Merge branch 'dev' into misc/interaction

Reviewed-on: #10

.gitignore

@@ -1,2 +1,5 @@
+.*
+!.gitignore
+
 /build
 /lake-packages

Main.lean

@@ -1,4 +1,115 @@
+import Lean.Data.Json
+import Lean.Environment
+
+import Pantograph.Version
 import Pantograph
 
-def main : IO Unit :=
+-- Main IO functions
-  IO.println s!"Hello, {hello}!"
+open Pantograph
+
+/-- Parse a command either in `{ "cmd": ..., "payload": ... }` form or `cmd { ... }` form. -/
+def parse_command (s: String): Except String Commands.Command := do
+  let s := s.trim
+  match s.get? 0 with
+  | .some '{' => -- Parse in Json mode
+    Lean.fromJson? (← Lean.Json.parse s)
+  | .some _ => -- Parse in line mode
+    let offset := s.posOf ' ' |> s.offsetOfPos
+    if offset = s.length then
+      return { cmd := s.take offset, payload := Lean.Json.null }
+    else
+      let payload ← s.drop offset |> Lean.Json.parse
+      return { cmd := s.take offset, payload := payload }
+  | .none => throw "Command is empty"
+
+unsafe def loop : MainM Unit := do
+  let state ← get
+  let command ← (← IO.getStdin).getLine
+  if command.trim.length = 0 then return ()
+  match parse_command command with
+  | .error error =>
+    let error  := Lean.toJson ({ error := "command", desc := error }: Commands.InteractionError)
+    -- Using `Lean.Json.compress` here to prevent newline
+    IO.println error.compress
+  | .ok command =>
+    let ret ← execute command
+    let str := match state.options.printJsonPretty with
+      | true => ret.pretty
+      | false => ret.compress
+    IO.println str
+  loop
+
+namespace Lean
+
+/-- This is better than the default version since it handles `.` and doesn't
+ crash the program when it fails. -/
+def setOptionFromString' (opts : Options) (entry : String) : ExceptT String IO Options := do
+  let ps := (entry.splitOn "=").map String.trim
+  let [key, val] ← pure ps | throw "invalid configuration option entry, it must be of the form '<key> = <value>'"
+  let key := Pantograph.str_to_name key
+  let defValue ← getOptionDefaultValue key
+  match defValue with
+  | DataValue.ofString _ => pure $ opts.setString key val
+  | DataValue.ofBool _   =>
+    match val with
+    | "true" => pure $ opts.setBool key true
+    | "false" => pure $ opts.setBool key false
+    | _ => throw  s!"invalid Bool option value '{val}'"
+  | DataValue.ofName _   => pure $ opts.setName key val.toName
+  | DataValue.ofNat _    =>
+    match val.toNat? with
+    | none   => throw s!"invalid Nat option value '{val}'"
+    | some v => pure $ opts.setNat key v
+  | DataValue.ofInt _    =>
+    match val.toInt? with
+    | none   => throw s!"invalid Int option value '{val}'"
+    | some v => pure $ opts.setInt key v
+  | DataValue.ofSyntax _ => throw s!"invalid Syntax option value"
+
+end Lean
+
+
+unsafe def main (args: List String): IO Unit := do
+  -- NOTE: A more sophisticated scheme of command line argument handling is needed.
+  -- Separate imports and options
+  if args == ["--version"] then do
+    println! s!"{version}"
+    return
+
+  Lean.enableInitializersExecution
+  Lean.initSearchPath (← Lean.findSysroot)
+
+  let options? ← args.filterMap (λ s => if s.startsWith "--" then .some <| s.drop 2 else .none)
+    |>.foldlM Lean.setOptionFromString' Lean.Options.empty
+    |>.run
+  let options ← match options? with
+    | .ok options => pure options
+    | .error e => throw $ IO.userError s!"Options cannot be parsed: {e}"
+  let imports:= args.filter (λ s => ¬ (s.startsWith "--"))
+
+  let env ← Lean.importModules
+    (imports := imports.map (λ str => { module := str_to_name str, runtimeOnly := false }))
+    (opts := {})
+    (trustLevel := 1)
+  let context: Context := {
+    imports
+  }
+  let coreContext: Lean.Core.Context := {
+    currNamespace := Lean.Name.str .anonymous "Aniva"
+    openDecls := [],     -- No 'open' directives needed
+    fileName := "<Pantograph>",
+    fileMap := { source := "", positions := #[0], lines := #[1] },
+    options := options
+  }
+  try
+    let termElabM := loop.run context |>.run' {}
+    let metaM := termElabM.run' (ctx := {
+      declName? := some "_pantograph",
+      errToSorry := false
+    })
+    let coreM := metaM.run'
+    IO.println "ready."
