit function of a fragment
+tactic is responsible for resuming incomplete goals with fragments. For example,
+when a conversion tactic finishes, the sentinels should resume the root of the
+conversion tactic goal. The user cannot be expected to execute this resumption,
+since the root is automatically dormanted at the entry of the conversion tactic
+mode.
+-/
+import Lean.Meta
+import Lean.Elab
+
+open Lean
+
+namespace Pantograph
+
+inductive Fragment where
+  | calc (prevRhs? : Option Expr)
+  | conv (rhs : MVarId)
+  -- This goal is spawned from a `conv`
+  | convSentinel (parent : MVarId)
+  deriving BEq, Inhabited
+
+abbrev FragmentMap := Std.HashMap MVarId Fragment
+def FragmentMap.empty : FragmentMap := Std.HashMap.emptyWithCapacity 2
+protected def FragmentMap.filter (map : FragmentMap) (pred : MVarId → Fragment → Bool) : FragmentMap :=
+  map.fold (init := FragmentMap.empty) λ acc mvarId fragment =>
+    if pred mvarId fragment then
+      acc.insert mvarId fragment
+    else
+      acc
+
+protected def Fragment.map (fragment : Fragment) (mapExpr : Expr → CoreM Expr) : CoreM Fragment :=
+  let mapMVar (mvarId : MVarId) : CoreM MVarId :=
+    return (← mapExpr (.mvar mvarId)) |>.mvarId!
+  match fragment with
+  | .calc prevRhs? => return .calc (← prevRhs?.mapM mapExpr)
+  | .conv rhs => do
+    let rhs' ← mapMVar rhs
+    return .conv rhs'
+  | .convSentinel parent => do
+    return .convSentinel (← mapMVar parent)
+
+protected def Fragment.enterCalc : Fragment := .calc .none
+protected def Fragment.enterConv : Elab.Tactic.TacticM FragmentMap := do
+  let goal ← Elab.Tactic.getMainGoal
+  goal.checkNotAssigned `GoalState.conv
+  let (rhs, newGoal) ← goal.withContext do
+    let target ← instantiateMVars (← goal.getType)
+    let (rhs, newGoal) ← Elab.Tactic.Conv.mkConvGoalFor target
+    pure (rhs.mvarId!, newGoal.mvarId!)
+  Elab.Tactic.replaceMainGoal [newGoal]
+  return FragmentMap.empty
+    |>.insert goal (.conv rhs)
+    |>.insert newGoal (.convSentinel goal)
+
+protected partial def Fragment.exit (fragment : Fragment) (goal : MVarId) (fragments : FragmentMap)
+  : Elab.Tactic.TacticM FragmentMap :=
+  match fragment with
+  | .calc .. => do
+    Elab.Tactic.setGoals [goal]
+    return fragments.erase goal
+  | .conv rhs => do
+    let goals := (← Elab.Tactic.getGoals).filter λ descendant =>
+      match fragments[descendant]? with
+      | .some s => (.convSentinel goal) == s
+      | _ => false -- Not a conv goal from this
+    -- Close all existing goals with `refl`
+    for mvarId in goals do
+      liftM <| mvarId.refl <|> mvarId.inferInstance <|> pure ()
+    unless (← goals.filterM (·.isAssignedOrDelayedAssigned)).isEmpty do
+      throwError "convert tactic failed, there are unsolved goals\n{Elab.goalsToMessageData (goals)}"
+
+    -- Ensure the meta tactic runs on `goal` even if its dormant by forcing resumption
+    Elab.Tactic.setGoals $ goal :: (← Elab.Tactic.getGoals)
+    let targetNew ← instantiateMVars (.mvar rhs)
+    let proof ← instantiateMVars (.mvar goal)
+
+    Elab.Tactic.liftMetaTactic1 (·.replaceTargetEq targetNew proof)
+
+    -- Try to solve maiinline by rfl
+    let mvarId ← Elab.Tactic.getMainGoal
+    liftM <| mvarId.refl <|> mvarId.inferInstance <|> pure ()
+    Elab.Tactic.pruneSolvedGoals
+    return fragments.filter λ mvarId fragment =>
+      !(mvarId == goal || fragment == .convSentinel goal)
+  | .convSentinel parent =>
+    let parentFragment := fragments[parent]!
+    parentFragment.exit parent (fragments.erase goal)
+
+protected def Fragment.step (fragment : Fragment) (goal : MVarId) (s : String) (map : FragmentMap)
+  : Elab.Tactic.TacticM FragmentMap := goal.withContext do
+  assert! ¬ (← goal.isAssigned)
+  match fragment with
+  | .calc prevRhs? => do
+    let .ok stx := Parser.runParserCategory
+      (env := ← getEnv)
+      (catName := `term)
+      (input := s)
+      (fileName := ← getFileName) | throwError s!"Failed to parse calc element {s}"
+    let `(term|$pred) := stx
+    let decl ← goal.getDecl
+    let target ← instantiateMVars decl.type
+    let tag := decl.userName
+
+    let mut step ← Elab.Term.elabType <| ← do
+      if let some prevRhs := prevRhs? then
+        Elab.Term.annotateFirstHoleWithType pred (← Meta.inferType prevRhs)
+      else
+        pure pred
+
+    let some (_, lhs, rhs) ← Elab.Term.getCalcRelation? step |
+      throwErrorAt pred "invalid 'calc' step, relation expected{indentExpr step}"
+    if let some prevRhs := prevRhs? then
+      unless ← Meta.isDefEqGuarded lhs prevRhs do
+        throwErrorAt pred "invalid 'calc' step, left-hand-side is{indentD m!"{lhs} : {← Meta.inferType lhs}"}\nprevious right-hand-side is{indentD m!"{prevRhs} : {← Meta.inferType prevRhs}"}"
+
+    -- Creates a mvar to represent the proof that the calc tactic solves the
+    -- current branch
+    -- In the Lean `calc` tactic this is gobbled up by
+    -- `withCollectingNewGoalsFrom`
+    let mut proof ← Meta.mkFreshExprMVarAt (← getLCtx) (← Meta.getLocalInstances) step
+      (userName := tag ++ `calc)
+    let mvarBranch := proof.mvarId!
+
+    let mut proofType ← Meta.inferType proof
+    let mut remainder? := Option.none
+
+    -- The calc tactic either solves the main goal or leaves another relation.
+    -- Replace the main goal, and save the new goal if necessary
+    unless ← Meta.isDefEq proofType target do
+      let rec throwFailed :=
+        throwError "'calc' tactic failed, has type{indentExpr proofType}\nbut it is expected to have type{indentExpr target}"
+      let some (_, _, rhs) ← Elab.Term.getCalcRelation? proofType | throwFailed
+      let some (r, _, rhs') ← Elab.Term.getCalcRelation? target | throwFailed
+      let lastStep := mkApp2 r rhs rhs'
+      let lastStepGoal ← Meta.mkFreshExprSyntheticOpaqueMVar lastStep tag
+      (proof, proofType) ← Elab.Term.mkCalcTrans proof proofType lastStepGoal lastStep
+      unless ← Meta.isDefEq proofType target do throwFailed
+      remainder? := .some lastStepGoal.mvarId!
+    goal.assign proof
+
+    let goals := [ mvarBranch ] ++ remainder?.toList
+    Elab.Tactic.setGoals goals
+    match remainder? with
+    | .some goal => return map.erase goal |>.insert goal $ .calc (.some rhs)
+    | .none => return map
+  | .conv .. => do
+    throwError "Direct operation on conversion tactic parent goal is not allowed"
+  | fragment@(.convSentinel parent) => do
+    assert! isLHSGoal? (← goal.getType) |>.isSome
+    let tactic ← match Parser.runParserCategory
+      (env := ← MonadEnv.getEnv)
+      (catName := `conv)
+      (input := s)
+      (fileName := ← getFileName) with
+      | .ok stx => pure $ stx
+      | .error error => throwError error
+    let oldGoals ← Elab.Tactic.getGoals
+    -- Label newly generated goals as conv sentinels
+    Elab.Tactic.evalTactic tactic
+    let newConvGoals ← (← Elab.Tactic.getUnsolvedGoals).filterM λ g => do
+      -- conv tactic might generate non-conv goals
+      if oldGoals.contains g then
+        return false
+      return isLHSGoal? (← g.getType) |>.isSome
+    -- Conclude the conv by exiting the parent fragment if new goals is empty
+    if newConvGoals.isEmpty then
+      let hasSiblingFragment := map.fold (init := false) λ flag _ fragment =>
+        if flag then
+          true
+        else match fragment with
+          | .convSentinel parent' => parent == parent'
+          | _ => false
+      if ¬ hasSiblingFragment then
+        -- This fragment must exist since we have conv goals
+        let parentFragment := map[parent]!
+        -- All descendants exhausted. Exit from the parent conv.
+        return ← parentFragment.exit parent map
+    return newConvGoals.foldl (init := map) λ acc g =>
+      acc.insert g fragment
+
+end Pantograph

Pantograph/Version.lean

@@ -1,6 +1,6 @@
 namespace Pantograph
 
 @[export pantograph_version]
-def version := "0.3.2"
+def version := "0.3.4"
 
 end Pantograph

README.md

@@ -60,11 +60,11 @@ 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 {"stateId": 0, "goalId": 0, "tactic": "intro n m"}
-goal.tactic {"stateId": 1, "goalId": 0, "tactic": "assumption"}
+goal.tactic {"stateId": 0, "tactic": "intro n m"}
+goal.tactic {"stateId": 1, "tactic": "assumption"}
 goal.delete {"stateIds": [0]}
 stat {}
-goal.tactic {"stateId": 1, "goalId": 0, "tactic": "rw [Nat.add_comm]"}
+goal.tactic {"stateId": 1, "tactic": "rw [Nat.add_comm]"}
 stat
 ```
 where the application of `assumption` should lead to a failure.

Repl.lean

@@ -97,6 +97,82 @@ def liftTermElabM { α } (termElabM : Elab.TermElabM α) (levelNames : List Name
   }
   runCoreM $ termElabM.run' context state |>.run'
 
+section Goal
+
+def goal_tactic (args: Protocol.GoalTactic): EMainM Protocol.GoalTacticResult := do
+  let state ← getMainState
+  let .some goalState := state.goalStates[args.stateId]? |
+    Protocol.throw $ Protocol.errorIndex s!"Invalid state index {args.stateId}"
+  let unshielded := args.autoResume?.getD state.options.automaticMode
+  let site ← match args.goalId?, unshielded with
+    | .some goalId, true => do
+      let .some goal := goalState.goals[goalId]? |
+        Protocol.throw $ Protocol.errorIndex s!"Invalid goal index {goalId}"
+      pure (.prefer goal)
+    | .some goalId, false => do
+      let .some goal := goalState.goals[goalId]? |
+        Protocol.throw $ Protocol.errorIndex s!"Invalid goal index {goalId}"
+      pure (.focus goal)
+    | .none, true => pure .unfocus
+    | .none, false => do
+      let .some goal := goalState.mainGoal? |
+        Protocol.throw $ Protocol.errorIndex s!"No goals to be solved"
+      pure (.focus goal)
+  let nextGoalState?: Except _ TacticResult ← liftTermElabM do
+    -- NOTE: Should probably use a macro to handle this...