+    discard <| coreM.toIO coreContext { env := env }
+  catch ex =>
+    IO.println "Uncaught IO exception"
+    IO.println ex.toString

Pantograph.lean

@@ -1 +1,174 @@
-def hello := "world"
+import Pantograph.Commands
+import Pantograph.Serial
+import Pantograph.Symbols
+import Pantograph.Tactic
+import Pantograph.SemihashMap
+
+namespace Pantograph
+
+structure Context where
+  imports: List String
+
+/-- Stores state of the REPL -/
+structure State where
+  options: Commands.Options := {}
+  goalStates: SemihashMap GoalState := SemihashMap.empty
+
+-- State monad
+abbrev MainM := ReaderT Context (StateT State Lean.Elab.TermElabM)
+-- For some reason writing `CommandM α := MainM (Except ... α)` disables certain
+-- monadic features in `MainM`
+abbrev CR α := Except Commands.InteractionError α
+
+def execute (command: Commands.Command): MainM Lean.Json := do
+  let run { α β: Type } [Lean.FromJson α] [Lean.ToJson β] (comm: α → MainM (CR β)): MainM Lean.Json :=
+    match Lean.fromJson? command.payload with
+    | .ok args => do
+      match (← comm args) with
+      | .ok result =>  return Lean.toJson result
+      | .error ierror => return Lean.toJson ierror
+    | .error error => return Lean.toJson $ errorCommand s!"Unable to parse json: {error}"
+  match command.cmd with
+  | "reset"          => run reset
+  | "stat"           => run stat
+  | "expr.echo"      => run expr_echo
+  | "lib.catalog"    => run lib_catalog
+  | "lib.inspect"    => run lib_inspect
+  | "options.set"    => run options_set
+  | "options.print"  => run options_print
+  | "goal.start"     => run goal_start
+  | "goal.tactic"    => run goal_tactic
+  | "goal.delete"    => run goal_delete
+  | cmd =>
+    let error: Commands.InteractionError :=
+      errorCommand s!"Unknown command {cmd}"
+    return Lean.toJson error
+  where
+  errorI (type desc: String): Commands.InteractionError := { error := type, desc := desc }
+  errorCommand := errorI "command"
+  errorIndex := errorI "index"
+  -- Command Functions
+  reset (_: Commands.Reset): MainM (CR Commands.StatResult) := do
+    let state ← get
+    let nGoals := state.goalStates.size
+    set { state with goalStates := SemihashMap.empty }
+    return .ok { nGoals }
+  stat (_: Commands.Stat): MainM (CR Commands.StatResult) := do
+    let state ← get
+    let nGoals := state.goalStates.size
+    return .ok { nGoals }
+  lib_catalog (_: Commands.LibCatalog): MainM (CR Commands.LibCatalogResult) := do
+    let env ← Lean.MonadEnv.getEnv
+    let names := env.constants.fold (init := #[]) (λ acc name info =>
+      match to_filtered_symbol name info with
+      | .some x => acc.push x
+      | .none => acc)
+    return .ok { symbols := names }
+  lib_inspect (args: Commands.LibInspect): MainM (CR Commands.LibInspectResult) := do
+    let state ← get
+    let env ← Lean.MonadEnv.getEnv
+    let name := str_to_name args.name
+    let info? := env.find? name
+    match info? with
+    | none => return .error $ errorIndex s!"Symbol not found {args.name}"
+    | some info =>
+      let module? := env.getModuleIdxFor? name >>=
+        (λ idx => env.allImportedModuleNames.get? idx.toNat) |>.map toString
+      let value? := match args.value?, info with
+        | .some true, _ => info.value?