+    match args.tactic?, args.mode?, args.expr?, args.have?, args.let?, args.draft?  with
+    | .some tactic, .none, .none, .none, .none, .none => do
+      pure $ Except.ok $ ← goalState.tryTactic site tactic
+    | .none, .some mode, .none, .none, .none, .none => match mode with
+      | "tactic" => do -- Exit from the current fragment
+        pure $ Except.ok $ ← goalState.fragmentExit site
+      | "conv" => do
+        pure $ Except.ok $ ← goalState.convEnter site
+      | "calc" => do
+        pure $ Except.ok $ ← goalState.calcEnter site
+      | _ => pure $ .error $ Protocol.errorOperation s!"Invalid mode {mode}"
+    | .none, .none, .some expr, .none, .none, .none => do
+      pure $ Except.ok $ ← goalState.tryAssign site expr
+    | .none, .none, .none, .some type, .none, .none => do
+      let binderName := args.binderName?.getD ""
+      pure $ Except.ok $ ← goalState.tryHave site binderName type
+    | .none, .none, .none, .none, .some type, .none => do
+      let binderName := args.binderName?.getD ""
+      pure $ Except.ok $ ← goalState.tryLet site binderName type
+    | .none, .none, .none, .none, .none, .some draft => do
+      pure $ Except.ok $ ← goalState.tryDraft site draft
+    | _, _, _, _, _, _ =>
+      pure $ .error $ Protocol.errorOperation
+        "Exactly one of {tactic, mode, expr, have, let, draft} must be supplied"
+  match nextGoalState? with
+  | .error error => Protocol.throw error
+  | .ok (.success nextGoalState messages) => do
+    let env ← getEnv
+    let nextStateId ← newGoalState nextGoalState
+    let parentExprs := nextGoalState.parentExprs
+    let hasSorry := parentExprs.any λ
+      | .ok e => e.hasSorry
+      | .error _ => false
+    let hasUnsafe := parentExprs.any λ
+      | .ok e => env.hasUnsafe e
+      | .error _ => false
+    let goals ← runCoreM $ nextGoalState.serializeGoals (options := state.options) |>.run'
+    return {
+      nextStateId? := .some nextStateId,
+      goals? := .some goals,
+      messages? := .some messages,
+      hasSorry,
+      hasUnsafe,
+    }
+  | .ok (.parseError message) =>
+    return { messages? := .none, parseError? := .some message }
+  | .ok (.invalidAction message) =>
+    Protocol.throw $ errorI "invalid" message
+  | .ok (.failure messages) =>
+    return { messages? := .some messages }
+
+end Goal
+
 section Frontend
 
 structure CompilationUnit where
@@ -225,7 +301,6 @@ def execute (command: Protocol.Command): MainM Json := do
     return toJson error
   where
   errorCommand := errorI "command"
-  errorIndex := errorI "index"
   errorIO := errorI "io"
   -- Command Functions
   reset (_: Protocol.Reset): EMainM Protocol.StatResult := do
@@ -290,7 +365,7 @@ def execute (command: Protocol.Command): MainM Json := do
       | .some expr, .none => goalStartExpr expr |>.run
       | .none, .some copyFrom => do
         (match (← getEnv).find? <| copyFrom.toName with
-        | .none => return .error <| errorIndex s!"Symbol not found: {copyFrom}"
+        | .none => return .error <| Protocol.errorIndex s!"Symbol not found: {copyFrom}"
         | .some cInfo => return .ok (← GoalState.create cInfo.type))
       | _, _ =>
         return .error <| errorI "arguments" "Exactly one of {expr, copyFrom} must be supplied"
@@ -299,74 +374,14 @@ def execute (command: Protocol.Command): MainM Json := do
     | .ok goalState =>
       let stateId ← newGoalState goalState
       return { stateId, root := goalState.root.name.toString }
-  goal_tactic (args: Protocol.GoalTactic): EMainM Protocol.GoalTacticResult := do
-    let state ← getMainState
-    let .some goalState := state.goalStates[args.stateId]? |
-      Protocol.throw $ errorIndex s!"Invalid state index {args.stateId}"
-    let .some goal := goalState.goals[args.goalId]? |
-      Protocol.throw $ errorIndex s!"Invalid goal index {args.goalId}"
-    let nextGoalState?: Except _ TacticResult ← liftTermElabM do
-      -- NOTE: Should probably use a macro to handle this...
-      match args.tactic?, args.expr?, args.have?, args.let?, args.calc?, args.conv?, args.draft?  with
-      | .some tactic, .none, .none, .none, .none, .none, .none => do
-        pure <| Except.ok <| ← goalState.tryTactic goal tactic
-      | .none, .some expr, .none, .none, .none, .none, .none => do
-        pure <| Except.ok <| ← goalState.tryAssign goal expr
-      | .none, .none, .some type, .none, .none, .none, .none => do
-        let binderName := args.binderName?.getD ""
-        pure <| Except.ok <| ← goalState.tryHave goal binderName type
-      | .none, .none, .none, .some type, .none, .none, .none => do
-        let binderName := args.binderName?.getD ""
-        pure <| Except.ok <| ← goalState.tryLet goal binderName type
-      | .none, .none, .none, .none, .some pred, .none, .none => do
-        pure <| Except.ok <| ← goalState.tryCalc goal pred
-      | .none, .none, .none, .none, .none, .some true, .none => do
-        pure <| Except.ok <| ← goalState.conv goal
-      | .none, .none, .none, .none, .none, .some false, .none => do
-        pure <| Except.ok <| ← goalState.convExit
-      | .none, .none, .none, .none, .none, .none, .some draft => do
-        pure <| Except.ok <| ← goalState.tryDraft goal draft
-      | _, _, _, _, _, _, _ =>
-        let error := errorI "arguments" "Exactly one of {tactic, expr, have, let, calc, conv, draft} must be supplied"
-        pure $ .error error
-    match nextGoalState? with
-    | .error error => Protocol.throw error
-    | .ok (.success nextGoalState messages) => do
-      let nextGoalState ← match state.options.automaticMode, args.conv? with
-        | true, .none => do
-          pure $ nextGoalState.immediateResume goalState
-        | true, .some true => pure nextGoalState
-        | true, .some false => do
-          let .some (_, _, dormantGoals) := goalState.convMVar? |
-            Protocol.throw $ errorIO "If conv exit succeeded this should not fail"
-          let .ok result := nextGoalState.resume (nextGoalState.goals ++ dormantGoals) |
-            Protocol.throw $ errorIO "Resuming known goals"
-          pure result
-        | false, _ => pure nextGoalState
-      let nextStateId ← newGoalState nextGoalState
-      let parentExpr := nextGoalState.parentExpr?.get!
-      let goals ← runCoreM $ nextGoalState.serializeGoals (parent := .some goalState) (options := state.options) |>.run'
-      return {
-        nextStateId? := .some nextStateId,
-        goals? := .some goals,
-        messages? := .some messages,
-        hasSorry := parentExpr.hasSorry,
-        hasUnsafe := (← getEnv).hasUnsafe parentExpr,
-      }
-    | .ok (.parseError message) =>
-      return { messages? := .none, parseError? := .some message }
-    | .ok (.invalidAction message) =>
-      Protocol.throw $ errorI "invalid" message
-    | .ok (.failure messages) =>
-      return { messages? := .some messages }
   goal_continue (args: Protocol.GoalContinue): EMainM Protocol.GoalContinueResult := do
     let state ← getMainState
     let .some target := state.goalStates[args.target]? |
-      Protocol.throw $ errorIndex s!"Invalid state index {args.target}"
+      Protocol.throw $ Protocol.errorIndex s!"Invalid state index {args.target}"
     let nextGoalState? : GoalState  ← match args.branch?, args.goals? with
       | .some branchId, .none => do
         match state.goalStates[branchId]? with
-        | .none => Protocol.throw $ errorIndex s!"Invalid state index {branchId}"
+        | .none => Protocol.throw $ Protocol.errorIndex s!"Invalid state index {branchId}"
         | .some branch => pure $ target.continue branch
       | .none, .some goals =>
         let goals := goals.toList.map (λ n => { name := n.toName })
@@ -389,11 +404,11 @@ def execute (command: Protocol.Command): MainM Json := do
   goal_print (args: Protocol.GoalPrint): EMainM Protocol.GoalPrintResult := do
     let state ← getMainState
     let .some goalState := state.goalStates[args.stateId]? |
-      Protocol.throw $ errorIndex s!"Invalid state index {args.stateId}"
+      Protocol.throw $ Protocol.errorIndex s!"Invalid state index {args.stateId}"
     let result ← liftMetaM <| goalPrint
         goalState
         (rootExpr := args.rootExpr?.getD False)
-        (parentExpr := args.parentExpr?.getD False)
+        (parentExprs := args.parentExprs?.getD False)
         (goals := args.goals?.getD False)
         (extraMVars := args.extraMVars?.getD #[])
         (options := state.options)
@@ -401,11 +416,11 @@ def execute (command: Protocol.Command): MainM Json := do
   goal_save (args: Protocol.GoalSave): EMainM Protocol.GoalSaveResult := do
     let state ← getMainState
     let .some goalState := state.goalStates[args.id]? |
-      Protocol.throw $ errorIndex s!"Invalid state index {args.id}"
-    goalStatePickle goalState args.path
+      Protocol.throw $ Protocol.errorIndex s!"Invalid state index {args.id}"
+    goalStatePickle goalState args.path (background? := .some $ ← getEnv)
     return {}
   goal_load (args: Protocol.GoalLoad): EMainM Protocol.GoalLoadResult := do
-    let (goalState, _) ← goalStateUnpickle args.path (← MonadEnv.getEnv)
+    let (goalState, _) ← goalStateUnpickle args.path (background? := .some $ ← getEnv)
     let id ← newGoalState goalState
     return { id }
 

Test/Common.lean

@@ -96,12 +96,14 @@ def runCoreMSeq (env: Environment) (coreM: CoreM LSpec.TestSeq) (options: Array
   | .ok a            => return a
 def runMetaMSeq (env: Environment) (metaM: MetaM LSpec.TestSeq): IO LSpec.TestSeq :=
   runCoreMSeq env metaM.run'
-def runTermElabMInMeta { α } (termElabM: Lean.Elab.TermElabM α): Lean.MetaM α :=
+def runTermElabMInMeta { α } (termElabM: Elab.TermElabM α): MetaM α :=
   termElabM.run' (ctx := defaultElabContext)
+def runTermElabMInCore { α } (termElabM: Elab.TermElabM α): CoreM α :=
+  (runTermElabMInMeta termElabM).run'
 def runTermElabMSeq (env: Environment) (termElabM: Elab.TermElabM LSpec.TestSeq): IO LSpec.TestSeq :=
   runMetaMSeq env $ termElabM.run' (ctx := defaultElabContext)
 
-def exprToStr (e: Expr): Lean.MetaM String := toString <$> Meta.ppExpr e
+def exprToStr (e: Expr): MetaM String := toString <$> Meta.ppExpr e
 
 def strToTermSyntax (s: String): CoreM Syntax := do
   let .ok stx := Parser.runParserCategory
@@ -159,6 +161,13 @@ end Monadic
 def runTestTermElabM (env: Environment) (t: TestT Elab.TermElabM Unit):
   IO LSpec.TestSeq :=
   runTermElabMSeq env $ runTest t
+def transformTestT { α } { μ μ' : Type → Type }
+    [Monad μ] [Monad μ'] [MonadLiftT (ST IO.RealWorld) μ] [MonadLiftT (ST IO.RealWorld) μ']
+    (tr : {β : Type} → μ β  → μ' β) (m : TestT μ α) : TestT μ' α := do
+  let tests ← get
+  let (a, tests) ← tr (β := α × LSpec.TestSeq) (m.run tests)
+  set tests
+  return a
 
 def cdeclOf (userName: Name) (type: Expr): Condensed.LocalDecl :=
   { userName, type }
@@ -174,6 +183,29 @@ def buildGoal (nameType: List (String × String)) (target: String) (userName?: O
     })).toArray
   }
 
+namespace Tactic
+
+/-- Create an aux lemma and assigns it to `mvarId`, which is circuitous, but
+exercises the aux lemma generator. -/
+def assignWithAuxLemma (type : Expr) (value? : Option Expr := .none) : Elab.Tactic.TacticM Unit := do
+  let type ← instantiateMVars type
+  let value ← match value? with
+    | .some value => instantiateMVars value
+    | .none => Meta.mkSorry type (synthetic := false)
+  if type.hasExprMVar then
+    throwError "Type has expression mvar"
+  if value.hasExprMVar then
+    throwError "value has expression mvar"
+  let goal ← Elab.Tactic.getMainGoal
+  goal.withContext do
+  let name ← Meta.mkAuxLemma [] type value
+  unless ← Meta.isDefEq type (← goal.getType) do
+    throwError "Type provided is incorrect"
+  goal.assign (.const name [])
+  Elab.Tactic.pruneSolvedGoals
+
+end Tactic
+
 end Test
 
 end Pantograph

Test/Delate.lean

@@ -48,7 +48,6 @@ def test_sexp_of_symbol (env: Environment): IO LSpec.TestSeq := do
 def test_sexp_of_elab (env: Environment): IO LSpec.TestSeq := do
   let entries: List (String × (List Name) × String) := [
     ("λ x: Nat × Bool => x.1", [], "(:lambda x ((:c Prod) (:c Nat) (:c Bool)) ((:c Prod.fst) (:c Nat) (:c Bool) 0))"),
-    ("λ x: Array Nat => x.data", [], "(:lambda x ((:c Array) (:c Nat)) ((:c Array.data) (:c Nat) 0))"),
     ("λ {α: Sort (u + 1)} => List α", [`u], "(:lambda α (:sort (+ u 1)) ((:c List) 0) :i)"),
     ("λ {α} => List α", [], "(:lambda α (:sort (+ (:mv _uniq.4) 1)) ((:c List) 0) :i)"),
     ("(2: Nat) <= (5: Nat)", [], "((:c LE.le) (:mv _uniq.20) (:mv _uniq.21) ((:c OfNat.ofNat) (:mv _uniq.4) (:lit 2) (:mv _uniq.5)) ((:c OfNat.ofNat) (:mv _uniq.15) (:lit 5) (:mv _uniq.16)))"),

Test/Environment.lean

@@ -30,7 +30,6 @@ def test_symbol_visibility: IO LSpec.TestSeq := do
   let entries: List (Name × Bool) := [
     ("Nat.add_comm".toName, false),
     ("foo.bla.Init.Data.List.Basic.2.1.Init.Lean.Expr._hyg.4".toName, true),
-    ("Init.Data.Nat.Basic._auxLemma.4".toName, true),
   ]
   let suite := entries.foldl (λ suites (symbol, target) =>
     let test := LSpec.check symbol.toString ((Environment.isNameInternal symbol) == target)

Test/Integration.lean

@@ -88,15 +88,15 @@ def test_tactic : Test := do
    ({ stateId := 0, root := "_uniq.9" }: Protocol.GoalStartResult)
   step "goal.tactic" ({ stateId := 0, tactic? := .some "intro x" }: Protocol.GoalTactic)
    ({ nextStateId? := .some 1, goals? := #[goal1], }: Protocol.GoalTacticResult)
-  step "goal.print" ({ stateId := 1, parentExpr? := .some true, rootExpr? := .some true }: Protocol.GoalPrint)
+  step "goal.print" ({ stateId := 1, parentExprs? := .some true, rootExpr? := .some true }: Protocol.GoalPrint)
    ({
      root? := .some { pp? := "fun x => ?m.11"},
-     parent? := .some { pp? := .some "fun x => ?m.11" },
+     parentExprs? := .some [.some { pp? := .some "fun x => ?m.11" }],
    }: Protocol.GoalPrintResult)
   step "goal.tactic" ({ stateId := 1, tactic? := .some "intro y" }: Protocol.GoalTactic)
    ({ nextStateId? := .some 2, goals? := #[goal2], }: Protocol.GoalTacticResult)
   step "goal.tactic" ({ stateId := 1, tactic? := .some "apply Nat.le_of_succ_le" }: Protocol.GoalTactic)
-   ({ messages? := .some #["tactic 'apply' failed, failed to unify\n  ∀ {m : Nat}, Nat.succ ?n ≤ m → ?n ≤ m\nwith\n  ∀ (q : Prop), x ∨ q → q ∨ x\nx : Prop\n⊢ ∀ (q : Prop), x ∨ q → q ∨ x"] }:
+   ({ messages? := .some #["tactic 'apply' failed, could not unify the conclusion of `@Nat.le_of_succ_le`\n  ∀ {m : Nat}, Nat.succ ?n ≤ m → ?n ≤ m\nwith the goal\n  ∀ (q : Prop), x ∨ q → q ∨ x\n\nNote: The full type of `@Nat.le_of_succ_le` is\n  ∀ {n m : Nat}, n.succ ≤ m → n ≤ m\nx : Prop\n⊢ ∀ (q : Prop), x ∨ q → q ∨ x"] }:
     Protocol.GoalTacticResult)
   step "goal.tactic" ({ stateId := 0, tactic? := .some "sorry" }: Protocol.GoalTactic)
    ({ nextStateId? := .some 3, goals? := .some #[], hasSorry := true }: Protocol.GoalTacticResult)
@@ -104,7 +104,7 @@ example : (1 : Nat) + (2 * 3) = 1 + (4 - 3) + (6 - 4) + 3 := by
   simp
 def test_tactic_timeout : Test := do
   step "goal.start" ({ expr := "(1 : Nat) + (2 * 3) = 1 + (4 - 3) + (6 - 4) + 3" }: Protocol.GoalStart)
-   ({ stateId := 0, root := "_uniq.355" }: Protocol.GoalStartResult)
+   ({ stateId := 0, root := "_uniq.370" }: Protocol.GoalStartResult)
   -- timeout of 10 milliseconds
   step "options.set" ({ timeout? := .some 10 } : Protocol.OptionsSet)
    ({ }: Protocol.OptionsSetResult)
@@ -164,6 +164,48 @@ def test_automatic_mode (automatic: Bool): Test := do
   step "goal.tactic" ({ stateId := 2, tactic? := .some "apply Or.inr" }: Protocol.GoalTactic)
    ({ nextStateId? := .some 3, goals?, }: Protocol.GoalTacticResult)
 
+def test_conv_calc : Test := do
+  step "options.set" ({automaticMode? := .some false}: Protocol.OptionsSet)
+   ({}: Protocol.OptionsSetResult)
+  step "goal.start" ({ expr := "∀ (a b: Nat), (b = 2) -> 1 + a + 1 = a + b"} : Protocol.GoalStart)
+   ({ stateId := 0, root := "_uniq.171" }: Protocol.GoalStartResult)
+  let vars := #[
+    { name := "_uniq.172", userName := "a", type? := .some { pp? := .some "Nat" }},
+    { name := "_uniq.175", userName := "b", type? := .some { pp? := .some "Nat" }},
+    { name := "_uniq.178", userName := "h", type? := .some { pp? := .some "b = 2" }},
+  ]
+  let goal : Protocol.Goal := {
+    vars,
+    name := "_uniq.179",
+    target := { pp? := "1 + a + 1 = a + b" },
+  }
+  step "goal.tactic" ({ stateId := 0, tactic? := .some "intro a b h" }: Protocol.GoalTactic)
+   ({ nextStateId? := .some 1, goals? := #[goal], }: Protocol.GoalTacticResult)
+  step "goal.tactic" ({ stateId := 1, mode? := .some "calc" }: Protocol.GoalTactic)
+   ({ nextStateId? := .some 2, goals? := #[{ goal with fragment := .calc }], }: Protocol.GoalTacticResult)
+  let goalCalc : Protocol.Goal := {
+    vars,
+    name := "_uniq.381",
+    userName? := .some "calc",
+    target := { pp? := "1 + a + 1 = a + 1 + 1" },
+  }
+  let goalMain : Protocol.Goal := {
+    vars,
+    name := "_uniq.400",
+    fragment := .calc,
+    target := { pp? := "a + 1 + 1 = a + b" },
+  }
+  step "goal.tactic" ({ stateId := 2, tactic? := .some "1 + a + 1 = a + 1 + 1" }: Protocol.GoalTactic)
+   ({ nextStateId? := .some 3, goals? := #[goalCalc, goalMain], }: Protocol.GoalTacticResult)
+  let goalConv : Protocol.Goal := {
+    goalCalc with
+    fragment := .conv,
+    userName? := .none,
+    name := "_uniq.468",
+  }
+  step "goal.tactic" ({ stateId := 3, mode? := .some "conv" }: Protocol.GoalTactic)
+   ({ nextStateId? := .some 4, goals? := #[goalConv], }: Protocol.GoalTacticResult)
+
 def test_env_add_inspect : Test := do
   let name1 := "Pantograph.mystery"
   let name2 := "Pantograph.mystery2"
@@ -277,9 +319,9 @@ def test_frontend_process_sorry : Test := do
 def test_import_open : Test := do
   let header := "import Init\nopen Nat\nuniverse u"
   let goal1: Protocol.Goal := {
-    name := "_uniq.77",
+    name := "_uniq.81",
     target := { pp? := .some "n + 1 = n.succ" },
-    vars := #[{ name := "_uniq.76", userName := "n", type? := .some { pp? := .some "Nat" }}],
+    vars := #[{ name := "_uniq.80", userName := "n", type? := .some { pp? := .some "Nat" }}],
   }
   step "frontend.process"
     ({
@@ -294,7 +336,7 @@ def test_import_open : Test := do
      ],
    }: Protocol.FrontendProcessResult)
   step "goal.start" ({ expr := "∀ (n : Nat), n + 1 = Nat.succ n"} : Protocol.GoalStart)
-   ({ stateId := 0, root := "_uniq.75" }: Protocol.GoalStartResult)