+        | .some false, _ => .none
+        | .none, .defnInfo _ => info.value?
+        | .none, _ => .none
+      return .ok {
+        type := ← serialize_expression state.options info.type,
+        value? := ← value?.mapM (λ v => serialize_expression state.options v),
+        module? := module?
+      }
+  expr_echo (args: Commands.ExprEcho): MainM (CR Commands.ExprEchoResult) := do
+    let state ← get
+    let env ← Lean.MonadEnv.getEnv
+    match syntax_from_str env args.expr with
+    | .error str => return .error $ errorI "parsing" str
+    | .ok syn => do
+      match (← syntax_to_expr syn) with
+      | .error str => return .error $ errorI "elab" str
+      | .ok expr => do
+        try
+          let type ← Lean.Meta.inferType expr
+          return .ok {
+              type := (← serialize_expression (options := state.options) type),
+              expr := (← serialize_expression (options := state.options) expr)
+          }
+        catch exception =>
+          return .error $ errorI "typing" (← exception.toMessageData.toString)
+  options_set (args: Commands.OptionsSet): MainM (CR Commands.OptionsSetResult) := do
+    let state ← get
+    let options := state.options
+    set { state with
+      options := {
+        -- FIXME: This should be replaced with something more elegant
+        printJsonPretty := args.printJsonPretty?.getD options.printJsonPretty,
+        printExprPretty := args.printExprPretty?.getD options.printExprPretty,
+        printExprAST := args.printExprAST?.getD options.printExprAST,
+        proofVariableDelta := args.proofVariableDelta?.getD options.proofVariableDelta,
+        printAuxDecls := args.printAuxDecls?.getD options.printAuxDecls,
+        printImplementationDetailHyps := args.printImplementationDetailHyps?.getD options.printImplementationDetailHyps
+      }
+    }
+    return .ok {  }
+  options_print (_: Commands.OptionsPrint): MainM (CR Commands.OptionsPrintResult) := do
+    return .ok (← get).options
+  goal_start (args: Commands.GoalStart): MainM (CR Commands.GoalStartResult) := do
+    let state ← get
+    let env ← Lean.MonadEnv.getEnv
+    let expr?: Except _ Lean.Expr ← (match args.expr, args.copyFrom with
+      | .some expr, .none =>
+        (match syntax_from_str env expr with
+        | .error str => return .error <| errorI "parsing" str
+        | .ok syn => do
+          (match (← syntax_to_expr syn) with
+          | .error str => return .error <| errorI "elab" str
+          | .ok expr => return .ok expr))
+      | .none, .some copyFrom =>
+        (match env.find? <| str_to_name copyFrom with
+        | .none => return .error <| errorIndex s!"Symbol not found: {copyFrom}"
+        | .some cInfo => return .ok cInfo.type)
+      | .none, .none =>
+        return .error <| errorI "arguments" "At least one of {expr, copyFrom} must be supplied"
+      | _, _ => return .error <| errorI "arguments" "Cannot populate both of {expr, copyFrom}")
+    match expr? with
+    | .error error => return .error error
+    | .ok expr =>
+      let goalState ← GoalState.create expr
+      let (goalStates, goalId) := state.goalStates.insert goalState
+      set { state with goalStates }
+      return .ok { goalId }
+  goal_tactic (args: Commands.GoalTactic): MainM (CR Commands.GoalTacticResult) := do
+    let state ← get
+    match state.goalStates.get? args.goalId with
+    | .none => return .error $ errorIndex s!"Invalid goal index {args.goalId}"
+    | .some goalState =>
+      let result ← GoalState.execute goalState args.tactic |>.run state.options
+      match result with
+      | .success goals =>
+        if goals.isEmpty then
+          return .ok {}
+        else
+          -- Append all goals
+          let (goalStates, goalIds, sGoals) := Array.foldl (λ acc itr =>
+            let (map, indices, serializedGoals) := acc
+            let (goalState, sGoal) := itr
+            let (map, index) := map.insert goalState
+            (map, index :: indices, sGoal :: serializedGoals)
+            ) (state.goalStates, [], []) goals
+          set { state with goalStates }
+          return .ok { goals? := .some sGoals.reverse.toArray, goalIds? := .some goalIds.reverse.toArray }
+      | .failure messages =>
+        return .ok { tacticErrors? := .some messages }
+  goal_delete (args: Commands.GoalDelete): MainM (CR Commands.GoalDeleteResult) := do
+    let state ← get
+    let goalStates := args.goalIds.foldl (λ map id => map.remove id) state.goalStates
+    set { state with goalStates }
+    return .ok {}
+
+end Pantograph

Pantograph/Commands.lean

@@ -0,0 +1,163 @@
+/-
+All the command input/output structures are stored here
+
+Note that no command other than `InteractionError` may have `error` as one of
+its field names to avoid confusion with error messages generated by the REPL.