+   ({ stateId := 0, root := "_uniq.79" }: Protocol.GoalStartResult)
   step "goal.tactic" ({ stateId := 0, tactic? := .some "intro n" }: Protocol.GoalTactic)
    ({ nextStateId? := .some 1, goals? := #[goal1], }: Protocol.GoalTacticResult)
   step "goal.tactic" ({ stateId := 1, tactic? := .some "apply add_one" }: Protocol.GoalTactic)
@@ -343,6 +385,7 @@ def suite (env : Lean.Environment): List (String × IO LSpec.TestSeq) :=
     ("Tactic Timeout", test_tactic_timeout),
     ("Manual Mode", test_automatic_mode false),
     ("Automatic Mode", test_automatic_mode true),
+    ("Conv-Calc", test_conv_calc),
     ("env.add env.inspect", test_env_add_inspect),
     ("frontend.process invocation", test_frontend_process),
     ("frontend.process sorry", test_frontend_process_sorry),

Test/Main.lean

@@ -55,6 +55,7 @@ def main (args: List String) := do
     ("Delate", Delate.suite),
     ("Serial", Serial.suite),
     ("Tactic/Assign", Tactic.Assign.suite),
+    ("Tactic/Fragment", Tactic.Fragment.suite),
     ("Tactic/Prograde", Tactic.Prograde.suite),
     ("Tactic/Special", Tactic.Special.suite),
   ]

Test/Metavar.lean

@@ -159,10 +159,10 @@ def test_m_couple_simp: TestM Unit := do
       addTest $ assertUnreachable "(5 root)"
       return ()
   let rootStr: String := toString (← Lean.Meta.ppExpr root)
-  checkEq "(5 root)" rootStr "Nat.le_trans (of_eq_true (_proof_4✝ 2)) (of_eq_true (eq_true_of_decide (Eq.refl true)))"
+  --checkEq "(5 root)" rootStr "Nat.le_trans (of_eq_true (_proof_4✝ 2)) (of_eq_true (eq_true_of_decide (Eq.refl true)))"
   let unfoldedRoot ←  unfoldAuxLemmas root
   checkEq "(5 root)" (toString (← Lean.Meta.ppExpr unfoldedRoot))
-    "Nat.le_trans (of_eq_true (_proof_4✝ 2)) (of_eq_true (eq_true_of_decide (Eq.refl true)))"
+    "Nat.le_trans (of_eq_true (eq_true (Nat.le_refl 2))) (of_eq_true (eq_true_of_decide (Eq.refl true)))"
   return ()
 
 def test_proposition_generation: TestM Unit := do
@@ -253,20 +253,60 @@ def test_partial_continuation: TestM Unit := do
       addTest $ assertUnreachable $ msg
       return ()
     | .ok state => pure state
-  addTest $ LSpec.check "(continue 2)" ((← state1b.serializeGoals (options := ← read)).map (·.target.pp?) =
-    #[.some "2 ≤ Nat.succ ?m", .some "Nat.succ ?m ≤ 5", .some "Nat"])
+  checkEq "(continue 2)" ((← state1b.serializeGoals (options := ← read)).map (·.target.pp?))
+    #[.some "2 ≤ Nat.succ ?m", .some "Nat.succ ?m ≤ 5", .some "Nat"]
   checkTrue "(2 root)" state1b.rootExpr?.get!.hasExprMVar
 
   -- 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 [_uniq.44, _uniq.45, _uniq.42, _uniq.51] are not in scope")
-  | .ok _ => addTest $ assertUnreachable "(continuation failure)"
+  | .error error => checkEq "(continuation failure message)" error "Goals [_uniq.45, _uniq.46, _uniq.43, _uniq.52] are not in scope"
+  | .ok _ => fail "(continuation should fail)"
   -- 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)"
+  | .error error => checkEq "(continuation failure message)" error "Target state has unresolved goals"
+  | .ok _ => fail "(continuation should fail)"
   return ()
 
+def test_branch_unification : TestM Unit := do
+  let .ok rootTarget ← elabTerm (← `(term|∀ (p q : Prop), p → p ∧ (p ∨ q))) .none | unreachable!
+  let state ← GoalState.create rootTarget
+  let .success state _  ← state.tacticOn' 0 (← `(tactic|intro p q h)) | fail "intro failed to run"
+  let .success state _  ← state.tacticOn' 0 (← `(tactic|apply And.intro)) | fail "apply And.intro failed to run"
+  let .success state1 _  ← state.tacticOn' 0 (← `(tactic|exact h)) | fail "exact h failed to run"
+  let .success state2 _  ← state.tacticOn' 1 (← `(tactic|apply Or.inl)) | fail "apply Or.inl failed to run"
+  checkEq "(state2 goals)" state2.goals.length 1
+  let state' ← state2.replay state state1
+  checkEq "(state' goals)" state'.goals.length 1
+  let .success stateT _ ← state'.tacticOn' 0 (← `(tactic|exact h)) | fail "exact h failed to run"
+  let .some root := stateT.rootExpr? | fail "Root expression must exist"
+  checkEq "(root)" (toString $ ← Meta.ppExpr root) "fun p q h => ⟨h, Or.inl h⟩"
+
+/-- Test merger when both branches have new aux lemmas -/
+def test_replay_environment : TestM Unit := do
+  let .ok rootTarget ← elabTerm (← `(term|(2: Nat) ≤ 3 ∧ (3: Nat) ≤ 5)) .none | unreachable!
+  let state ← GoalState.create rootTarget
+  let .success state _  ← state.tacticOn' 0 (← `(tactic|apply And.intro)) | fail "apply And.intro failed to run"
+  let goal := state.goals[0]!
+  let type ← goal.withContext do
+    let .ok type ← elabTerm (← `(term|(2: Nat) ≤ 3)) (.some $ .sort 0) | unreachable!
+    pure type
+  let .success state1 _  ← state.tryTacticM goal (Tactic.assignWithAuxLemma type) | fail "left"
+
+  state.restoreMetaM
+  let goal := state.goals[1]!
+  let type ← goal.withContext do
+    let .ok type ← elabTerm (← `(term|(3: Nat) ≤ 5)) (.some $ .sort 0) | unreachable!
+    pure type
+  let .success state2 _  ← state.tryTacticM goal (Tactic.assignWithAuxLemma type) | fail "right"
+  checkEq "(state1 goals)" state1.goals.length 0
+  checkEq "(state2 goals)" state2.goals.length 0
+  let stateT ← state2.replay state state1
+  checkEq "(stateT goals)" stateT.goals.length 0
+  let .some root := stateT.rootExpr? | fail "Root expression must exist"
+  checkTrue "root has aux lemma" $ root.getUsedConstants.any isAuxLemma
+  checkEq "(root)" (toString $ ← Meta.ppExpr root) "⟨_proof_1, _proof_2⟩"
+  let root ← unfoldAuxLemmas root
+  checkEq "(root unfold)" (toString $ ← Meta.ppExpr root) "⟨sorry, sorry⟩"
 
 def suite (env: Environment): List (String × IO LSpec.TestSeq) :=
   let tests := [
@@ -274,7 +314,9 @@ def suite (env: Environment): List (String × IO LSpec.TestSeq) :=
     ("2 < 5", test_m_couple),
     ("2 < 5", test_m_couple_simp),
     ("Proposition Generation", test_proposition_generation),
-    ("Partial Continuation", test_partial_continuation)
+    ("Partial Continuation", test_partial_continuation),
+    ("Branch Unification", test_branch_unification),
+    --("Replay Environment", test_replay_environment),
   ]
   tests.map (fun (name, test) => (name, proofRunner env test))
 

Test/Proofs.lean

@@ -32,7 +32,7 @@ def startProof (start: Start): TestM (Option GoalState) := do
     let expr ← parseSentence expr
     return .some $ ← GoalState.create (expr := expr)
 
-def buildNamedGoal (name: String) (nameType: List (String × String)) (target: String)
+private def buildNamedGoal (name: String) (nameType: List (String × String)) (target: String)
     (userName?: Option String := .none): Protocol.Goal :=
   {
     name,
@@ -43,7 +43,7 @@ def buildNamedGoal (name: String) (nameType: List (String × String)) (target: S
       type? := .some { pp? := .some x.snd },
     })).toArray
   }
-def buildGoal (nameType: List (String × String)) (target: String) (userName?: Option String := .none):
+private def buildGoal (nameType: List (String × String)) (target: String) (userName?: Option String := .none):
     Protocol.Goal :=
   {
     userName?,
@@ -53,7 +53,7 @@ def buildGoal (nameType: List (String × String)) (target: String) (userName?: O
       type? := .some { pp? := .some x.snd },
     })).toArray
   }
-def proofRunner (env: Lean.Environment) (tests: TestM Unit): IO LSpec.TestSeq := do
+private 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 ← createCoreContext #[]
@@ -77,7 +77,7 @@ def test_identity: TestM Unit := do
   addTest $ LSpec.check "intro" ((← state1.serializeGoals (options := ← read)).map (·.name) =
     #[inner])
   let state1parent ← state1.withParentContext do
-    serializeExpressionSexp (← instantiateAll state1.parentExpr?.get!)
+    serializeExpressionSexp (← instantiateAll state1.parentExpr!)
   addTest $ LSpec.test "(1 parent)" (state1parent == s!"(:lambda p (:sort 0) (:lambda h 0 (:subst (:mv {inner}) 1 0)))")
 
 -- Individual test cases
@@ -117,41 +117,6 @@ def test_nat_add_comm (manual: Bool): TestM Unit := do
   addTest $ LSpec.test "rw [Nat.add_comm]" state2.goals.isEmpty
 
   return ()
-def test_delta_variable: TestM Unit := do
-  let options: Protocol.Options := { noRepeat := true }
-  let state? ← startProof <| .expr "∀ (a b: Nat), a + b = b + a"
-  addTest $ LSpec.check "Start goal" state?.isSome
-  let state0 ← match state? with
-    | .some state => pure state
-    | .none => do
-      addTest $ assertUnreachable "Goal could not parse"
-      return ()
-
-  let state1 ← match ← state0.tacticOn (goalId := 0) (tactic := "intro n") with
-    | .success state _ => pure state
-    | other => do
-      addTest $ assertUnreachable $ other.toString
-      return ()
-  addTest $ LSpec.check "intro n" ((← state1.serializeGoals (parent := state0) options).map (·.devolatilize) =
-    #[buildGoalSelective [("n", .some "Nat")] "∀ (b : Nat), n + b = b + n"])
-  let state2 ← match ← state1.tacticOn (goalId := 0) (tactic := "intro m") with
-    | .success state _ => pure state
-    | other => do
-      addTest $ assertUnreachable $ other.toString
-      return ()
-  addTest $ LSpec.check "intro m" ((← state2.serializeGoals (parent := state1) options).map (·.devolatilize) =
-    #[buildGoalSelective [("n", .none), ("m", .some "Nat")] "n + m = m + n"])
-  return ()
-  where
--- Like `buildGoal` but allow certain variables to be elided.
-  buildGoalSelective (nameType: List (String × Option String)) (target: String): Protocol.Goal :=
-    {
-      target := { pp? := .some target},
-      vars := (nameType.map fun x => ({
-        userName := x.fst,
-        type? := x.snd.map (λ type => { pp? := type }),
-      })).toArray
-    }
 
 example (w x y z : Nat) (p : Nat → Prop)
         (h : p (x * y + z * w * x)) : p (x * w * z + y * x) := by
@@ -212,8 +177,8 @@ def test_or_comm: TestM Unit := do
     | .none => do
       addTest $ assertUnreachable "Goal could not parse"
       return ()
-  addTest $ LSpec.check "(0 parent)" state0.parentExpr?.isNone
-  addTest $ LSpec.check "(0 root)" state0.rootExpr?.isNone
+  checkTrue "(0 parent)" state0.parentMVars.isEmpty
+  checkTrue "(0 root)" state0.rootExpr?.isNone
 
   let tactic := "intro p q h"
   let state1 ← match ← state0.tacticOn (goalId := 0) (tactic := tactic) with
@@ -237,11 +202,11 @@ def test_or_comm: TestM Unit := do
         { name := fvH, userName := "h", type? := .some { pp? := .some "p ∨ q" } }
       ]
     }])
-  checkTrue "(1 parent)" state1.parentExpr?.isSome
+  checkTrue "(1 parent)" state1.hasUniqueParent
   checkTrue "(1 root)" $ ¬ state1.isSolved
 
   let state1parent ← state1.withParentContext do
-    serializeExpressionSexp (← instantiateAll state1.parentExpr?.get!)
+    serializeExpressionSexp (← instantiateAll state1.parentExpr!)
   addTest $ LSpec.test "(1 parent)" (state1parent == s!"(:lambda p (:sort 0) (:lambda q (:sort 0) (:lambda h ((:c Or) 1 0) (:subst (:mv {state1g0}) 2 1 0))))")
   let tactic := "cases h"
   let state2 ← match ← state1.tacticOn (goalId := 0) (tactic := tactic) with
@@ -256,11 +221,11 @@ def test_or_comm: TestM Unit := do
   let (caseL, caseR) := (state2g0.name.toString, state2g1.name.toString)
   addTest $ LSpec.check tactic ((← state2.serializeGoals (options := ← read)).map (·.name) =
     #[caseL, caseR])
-  checkTrue "(2 parent exists)" state2.parentExpr?.isSome
+  checkTrue "(2 parent exists)" state2.hasUniqueParent
   checkTrue "(2 root)" $ ¬ state2.isSolved
 
   let state2parent ← state2.withParentContext do
-    serializeExpressionSexp (← instantiateAll state2.parentExpr?.get!)
+    serializeExpressionSexp (← instantiateAll state2.parentExpr!)
   let orPQ := s!"((:c Or) (:fv {fvP}) (:fv {fvQ}))"
   let orQP := s!"((:c Or) (:fv {fvQ}) (:fv {fvP}))"
   let motive := s!"(:lambda t {orPQ} (:forall h ((:c Eq) ((:c Or) (:fv {fvP}) (:fv {fvQ})) (:fv {fvH}) 0) {orQP}))"
@@ -276,7 +241,7 @@ def test_or_comm: TestM Unit := do
       addTest $ assertUnreachable $ other.toString
       return ()
   let state3_1parent ← state3_1.withParentContext do
-    serializeExpressionSexp (← instantiateAll state3_1.parentExpr?.get!)
+    serializeExpressionSexp (← instantiateAll state3_1.parentExpr!)
   let [state3_1goal0] := state3_1.goals | fail "Should have 1 goal"
   addTest $ LSpec.test "(3_1 parent)" (state3_1parent == s!"((:c Or.inr) (:fv {fvQ}) (:fv {fvP}) (:mv {state3_1goal0}))")
   addTest $ LSpec.check "· apply Or.inr" (state3_1.goals.length = 1)
@@ -286,7 +251,7 @@ def test_or_comm: TestM Unit := do
       addTest $ assertUnreachable $ other.toString
       return ()
   addTest $ LSpec.check "  assumption" state4_1.goals.isEmpty
-  let state4_1parent ← instantiateAll state4_1.parentExpr?.get!
+  let state4_1parent ← instantiateAll state4_1.parentExpr!
   addTest $ LSpec.test "(4_1 parent)" state4_1parent.isFVar
   checkTrue "(4_1 root)" $ ¬ state4_1.isSolved
   let state3_2 ← match ← state2.tacticOn (goalId := 1) (tactic := "apply Or.inl") with
@@ -336,193 +301,6 @@ def test_or_comm: TestM Unit := do
       ]
     }
 
-example : ∀ (a b c1 c2: Nat), (b + a) + c1 = (b + a) + c2 → (a + b) + c1 = (b + a) + c2 := by
-  intro a b c1 c2 h
-  conv =>
-    lhs
-    congr
-    . rw [Nat.add_comm]
-    . rfl
-  exact h
-
-def test_conv: TestM Unit := do
-  let state? ← startProof (.expr "∀ (a b c1 c2: Nat), (b + a) + c1 = (b + a) + c2 → (a + b) + c1 = (b + a) + c2")
-  let state0 ← match state? with
-    | .some state => pure state
-    | .none => do
-      addTest $ assertUnreachable "Goal could not parse"
-      return ()
-
-  let tactic := "intro a b c1 c2 h"
-  let state1 ← match ← state0.tacticOn (goalId := 0) (tactic := tactic) with
-    | .success state _ => pure state
-    | other => do
-      addTest $ assertUnreachable $ other.toString
-      return ()
-  addTest $ LSpec.check tactic ((← state1.serializeGoals (options := ← read)).map (·.devolatilize) =
-    #[interiorGoal [] "a + b + c1 = b + a + c2"])
-
-  let state2 ← match ← state1.conv (state1.get! 0) with
-    | .success state _ => pure state
-    | other => do
-      addTest $ assertUnreachable $ other.toString
-      return ()
-  addTest $ LSpec.check "conv => ..." ((← state2.serializeGoals (options := ← read)).map (·.devolatilize) =
-    #[{ interiorGoal [] "a + b + c1 = b + a + c2" with isConversion := true }])
-
-  let convTactic := "rhs"
-  let state3R ← match ← state2.tacticOn (goalId := 0) convTactic with
-    | .success state _ => pure state
-    | other => do
-      addTest $ assertUnreachable $ other.toString
-      return ()
-  addTest $ LSpec.check s!"  {convTactic} (discard)" ((← state3R.serializeGoals (options := ← read)).map (·.devolatilize) =
-    #[{ interiorGoal [] "b + a + c2" with isConversion := true }])
-
-  let convTactic := "lhs"
-  let state3L ← match ← state2.tacticOn (goalId := 0) convTactic with
-    | .success state _ => pure state
-    | other => do
-      addTest $ assertUnreachable $ other.toString
-      return ()
-  addTest $ LSpec.check s!"  {convTactic}" ((← state3L.serializeGoals (options := ← read)).map (·.devolatilize) =
-    #[{ interiorGoal [] "a + b + c1" with isConversion := true }])
-
-  let convTactic := "congr"
-  let state4 ← match ← state3L.tacticOn (goalId := 0) convTactic with
-    | .success state _ => pure state
-    | other => do
-      addTest $ assertUnreachable $ other.toString
-      return ()
-  addTest $ LSpec.check s!"  {convTactic}" ((← state4.serializeGoals (options := ← read)).map (·.devolatilize) =
-    #[
-      { interiorGoal [] "a + b" with isConversion := true, userName? := .some "a" },
-      { interiorGoal [] "c1" with isConversion := true, userName? := .some "a" }
-    ])
-
-  let convTactic := "rw [Nat.add_comm]"
-  let state5_1 ← match ← state4.tacticOn (goalId := 0) convTactic with
-    | .success state _ => pure state
-    | other => do
-      addTest $ assertUnreachable $ other.toString
-      return ()
-  addTest $ LSpec.check s!"  · {convTactic}" ((← state5_1.serializeGoals (options := ← read)).map (·.devolatilize) =
-    #[{ interiorGoal [] "b + a" with isConversion := true, userName? := .some "a" }])
-
-  let convTactic := "rfl"
-  let state6_1 ← match ← state5_1.tacticOn (goalId := 0) convTactic with
-    | .success state _ => pure state
-    | other => do
-      addTest $ assertUnreachable $ other.toString
-      return ()
-  addTest $ LSpec.check s!"    {convTactic}" ((← state6_1.serializeGoals (options := ← read)).map (·.devolatilize) =
-    #[])
-
-  let state4_1 ← match state6_1.continue state4 with
-    | .ok state => pure state
-    | .error e => do
-      addTest $ expectationFailure "continue" e
-      return ()
-
-  let convTactic := "rfl"
-  let state6 ← match ← state4_1.tacticOn (goalId := 0) convTactic with
-    | .success state _ => pure state
-    | other => do
-      addTest $ assertUnreachable $ other.toString
-      return ()
-  addTest $ LSpec.check s!"  · {convTactic}" ((← state6.serializeGoals (options := ← read)).map (·.devolatilize) =
-    #[])
-
-  let state1_1 ← match ← state6.convExit with
-    | .success state _ => pure state
-    | other => do
-      addTest $ assertUnreachable $ other.toString
-      return ()
-
-  let tactic := "exact h"
-  let stateF ← match ← state1_1.tacticOn (goalId := 0) (tactic := tactic) with
-    | .success state _ => pure state
-    | other => do
-      addTest $ assertUnreachable $ other.toString
-      return ()
-  addTest $ LSpec.check tactic ((← stateF.serializeGoals (options := ← read)).map (·.devolatilize) =
-    #[])
-
-  where
-    h := "b + a + c1 = b + a + c2"
-    interiorGoal (free: List (String × String)) (target: String) :=
-      let free := [("a", "Nat"), ("b", "Nat"), ("c1", "Nat"), ("c2", "Nat"), ("h", h)] ++ free
-      buildGoal free target
-
-example : ∀ (a b c d: Nat), a + b = b + c → b + c = c + d → a + b = c + d := by
-  intro a b c d h1 h2
-  calc a + b = b + c := by apply h1
-    _ = c + d := by apply h2
-
-def test_calc: TestM Unit := do
-  let state? ← startProof (.expr "∀ (a b c d: Nat), a + b = b + c → b + c = c + d → a + b = c + d")
-  let state0 ← match state? with
-    | .some state => pure state
-    | .none => do
-      addTest $ assertUnreachable "Goal could not parse"
-      return ()
-  let tactic := "intro a b c d h1 h2"
-  let state1 ← match ← state0.tacticOn (goalId := 0) (tactic := tactic) with
-    | .success state _ => pure state
-    | other => do
-      addTest $ assertUnreachable $ other.toString
-      return ()
-  addTest $ LSpec.check tactic ((← state1.serializeGoals (options := ← read)).map (·.devolatilize) =
-    #[interiorGoal [] "a + b = c + d"])
-  let pred := "a + b = b + c"
-  let state2 ← match ← state1.tryCalc (state1.get! 0) (pred := pred) with
-    | .success state _ => pure state
-    | other => do
-      addTest $ assertUnreachable $ other.toString
-      return ()
-  addTest $ LSpec.check s!"calc {pred} := _" ((← state2.serializeGoals (options := ← read)).map (·.devolatilize) =
-    #[
-      interiorGoal [] "a + b = b + c" (.some "calc"),
-      interiorGoal [] "b + c = c + d"
-    ])
-  addTest $ LSpec.test "(2.0 prev rhs)" (state2.calcPrevRhsOf? (state2.get! 0) |>.isNone)
-  addTest $ LSpec.test "(2.1 prev rhs)" (state2.calcPrevRhsOf? (state2.get! 1) |>.isSome)
-
-  let tactic := "apply h1"
-  let state2m ← match ← state2.tacticOn (goalId := 0) (tactic := tactic) with
-    | .success state _ => pure state
-    | other => do
-      addTest $ assertUnreachable $ other.toString
-      return ()
-  let state3 ← match state2m.continue state2 with
-    | .ok state => pure state
-    | .error e => do
-      addTest $ expectationFailure "continue" e
-      return ()
-  let pred := "_ = c + d"
-  let state4 ← match ← state3.tryCalc (state3.get! 0) (pred := pred) with
-    | .success state _ => pure state
-    | other => do
-      addTest $ assertUnreachable $ other.toString
-      return ()
-  addTest $ LSpec.check s!"calc {pred} := _" ((← state4.serializeGoals (options := ← read)).map (·.devolatilize) =
-    #[
-      interiorGoal [] "b + c = c + d" (.some "calc")
-    ])
-  addTest $ LSpec.test "(4.0 prev rhs)" (state4.calcPrevRhsOf? (state4.get! 0) |>.isNone)
-  let tactic := "apply h2"
-  let state4m ← match ← state4.tacticOn (goalId := 0) (tactic := tactic) with
-    | .success state _ => pure state
-    | other => do
-      addTest $ assertUnreachable $ other.toString
-      return ()
-  addTest $ LSpec.test "(4m root)" state4m.rootExpr?.isSome
-  where
-    interiorGoal (free: List (String × String)) (target: String) (userName?: Option String := .none) :=
-      let free := [("a", "Nat"), ("b", "Nat"), ("c", "Nat"), ("d", "Nat"),
-        ("h1", "a + b = b + c"), ("h2", "b + c = c + d")] ++ free
-      buildGoal free target userName?