+-/
+import Lean.Data.Json
+
+namespace Pantograph.Commands
+
+
+/-- Main Option structure, placed here to avoid name collision -/
+structure Options where
+  -- When false, suppress newlines in Json objects. Useful for machine-to-machine interaction.
+  -- This should be  false` by default to avoid any surprises with parsing.
+  printJsonPretty: Bool    := false
+  -- When enabled, pretty print every expression
+  printExprPretty: Bool    := true
+  -- When enabled, print the raw AST of expressions
+  printExprAST: Bool       := false
+  -- When enabled, the types and values of persistent variables in a proof goal
+  -- are not shown unless they are new to the proof step. Reduces overhead
+  proofVariableDelta: Bool := false
+  -- See `pp.auxDecls`
+  printAuxDecls: Bool      := false
+  -- See `pp.implementationDetailHyps`
+  printImplementationDetailHyps: Bool := false
+  deriving Lean.ToJson
+
+abbrev OptionsT := ReaderT Options
+
+--- Expression Objects ---
+
+structure BoundExpression where
+  binders: Array (String × String)
+  target: String
+  deriving Lean.ToJson
+structure Expression where
+  -- Pretty printed expression
+  pp?: Option String             := .none
+  -- AST structure
+  sexp?: Option String           := .none
+  deriving Lean.ToJson
+
+structure Variable where
+  name: String
+  /-- Does the name contain a dagger -/
+  isInaccessible?: Option Bool := .none
+  type?: Option Expression  := .none
+  value?: Option Expression := .none
+  deriving Lean.ToJson
+structure Goal where
+  /-- String case id -/
+  caseName?: Option String  := .none
+  /-- Is the goal in conversion mode -/
+  isConversion: Bool        := false
+  /-- target expression type -/
+  target: Expression
+  /-- Variables -/
+  vars: Array Variable      := #[]
+  deriving Lean.ToJson
+
+
+
+--- Individual Commands and return types ---
+
+structure Command where
+  cmd: String
+  payload: Lean.Json
+  deriving Lean.FromJson
+
+structure InteractionError where
+  error: String
+  desc: String
+  deriving Lean.ToJson
+
+
+--- Individual command and return types ---
+
+
+structure Reset where
+  deriving Lean.FromJson
+structure Stat where
+  deriving Lean.FromJson
+structure StatResult where
+  -- Number of goals states
+  nGoals: Nat
+  deriving Lean.ToJson
+
+-- Return the type of an expression
+structure ExprEcho where
+  expr: String
+  deriving Lean.FromJson
+structure ExprEchoResult where
+  expr: Expression
+  type: Expression
+  deriving Lean.ToJson
+
+-- Print all symbols in environment
+structure LibCatalog where
+  deriving Lean.FromJson
+structure LibCatalogResult where
+  symbols: Array String
+  deriving Lean.ToJson
+-- Print the type of a symbol
+structure LibInspect where
+  name: String
+  -- If true/false, show/hide the value expressions; By default definitions
+  -- values are shown and theorem values are hidden.
+  value?: Option Bool := .some false
+  deriving Lean.FromJson
+structure LibInspectResult where
+  type: Expression
+  value?: Option Expression := .none
+  module?: Option String
+  deriving Lean.ToJson
+
+/-- Set options; See `Options` struct above for meanings -/
+structure OptionsSet where
+  printJsonPretty?: Option Bool
+  printExprPretty?: Option Bool
+  printExprAST?: Option Bool
+  proofVariableDelta?: Option Bool
+  printAuxDecls?: Option Bool
+  printImplementationDetailHyps?: Option Bool
+  deriving Lean.FromJson
+structure OptionsSetResult where
+  deriving Lean.ToJson
+structure OptionsPrint where
+  deriving Lean.FromJson
+abbrev OptionsPrintResult := Options
+
+structure GoalStart where
+  -- Only one of the fields below may be populated.
+  expr: Option String     -- Proof expression
+  copyFrom: Option String -- Theorem name
+  deriving Lean.FromJson
+structure GoalStartResult where
+  goalId: Nat := 0 -- Proof tree id
+  deriving Lean.ToJson
+structure GoalTactic where
+  -- Identifiers for tree, state, and goal
+  goalId: Nat
+  tactic: String
+  deriving Lean.FromJson
+structure GoalTacticResult where
+  -- Existence of this field shows success
+  goals?: Option (Array Goal)          := .none
+  -- Next proof state id, if successful
+  goalIds?: Option (Array Nat)          := .none
+  -- Existence of this field shows failure
+  tacticErrors?: Option (Array String) := .none
+  deriving Lean.ToJson
+
+-- Remove a bunch of goals.
+structure GoalDelete where
+  goalIds: List Nat
+  deriving Lean.FromJson
+structure GoalDeleteResult where
+  deriving Lean.ToJson
+
+
+end Pantograph.Commands

Pantograph/SemihashMap.lean

@@ -0,0 +1,149 @@
+
+namespace Pantograph.SemihashMap
+
+structure Imp (β: Type u) where
+  data: Array (Option β)
+
+  -- Number of elements currently in use
+  size: Nat
+
+  -- Next index that has never been touched
+  allocFront: Nat
+
+  -- Deallocated indices
+  deallocs: Array Nat
+
+  -- Number of valid entries in `deallocs` array
+  lastDealloc: Nat
+
+namespace Imp
+
+structure WF (m: Imp β): Prop where
+  capacity: m.data.size = m.deallocs.size
+  front_dealloc: ∀ i: Fin m.deallocs.size, (i < m.allocFront) → (m.deallocs.get i) < m.allocFront
+  front_data: ∀ i: Fin m.data.size, (i ≥ m.allocFront) → (m.data.get i).isNone
+
+def empty (capacity := 16): Imp β :=
+  {
+    data := mkArray capacity .none,
+    size := 0,
+    allocFront := 0,
+    deallocs := mkArray capacity 0,
+    lastDealloc := 0,
+  }
+
+private theorem list_get_replicate (x: α) (i: Fin (List.replicate n x).length):
+    List.get (List.replicate n x) i = x := by
+  sorry
+
+theorem empty_wf : WF (empty n: Imp β) := by
+  unfold empty
+  apply WF.mk
+  case capacity =>
+    conv =>
+      lhs
+      congr
+      simp
+    conv =>
+      rhs
+      congr
+      simp
+    simp
+  case front_dealloc =>
+    simp_all
+    intro i
+    intro a
+    contradiction
+  case front_data =>
+    simp_all
+    intro i
+    unfold Imp.data at i
+    simp at i
+    conv =>
+      lhs
+      unfold Array.get
+      unfold mkArray
+      simp [List.replicate]
+      rewrite [list_get_replicate]
+
+-- FIXME: Merge this with the well-formed versions below so proof and code can
+-- mesh seamlessly.