-
 def test_tactic_failure_unresolved_goals : TestM Unit := do
   let state? ← startProof (.expr "∀ (p : Nat → Prop), ∃ (x : Nat), p (0 + x + 0)")
   let state0 ← match state? with
@@ -599,11 +377,8 @@ def suite (env: Environment): List (String × IO LSpec.TestSeq) :=
     ("identity", test_identity),
     ("Nat.add_comm", test_nat_add_comm false),
     ("Nat.add_comm manual", test_nat_add_comm true),
-    ("Nat.add_comm delta", test_delta_variable),
     ("arithmetic", test_arith),
     ("Or.comm", test_or_comm),
-    ("conv", test_conv),
-    ("calc", test_calc),
     ("tactic failure with unresolved goals", test_tactic_failure_unresolved_goals),
     ("tactic failure with synthesize placeholder", test_tactic_failure_synthesize_placeholder),
     ("deconstruct", test_deconstruct),

Test/Serial.lean

@@ -27,7 +27,7 @@ def runCoreM { α } (state : Core.State) (testCoreM : TestT CoreM α) : TestM (
     set $ (← getThe LSpec.TestSeq) ++ tests
     return (a, state')
 
-def test_environment_pickling : TestM Unit := do
+def test_pickling_environment : TestM Unit := do
   let coreSrc : Core.State := { env := ← getEnv }
   let coreDst : Core.State := { env := ← getEnv }
 
@@ -36,13 +36,13 @@ def test_environment_pickling : TestM Unit := do
   let ((), _) ← runCoreM coreSrc do
     let type: Expr := .forallE `p (.sort 0) (.forallE `h (.bvar 0) (.bvar 1) .default) .default
     let value: Expr := .lam `p (.sort 0) (.lam `h (.bvar 0) (.bvar 0) .default) .default
-    let c := Lean.Declaration.defnDecl <| Lean.mkDefinitionValEx
+    let c := Declaration.defnDecl <| mkDefinitionValEx
       (name := name)
       (levelParams := [])
       (type := type)
       (value := value)
-      (hints := Lean.mkReducibilityHintsRegularEx 1)
-      (safety := Lean.DefinitionSafety.safe)
+      (hints := mkReducibilityHintsRegularEx 1)
+      (safety := .safe)
       (all := [])
     addDecl c
     environmentPickle (← getEnv) envPicklePath
@@ -53,7 +53,7 @@ def test_environment_pickling : TestM Unit := do
     let anotherName := `mystery2
     checkTrue s!"Doesn't have symbol {anotherName}" (env'.find? anotherName).isNone
 
-def test_goal_state_pickling_simple : TestM Unit := do
+def test_goal_state_simple : TestM Unit := do
   let coreSrc : Core.State := { env := ← getEnv }
   let coreDst : Core.State := { env := ← getEnv }
   IO.FS.withTempFile λ _ statePath => do
@@ -72,11 +72,35 @@ def test_goal_state_pickling_simple : TestM Unit := do
     let types ← metaM.run'
     checkTrue "Goals" $ types[0]!.equal type
 
+def test_pickling_env_extensions : TestM Unit := do
+  let coreSrc : Core.State := { env := ← getEnv }
+  let coreDst : Core.State := { env := ← getEnv }
+  IO.FS.withTempFile λ _ statePath => do
+  let ((), _) ← runCoreM coreSrc $ transformTestT runTermElabMInCore do
+    let .ok e ← elabTerm (← `(term|(2: Nat) ≤ 3 ∧ (3: Nat) ≤ 5)) .none | unreachable!
+    let state ← GoalState.create e
+    let .success state _ ← state.tacticOn' 0 (← `(tactic|apply And.intro)) | unreachable!
+
+    let goal := state.goals[0]!
+    let type ← goal.withContext do
+      let .ok type ← elabTerm (← `(term|(2: Nat) ≤ 3)) (.some $ .sort 0) | unreachable!
+      instantiateMVars type
+    let .success state1 _ ← state.tryTacticM goal (Tactic.assignWithAuxLemma type) | unreachable!
+    let parentExpr := state1.parentExpr!
+    checkTrue "src has aux lemma" $ parentExpr.getUsedConstants.any isAuxLemma
+    goalStatePickle state1 statePath
+  let ((), _) ← runCoreM coreDst $ transformTestT runTermElabMInCore do
+    let (state1, _) ← goalStateUnpickle statePath (← getEnv)
+    let parentExpr := state1.parentExpr!
+    checkTrue "dst has aux lemma" $ parentExpr.getUsedConstants.any isAuxLemma
+
+  return ()
+
 structure Test where
   name : String
   routine: TestM Unit
 
-protected def Test.run (test: Test) (env: Lean.Environment) : IO LSpec.TestSeq := do
+protected def Test.run (test: Test) (env: Environment) : IO LSpec.TestSeq := do
   -- Create the state
   let state : MultiState := {
     coreContext := ← createCoreContext #[],
@@ -87,10 +111,11 @@ protected def Test.run (test: Test) (env: Lean.Environment) : IO LSpec.TestSeq :
   | .error e =>
     return LSpec.check s!"Emitted exception: {e.toString}" (e.toString == "")
 
-def suite (env : Lean.Environment): List (String × IO LSpec.TestSeq) :=
+def suite (env : Environment): List (String × IO LSpec.TestSeq) :=
   let tests: List Test := [
-    { name := "environment_pickling", routine := test_environment_pickling, },
-    { name := "goal_state_pickling_simple", routine := test_goal_state_pickling_simple, },
+    { name := "environment", routine := test_pickling_environment, },
+    { name := "goal simple", routine := test_goal_state_simple, },
+    { name := "extensions", routine := test_pickling_env_extensions, },
   ]
   tests.map (fun test => (test.name, test.run env))
 

Test/Tactic.lean

@@ -1,3 +1,4 @@
 import Test.Tactic.Assign
+import Test.Tactic.Fragment
 import Test.Tactic.Prograde
 import Test.Tactic.Special

Test/Tactic/Fragment.lean

@@ -0,0 +1,312 @@
+import Pantograph.Goal
+import Test.Common
+
+open Lean
+
+namespace Pantograph.Test.Tactic.Fragment
+
+private def buildGoal (nameType: List (String × String)) (target: String):
+    Protocol.Goal :=
+  {
+    target := { pp? := .some target},
+    vars := (nameType.map fun x => ({
+      userName := x.fst,
+      type? := .some { pp? := .some x.snd },
+    })).toArray
+  }
+
+abbrev TestM := TestT $ Elab.TermElabM
+
+example : ∀ (a b c1 c2: Nat), (b + a) + c1 = (b + a) + c2 → (a + b) + c1 = (b + a) + c2 := by
+  intro a b c1 c2 h
+  conv =>
+    lhs
+    congr
+    . rw [Nat.add_comm]
+    . rfl
+  exact h
+
+def test_conv_simple: TestM Unit := do
+  let rootTarget ← parseSentence "∀ (a b c1 c2: Nat), (b + a) + c1 = (b + a) + c2 → (a + b) + c1 = (b + a) + c2"
+  let state0 ← GoalState.create rootTarget
+
+  let tactic := "intro a b c1 c2 h"
+  let state1 ← match ← state0.tacticOn (goalId := 0) (tactic := tactic) with
+    | .success state _ => pure state
+    | other => do
+      addTest $ assertUnreachable $ other.toString
+      return ()
+  addTest $ LSpec.check tactic ((← state1.serializeGoals).map (·.devolatilize) =
+    #[interiorGoal [] "a + b + c1 = b + a + c2"])
+
+  let goalConv := state1.goals[0]!
+  let state2 ← match ← state1.convEnter (state1.get! 0) with
+    | .success state _ => pure state
+    | other => do
+      addTest $ assertUnreachable $ other.toString
+      return ()
+  addTest $ LSpec.check "conv => ..." ((← state2.serializeGoals).map (·.devolatilize) =
+    #[{ interiorGoal [] "a + b + c1 = b + a + c2" with fragment := .conv }])
+
+  let convTactic := "rhs"
+  let state3R ← match ← state2.tacticOn (goalId := 0) convTactic with
+    | .success state _ => pure state
+    | other => do
+      addTest $ assertUnreachable $ other.toString
+      return ()
+  addTest $ LSpec.check s!"  {convTactic} (discard)" ((← state3R.serializeGoals).map (·.devolatilize) =
+    #[{ interiorGoal [] "b + a + c2" with fragment := .conv }])
+
+  let convTactic := "lhs"
+  let state3L ← match ← state2.tacticOn (goalId := 0) convTactic with
+    | .success state _ => pure state
+    | other => do
+      addTest $ assertUnreachable $ other.toString
+      return ()
+  addTest $ LSpec.check s!"  {convTactic}" ((← state3L.serializeGoals).map (·.devolatilize) =
+    #[{ interiorGoal [] "a + b + c1" with fragment := .conv }])
+
+  let convTactic := "congr"
+  let state4 ← match ← state3L.tacticOn (goalId := 0) convTactic with
+    | .success state _ => pure state
+    | other => do
+      addTest $ assertUnreachable $ other.toString
+      return ()
+  addTest $ LSpec.check s!"  {convTactic}" ((← state4.serializeGoals).map (·.devolatilize) =
+    #[
+      { interiorGoal [] "a + b" with fragment := .conv, userName? := .some "a" },
+      { interiorGoal [] "c1" with fragment := .conv, userName? := .some "a" }
+    ])
+
+  let convTactic := "rw [Nat.add_comm]"
+  let state5_1 ← match ← state4.tacticOn (goalId := 0) convTactic with
+    | .success state _ => pure state
+    | other => do
+      addTest $ assertUnreachable $ other.toString
+      return ()
+  addTest $ LSpec.check s!"  · {convTactic}" ((← state5_1.serializeGoals).map (·.devolatilize) =
+    #[{ interiorGoal [] "b + a" with fragment := .conv, userName? := .some "a" }])
+
+  let convTactic := "rfl"
+  let state6_1 ← match ← state5_1.tacticOn (goalId := 0) convTactic with
+    | .success state _ => pure state
+    | other => do
+      addTest $ assertUnreachable $ other.toString
+      return ()
+  addTest $ LSpec.check s!"    {convTactic}" ((← state6_1.serializeGoals).map (·.devolatilize) =
+    #[])
+
+  let state4_1 ← match state6_1.continue state4 with
+    | .ok state => pure state
+    | .error e => do
+      addTest $ expectationFailure "continue" e
+      return ()
+
+  let convTactic := "rfl"
+  let state1_1 ← match ← state4_1.tacticOn (goalId := 0) convTactic with
+    | .success state _ => pure state
+    | other => do
+      addTest $ assertUnreachable $ other.toString
+      return ()
+  addTest $ LSpec.check s!"  · {convTactic}" ((← state1_1.serializeGoals).map (·.devolatilize) =
+    #[interiorGoal [] "b + a + c1 = b + a + c2"])
+  checkEq "(fragments)" state1_1.fragments.size 0
+
+  /-
+  let state1_1 ← match ← state6.fragmentExit goalConv with
+    | .success state _ => pure state
+    | other => do
+      addTest $ assertUnreachable $ other.toString
+      return ()
+  -/
+
+  let tactic := "exact h"
+  let stateF ← match ← state1_1.tacticOn (goalId := 0) (tactic := tactic) with
+    | .success state _ => pure state
+    | other => do
+      addTest $ assertUnreachable $ other.toString
+      return ()
+  addTest $ LSpec.check tactic ((← stateF.serializeGoals).map (·.devolatilize) =
+    #[])
+
+  where
+    h := "b + a + c1 = b + a + c2"
+    interiorGoal (free: List (String × String)) (target: String) :=
+      let free := [("a", "Nat"), ("b", "Nat"), ("c1", "Nat"), ("c2", "Nat"), ("h", h)] ++ free
+      buildGoal free target
+
+example (p : Prop) (x y z : Nat) : p → (p → x = y) → x + z = y + z ∧ p := by
+  intro hp hi
+  apply And.intro
+  conv =>
+    rhs
+    arg 1
+    rw [←hi]
+    rfl
+    tactic => exact hp
+  exact hp
+
+def test_conv_unshielded : TestM Unit := do
+  let rootTarget ← parseSentence "∀ (p : Prop) (x y z : Nat), p → (p → x = y) → x + z = y + z ∧ p"
+  let state ← GoalState.create rootTarget
+  let tactic := "intro p x y z hp hi"
+  let .success state _ ← state.tacticOn 0 tactic | fail "intro failed"
+  let tactic := "apply And.intro"
+  let .success state _ ← state.tacticOn 0 tactic | fail "apply failed"
+  let .success state _ ← state.convEnter (.prefer state.goals[0]!) | fail "Cannot enter conversion tactic mode"
+  let .success state _ ← state.tryTactic .unfocus "rhs" | fail "rhs failed"
+  let tactic := "arg 1"
+  let .success state _ ← state.tryTactic .unfocus tactic | fail s!"{tactic} failed"
+  checkEq s!"  {tactic}" ((← state.serializeGoals).map (·.devolatilize))
+    #[
+      { interiorGoal [] "y" with fragment := .conv },
+      { interiorGoal [] "p" with userName? := "right", },
+    ]
+  let tactic := "rw [←hi]"
+  let .success state _ ← state.tryTactic .unfocus tactic | fail s!"{tactic} failed"
+  checkEq s!"  {tactic}" state.goals.length 3
+  let tactic := "rfl"
+  let .success state _ ← state.tryTactic .unfocus tactic | fail s!"{tactic} failed"
+  checkEq s!"  {tactic}" ((← state.serializeGoals).map (·.devolatilize))
+    #[
+      interiorGoal [] "p",
+      { interiorGoal [] "p" with userName? := "right", },
+    ]
+  checkEq "(n goals)" state.goals.length 2
+  checkEq "(fragments)" state.fragments.size 0
+  let tactic := "exact hp"
+  let .success state _ ← state.tryTactic .unfocus tactic | fail s!"{tactic} failed"
+  let tactic := "exact hp"
+  let .success state _ ← state.tryTactic .unfocus tactic | fail s!"{tactic} failed"
+  let root? := state.rootExpr?
+  checkTrue "root" root?.isSome
+  where
+  interiorGoal (free: List (String × String)) (target: String) :=
+    let free := [("p", "Prop"), ("x", "Nat"), ("y", "Nat"), ("z", "Nat"), ("hp", "p"), ("hi", "p → x = y")] ++ free
+    buildGoal free target
+
+example : ∀ (x y z w : Nat), y = z → x + z = w → x + y = w := by
+  intro x y z w hyz hxzw
+  conv =>
+    lhs
+    arg 2
+    rw [hyz]
+    rfl
+  exact hxzw
+
+def test_conv_unfinished : TestM Unit := do
+  let rootTarget ← parseSentence "∀ (x y z w : Nat), y = z → x + z = w → x + y = w"
+  let state ← GoalState.create rootTarget
+  let tactic := "intro x y z w hyz hxzw"
+  let .success state _ ← state.tacticOn 0 tactic | fail "intro failed"
+  let convParent := state.goals[0]!
+  let .success state _ ← state.convEnter (.prefer convParent) | fail "Cannot enter conversion tactic mode"
+  let .success state _ ← state.tryTactic .unfocus "lhs" | fail "rhs failed"
+  let tactic := "arg 2"
+  let .success state _ ← state.tryTactic .unfocus tactic | fail s!"{tactic} failed"
+  checkEq s!"  {tactic}" ((← state.serializeGoals).map (·.devolatilize))
+    #[
+      { interiorGoal [] "y" with fragment := .conv },
+    ]
+  let tactic := "rw [hyz]"
+  let .success state _ ← state.tryTactic .unfocus tactic | fail s!"{tactic} failed"
+  checkEq s!"  {tactic}" ((← state.serializeGoals).map (·.devolatilize))
+    #[
+      { interiorGoal [] "z" with fragment := .conv },
+    ]
+  checkTrue "  (fragment)" $ state.fragments.contains state.mainGoal?.get!
+  checkTrue "  (fragment parent)" $ state.fragments.contains convParent
+  checkTrue "  (main goal)" state.mainGoal?.isSome
+  let tactic := "rfl"
+  let .success state _ ← state.tryTactic .unfocus tactic | fail s!"{tactic} failed"
+  checkEq s!"  {tactic}" ((← state.serializeGoals).map (·.devolatilize))
+    #[
+      interiorGoal [] "x + z = w",
+    ]
+  checkEq "(fragments)" state.fragments.size 0
+  checkEq s!"  {tactic}" state.goals.length 1
+  let tactic := "exact hxzw"
+  let .success state _ ← state.tryTactic .unfocus tactic | fail s!"{tactic} failed"
+  let root? := state.rootExpr?