+@[inline] def insert (map: Imp β) (v: β): (Imp β × Nat) :=
+  match map.lastDealloc with
+  | 0 => -- Capacity is full, buffer expansion is required
+    if map.size == map.data.size then
+      let nextIndex := map.data.size
+      let extendCapacity := map.size
+      let result: Imp β := {
+        data := (map.data.append #[Option.some v]).append (mkArray extendCapacity .none),
+        size := map.size + 1,
+        allocFront := map.size + 1,
+        deallocs := mkArray (map.data.size + 1 + extendCapacity) 0,
+        lastDealloc := 0,
+      }
+      (result, nextIndex)
+    else
+      let nextIndex := map.size
+      let result: Imp β := {
+        map
+        with
+        data := map.data.set ⟨nextIndex, sorry⟩ (Option.some v),
+        size := map.size + 1,
+        allocFront := map.allocFront + 1,
+      }
+      (result, nextIndex)
+  | (.succ k) => -- Allocation list has space
+    let nextIndex := map.deallocs.get! k
+    let result: Imp β := {
+      map with
+      data := map.data.set ⟨nextIndex, sorry⟩ (Option.some v),
+      size := map.size + 1,
+      lastDealloc := map.lastDealloc - 1
+    }
+    (result, nextIndex)
+
+@[inline] def remove (map: Imp β) (index: Fin (map.size)): Imp β :=
+  have h: index.val < map.data.size := by sorry
+  match map.data.get ⟨index.val, h⟩ with
+  | .none => map
+  | .some _ =>
+    {
+      map with
+      data := map.data.set ⟨index, sorry⟩ .none,
+      size := map.size - 1,
+      deallocs := map.deallocs.set ⟨map.lastDealloc, sorry⟩ index,
+      lastDealloc := map.lastDealloc + 1,
+    }
+
+/-- Retrieval is efficient -/
+@[inline] def get? (map: Imp β) (index: Fin (map.size)): Option β :=
+  have h: index.val < map.data.size := by sorry
+  map.data.get ⟨index.val, h⟩
+@[inline] def capacity (map: Imp β): Nat := map.data.size
+
+end Imp
+
+
+/--
+This is like a hashmap but you cannot control the keys.
+-/
+def _root_.Pantograph.SemihashMap β := {m: Imp β // m.WF}
+
+@[inline] def empty (capacity := 16): SemihashMap β :=
+  ⟨ Imp.empty capacity, Imp.empty_wf ⟩
+@[inline] def insert (map: SemihashMap β) (v: β): (SemihashMap β × Nat) :=
+  let ⟨imp, pre⟩ := map
+  let ⟨result, id⟩ := imp.insert v
+  ( ⟨ result, sorry ⟩, id)
+@[inline] def remove (map: SemihashMap β) (index: Nat): SemihashMap β :=
+  let ⟨imp, pre⟩ := map
+  let result := imp.remove ⟨index, sorry⟩
+  ⟨ result, sorry ⟩
+@[inline] def get? (map: SemihashMap β) (index: Nat): Option β :=
+  let ⟨imp, _⟩ := map
+  imp.get? ⟨index, sorry⟩
+@[inline] def size (map: SemihashMap β): Nat :=
+  let ⟨imp, _⟩ := map
+  imp.size
+
+end Pantograph.SemihashMap

Pantograph/Serial.lean

@@ -0,0 +1,259 @@
+/-
+All serialisation functions
+-/
+import Lean
+
+import Pantograph.Commands
+
+namespace Pantograph
+open Lean
+
+--- Input Functions ---
+
+
+/-- Read a theorem from the environment -/
+def expr_from_const (env: Environment) (name: Name): Except String Lean.Expr :=
+  match env.find? name with
+  | none       => throw s!"Symbol not found: {name}"
+  | some cInfo => return cInfo.type
+/-- Read syntax object from string -/
+def syntax_from_str (env: Environment) (s: String): Except String Syntax :=
+  Parser.runParserCategory
+    (env := env)
+    (catName := `term)
+    (input := s)
+    (fileName := "<stdin>")
+
+
+def syntax_to_expr_type (syn: Syntax): Elab.TermElabM (Except String Expr) := do
+  try
+    let expr ← Elab.Term.elabType syn
+    -- Immediately synthesise all metavariables if we need to leave the elaboration context.