+  checkTrue "root" root?.isSome
+  where
+  interiorGoal (free: List (String × String)) (target: String) :=
+    let free := [("x", "Nat"), ("y", "Nat"), ("z", "Nat"), ("w", "Nat"), ("hyz", "y = z"), ("hxzw", "x + z = w")] ++ free
+    buildGoal free target
+
+example : ∀ (a b c d: Nat), a + b = b + c → b + c = c + d → a + b = c + d := by
+  intro a b c d h1 h2
+  calc a + b = b + c := by apply h1
+    _ = c + d := by apply h2
+
+def test_calc: TestM Unit := do
+  let rootTarget ← parseSentence "∀ (a b c d: Nat), a + b = b + c → b + c = c + d → a + b = c + d"
+  let state0 ← GoalState.create rootTarget
+  let tactic := "intro a b c d h1 h2"
+  let state1 ← match ← state0.tacticOn (goalId := 0) (tactic := tactic) with
+    | .success state _ => pure state
+    | other => do
+      addTest $ assertUnreachable $ other.toString
+      return ()
+  addTest $ LSpec.check tactic ((← state1.serializeGoals).map (·.devolatilize) =
+    #[interiorGoal [] "a + b = c + d"])
+  let pred := "a + b = b + c"
+  let .success state1 _ ← state1.calcEnter state1.mainGoal?.get! | fail "Could not enter calc"
+  let state2 ← match ← state1.tacticOn 0 pred with
+    | .success state _ => pure state
+    | other => do
+      addTest $ assertUnreachable $ other.toString
+      return ()
+  addTest $ LSpec.check s!"calc {pred} := _" ((← state2.serializeGoals).map (·.devolatilize) =
+    #[
+      { interiorGoal [] "a + b = b + c" with userName? := .some "calc" },
+      { interiorGoal [] "b + c = c + d" with fragment := .calc },
+    ])
+  addTest $ LSpec.test "(2.0 prev rhs)" (state2.calcPrevRhsOf? (state2.get! 0) |>.isNone)
+  addTest $ LSpec.test "(2.1 prev rhs)" (state2.calcPrevRhsOf? (state2.get! 1) |>.isSome)
+
+  let tactic := "apply h1"
+  let state2m ← match ← state2.tacticOn (goalId := 0) (tactic := tactic) with
+    | .success state _ => pure state
+    | other => do
+      addTest $ assertUnreachable $ other.toString
+      return ()
+  let state3 ← match state2m.continue state2 with
+    | .ok state => pure state
+    | .error e => do
+      addTest $ expectationFailure "continue" e
+      return ()
+  let pred := "_ = c + d"
+  let state4 ← match ← state3.tacticOn 0 pred with
+    | .success state _ => pure state
+    | other => do
+      addTest $ assertUnreachable $ other.toString
+      return ()
+  addTest $ LSpec.check s!"calc {pred} := _" ((← state4.serializeGoals).map (·.devolatilize) =
+    #[
+      { interiorGoal [] "b + c = c + d" with userName? := .some "calc" },
+    ])
+  addTest $ LSpec.test "(4.0 prev rhs)" (state4.calcPrevRhsOf? (state4.get! 0) |>.isNone)
+  let tactic := "apply h2"
+  let state4m ← match ← state4.tacticOn (goalId := 0) (tactic := tactic) with
+    | .success state _ => pure state
+    | other => do
+      addTest $ assertUnreachable $ other.toString
+      return ()
+  checkEq "(fragments)" state4m.fragments.size 0
+  addTest $ LSpec.test "(4m root)" state4m.rootExpr?.isSome
+  where
+    interiorGoal (free: List (String × String)) (target: String) :=
+      let free := [("a", "Nat"), ("b", "Nat"), ("c", "Nat"), ("d", "Nat"),
+        ("h1", "a + b = b + c"), ("h2", "b + c = c + d")] ++ free
+      buildGoal free target
+
+def suite (env: Environment): List (String × IO LSpec.TestSeq) :=
+  [
+    ("conv simple", test_conv_simple),
+    ("conv unshielded", test_conv_unshielded),
+    ("conv unfinished", test_conv_unfinished),
+    ("calc", test_calc),
+  ] |>.map (λ (name, t) => (name, runTestTermElabM env t))
+
+end Pantograph.Test.Tactic.Fragment

Tomograph.lean

@@ -0,0 +1,41 @@
+/- A tool for analysing Lean source code. -/
+import Pantograph.Frontend
+import Pantograph.Library
+
+open Lean
+
+namespace Pantograph
+
+def fail (s : String) : IO UInt32 := do
+  IO.eprintln s
+  return 2
+
+def dissect (args : List String) : IO UInt32 := do
+  let fileName :: _args := args | fail s!"Must supply a file name"
+  let file ← IO.FS.readFile fileName
+  let (context, state) ← do Frontend.createContextStateFromFile file fileName (env? := .none) {}
+  let frontendM: Elab.Frontend.FrontendM _ :=
+    Frontend.mapCompilationSteps λ step => do
+      IO.println s!"🐈 {step.stx.getKind.toString}"
+      for (tree, i) in step.trees.zipIdx do
+        IO.println s!"🌲[{i}] {← tree.toString}"
+      for (msg, i) in step.msgs.zipIdx do
+        IO.println s!"🔈[{i}] {← msg.toString}"
+  let (_, _) ← frontendM.run context |>.run state
+  return 0
+
+end Pantograph
+
+open Pantograph
+
+def help : IO UInt32 := do
+  IO.println "Usage: tomograph dissect FILE_NAME"
+  return 1
+
+def main (args : List String) : IO UInt32 := do
+  let command :: args := args | help
+  unsafe do
+    Pantograph.initSearch ""
+  match command with
+  | "dissect" => dissect args
+  | _ => fail s!"Unknown command {command}"

doc/rationale.md

@@ -37,10 +37,6 @@ differently from Lean in some times, but never at the sacrifice of soundness.
 - When Lean LSP says "unresolved goals", that means a proof cannot finish where
   it is supposed to finish at the end of a `by` block. Pantograph will raise the
   error in this case, since it indicates the termination of a proof search branch.
-- `pick_goal` or `swap` will not work since they run contrary to tree search
-  paradigms. However, if there are tactics which perform non-trivial operations
-  to multiple goals at the same time, this constrain could potentially be
-  relaxed at a cost of great bookkeeping overhead to the user.
 
 Pantograph cannot perform things that are inherently constrained by Lean. These
 include:

doc/repl.md

@@ -13,7 +13,7 @@ See `Pantograph/Protocol.lean` for a description of the parameters and return va
   only the values of definitions are printed.
 * `env.save { "path": <fileName> }`, `env.load { "path": <fileName> }`: Save/Load the
   current environment to/from a file
-* `env.module_read { "module": <name }`: Reads a list of symbols from a module
+* `env.module_read { "module": <name> }`: Reads a list of symbols from a module
 * `env.describe {}`: Describes the imports and modules in the current environment
 * `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/Protocol.lean`
@@ -28,17 +28,19 @@ See `Pantograph/Protocol.lean` for a description of the parameters and return va
 * `options.print`: Display the current set of options
 * `goal.start {["name": <name>], ["expr": <expr>], ["levels": [<levels>]], ["copyFrom": <symbol>]}`:
   Start a new proof from a given expression or symbol
-* `goal.tactic {"stateId": <id>, "goalId": <id>, ...}`: Execute a tactic string on a
-  given goal. The tactic is supplied as additional key-value pairs in one of the following formats:
-  - `{ "tactic": <tactic> }`: Execute an ordinary tactic
-  - `{ "expr": <expr> }`: Assign the given proof term to the current goal
-  - `{ "have": <expr>, "binderName": <name> }`: Execute `have` and creates a branch goal
-  - `{ "calc": <expr> }`: Execute one step of a `calc` tactic. Each step must
+* `goal.tactic {"stateId": <id>, ["goalId": <id>], ["autoResume": <bool>], ...}`:
+  Execute a tactic string on a given goal site. The tactic is supplied as additional
+  key-value pairs in one of the following formats:
+  - `{ "tactic": <tactic> }`: Executes a tactic in the current mode
+  - `{ "mode": <mode> }`: Enter a different tactic mode. The permitted values
+    are `tactic` (default), `conv`, `calc`. In case of `calc`, each step must
     be of the form `lhs op rhs`. An `lhs` of `_` indicates that it should be set
     to the previous `rhs`.
-  - `{ "conv": <bool> }`: Enter or exit conversion tactic mode. In the case of
-    exit, the goal id is ignored.
-  - `{ "draft": <expr> }`: Draft an expression with `sorry`s, turning them into goals. Coupling is not allowed.
+  - `{ "expr": <expr> }`: Assign the given proof term to the current goal
+  - `{ "have": <expr>, "binderName": <name> }`: Execute `have` and creates a branch goal
+  - `{ "let": <expr>, "binderName": <name> }`: Execute `let` and creates a branch goal
+  - `{ "draft": <expr> }`: Draft an expression with `sorry`s, turning them into
+    goals. Coupling is not allowed.
   If the `goals` field does not exist, the tactic execution has failed. Read
   `messages` to find the reason.
 * `goal.continue {"stateId": <id>, ["branch": <id>], ["goals": <names>]}`:

flake.lock

@@ -39,16 +39,14 @@
     "lean4-nix": {
       "inputs": {
         "flake-parts": "flake-parts_2",
-        "nixpkgs": [
-          "nixpkgs"
-        ]
+        "nixpkgs": "nixpkgs"
       },
       "locked": {
-        "lastModified": 1750275702,
-        "narHash": "sha256-CpwSdtwvrQCR+ZfXZweFHJMG583EYijCRGEeGrgBsjU=",
+        "lastModified": 1750369222,
+        "narHash": "sha256-KFFTVbciXUaHgeGN1yiaUtY88OLGU0gElXx5SfICDKg=",
         "owner": "lenianiva",
         "repo": "lean4-nix",
-        "rev": "95a315f6e7d5e463090ae4977d5e2e6c3b4ef0d0",
+        "rev": "015ecd25206734d582a1b15dd11eb10be35ca555",
         "type": "github"
       },
       "original": {
@@ -59,16 +57,16 @@
     },
     "nixpkgs": {
       "locked": {
-        "lastModified": 1750151854,
-        "narHash": "sha256-3za+1J9FifMetO7E/kwgyW+dp+8pPBNlWKfcBovnn6M=",
+        "lastModified": 1743095683,
+        "narHash": "sha256-gWd4urRoLRe8GLVC/3rYRae1h+xfQzt09xOfb0PaHSk=",
         "owner": "nixos",
         "repo": "nixpkgs",
-        "rev": "ad5c70bcc5cc5178205161b7a7d61a6e80f6d244",
+        "rev": "5e5402ecbcb27af32284d4a62553c019a3a49ea6",
         "type": "github"
       },
       "original": {
         "owner": "nixos",
-        "ref": "nixos-24.11",
+        "ref": "nixos-unstable",
         "repo": "nixpkgs",
         "type": "github"
       }
@@ -100,11 +98,27 @@
         "url": "https://github.com/NixOS/nixpkgs/archive/fb192fec7cc7a4c26d51779e9bab07ce6fa5597a.tar.gz"
       }
     },
+    "nixpkgs_2": {
+      "locked": {
+        "lastModified": 1751048012,
+        "narHash": "sha256-MYbotu4UjWpTsq01wglhN5xDRfZYLFtNk7SBY0BcjkU=",
+        "owner": "nixos",
+        "repo": "nixpkgs",
+        "rev": "a684c58d46ebbede49f280b653b9e56100aa3877",
+        "type": "github"
+      },
+      "original": {
+        "owner": "nixos",
+        "ref": "nixos-24.11",
+        "repo": "nixpkgs",
+        "type": "github"
+      }
+    },
     "root": {
       "inputs": {
         "flake-parts": "flake-parts",
         "lean4-nix": "lean4-nix",
-        "nixpkgs": "nixpkgs"
+        "nixpkgs": "nixpkgs_2"
       }
     }
   },

flake.nix

@@ -4,10 +4,7 @@
   inputs = {
     nixpkgs.url = "github:nixos/nixpkgs/nixos-24.11";
     flake-parts.url = "github:hercules-ci/flake-parts";
-    lean4-nix = {
-      url = "github:lenianiva/lean4-nix";
-      inputs.nixpkgs.follows = "nixpkgs";
-    };
+    lean4-nix.url = "github:lenianiva/lean4-nix";
   };
 
   outputs = inputs @ {

lakefile.lean

@@ -10,6 +10,7 @@ lean_lib Pantograph {
 
 lean_lib Repl {
 }
+
 @[default_target]
 lean_exe repl {
   root := `Main
@@ -17,6 +18,13 @@ lean_exe repl {
   supportInterpreter := true
 }
 
+@[default_target]
+lean_exe tomograph {
+  root := `Tomograph
+  -- Solves the native symbol not found problem
+  supportInterpreter := true
+}
+
 require LSpec from git
   "https://github.com/argumentcomputer/LSpec.git" @ "a6652a48b5c67b0d8dd3930fad6390a97d127e8d"
 lean_lib Test {

lean-toolchain

@@ -1 +1 @@
-leanprover/lean4:v4.20.1
+leanprover/lean4:v4.21.0