+    -- See https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/topic/Unknown.20universe.20metavariable/near/360130070
+    --Elab.Term.synthesizeSyntheticMVarsNoPostponing
+    let expr ← instantiateMVars expr
+    return .ok expr
+  catch ex => return .error (← ex.toMessageData.toString)
+def syntax_to_expr (syn: Syntax): Elab.TermElabM (Except String Expr) := do
+  try
+    let expr ← Elab.Term.elabTerm (stx := syn) (expectedType? := .none)
+    -- Immediately synthesise all metavariables if we need to leave the elaboration context.
+    -- See https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/topic/Unknown.20universe.20metavariable/near/360130070
+    --Elab.Term.synthesizeSyntheticMVarsNoPostponing
+    let expr ← instantiateMVars expr
+    return .ok expr
+  catch ex => return .error (← ex.toMessageData.toString)
+
+
+--- Output Functions ---
+
+def type_expr_to_bound (expr: Expr): MetaM Commands.BoundExpression := do
+  Meta.forallTelescope expr fun arr body => do
+    let binders ← arr.mapM fun fvar => do
+      return (toString (← fvar.fvarId!.getUserName), toString (← Meta.ppExpr (← fvar.fvarId!.getType)))
+    return { binders, target := toString (← Meta.ppExpr body) }
+
+private def name_to_ast: Lean.Name → String
+  | .anonymous
+  | .num _ _ => ":anon"
+  | n@(.str _ _) => toString n
+
+private def level_depth: Level → Nat
+  | .zero => 0
+  | .succ l => 1 + (level_depth l)
+  | .max u v | .imax u v => 1 + max (level_depth u) (level_depth v)
+  | .param _ | .mvar _ => 0
+
+theorem level_depth_max_imax (u v: Level): (level_depth (Level.max u v) = level_depth (Level.imax u v)) := by
+  constructor
+theorem level_max_depth_decrease (u v: Level): (level_depth u < level_depth (Level.max u v)) := by
+  have h1: level_depth (Level.max u v) = 1 + Nat.max (level_depth u) (level_depth v) := by constructor
+  rewrite [h1]
+  simp_arith
+  conv =>
+    rhs
+    apply Nat.max_def
+  sorry
+theorem level_offset_decrease (u v: Level): (level_depth u ≤ level_depth (Level.max u v).getLevelOffset) := sorry
+
+/-- serialize a sort level. Expression is optimized to be compact e.g. `(+ u 2)` -/
+def serialize_sort_level_ast (level: Level): String :=
+  let k := level.getOffset
+  let u := level.getLevelOffset
+  let u_str := match u with
+    | .zero => "0"
+    | .succ _ => panic! "getLevelOffset should not return .succ"
+    | .max v w =>
+      let v := serialize_sort_level_ast v
+      let w := serialize_sort_level_ast w
+      s!"(:max {v} {w})"
+    | .imax v w =>
+      let v := serialize_sort_level_ast v
+      let w := serialize_sort_level_ast w
+      s!"(:imax {v} {w})"
+    | .param name =>
+      let name := name_to_ast name
+      s!"{name}"
+    | .mvar id =>
+      let name := name_to_ast id.name
+      s!"(:mv {name})"
+  match k, u with
+  | 0, _ => u_str
+  | _, .zero => s!"{k}"
+  | _, _ => s!"(+ {u_str} {k})"
+  termination_by serialize_sort_level_ast level => level_depth level
+  decreasing_by
+  . sorry
+
+/--
+ Completely serializes an expression tree. Json not used due to compactness
+-/
+def serialize_expression_ast (expr: Expr): MetaM String := do
+  match expr with
+  | .bvar deBruijnIndex =>
+    -- This is very common so the index alone is shown. Literals are handled below.
+    -- The raw de Bruijn index should never appear in an unbound setting. In
+    -- Lean these are handled using a `#` prefix.
+    return s!"{deBruijnIndex}"
+  | .fvar fvarId =>
+    let name := (← fvarId.getDecl).userName
+    return s!"(:fv {name})"
+  | .mvar mvarId =>
+    let name := name_to_ast mvarId.name
+    return s!"(:mv {name})"
+  | .sort level =>
+    let level := serialize_sort_level_ast level
+    return s!"(:sort {level})"
+  | .const declName _ =>
+    -- The universe level of the const expression is elided since it should be
+    -- inferrable from surrounding expression
+    return s!"(:c {declName})"
+  | .app fn arg =>
+    let fn' ← serialize_expression_ast fn
+    let arg' ← serialize_expression_ast arg
+    return s!"({fn'} {arg'})"
+  | .lam binderName binderType body binderInfo =>
+    let binderName' := name_to_ast binderName
+    let binderType' ← serialize_expression_ast binderType
+    let body' ← serialize_expression_ast body
+    let binderInfo' := binder_info_to_ast binderInfo
+    return s!"(:lambda {binderName'} {binderType'} {body'}{binderInfo'})"
+  | .forallE binderName binderType body binderInfo =>
+    let binderName' := name_to_ast binderName
+    let binderType' ← serialize_expression_ast binderType
+    let body' ← serialize_expression_ast body
+    let binderInfo' := binder_info_to_ast binderInfo
+    return s!"(:forall {binderName'} {binderType'} {body'}{binderInfo'})"
+  | .letE name type value body _ =>
+    -- Dependent boolean flag diacarded
+    let name' := name_to_ast name
+    let type' ← serialize_expression_ast type
+    let value' ← serialize_expression_ast value
+    let body' ← serialize_expression_ast body
+    return s!"(:let {name'} {type'} {value'} {body'})"
+  | .lit v =>
+    -- To not burden the downstream parser who needs to handle this, the literal
+    -- is wrapped in a :lit sexp.
+    let v' := match v with
+      | .natVal val => toString val
+      | .strVal val => s!"\"{val}\""
+    return s!"(:lit {v'})"
+  | .mdata _ expr =>
+    -- NOTE: Equivalent to expr itself, but mdata influences the prettyprinter
+    -- It may become necessary to incorporate the metadata.
+    return (← serialize_expression_ast expr)
+  | .proj typeName idx struct =>
+    let struct' ← serialize_expression_ast struct
+    return s!"(:proj {typeName} {idx} {struct'})"
+
+  where
+  -- Elides all unhygenic names
+  binder_info_to_ast : Lean.BinderInfo → String
+    | .default => ""
+    | .implicit => " :implicit"
+    | .strictImplicit => " :strictImplicit"
+    | .instImplicit => " :instImplicit"
+
+def serialize_expression (options: Commands.Options) (e: Expr): MetaM Commands.Expression := do
+  let pp := toString (← Meta.ppExpr e)
+  let pp?: Option String := match options.printExprPretty with
+      | true => .some pp
+      | false => .none
+  let sexp: String := (← serialize_expression_ast e)
+  let sexp?: Option String := match options.printExprAST with
+      | true => .some sexp
+      | false => .none
+  return {
+    pp?,
+    sexp?
+  }
+
+/-- Adapted from ppGoal -/
+def serialize_goal (options: Commands.Options) (mvarDecl: MetavarDecl) (parentDecl?: Option MetavarDecl)
+      : MetaM Commands.Goal := do
+  -- Options for printing; See Meta.ppGoal for details
+  let showLetValues  := true
+  let ppAuxDecls     := options.printAuxDecls
+  let ppImplDetailHyps := options.printImplementationDetailHyps
+  let lctx           := mvarDecl.lctx
+  let lctx           := lctx.sanitizeNames.run' { options := (← getOptions) }
+  Meta.withLCtx lctx mvarDecl.localInstances do
+    let ppVarNameOnly (localDecl: LocalDecl): MetaM Commands.Variable := do
+      match localDecl with
+      | .cdecl _ _ varName _ _ _ =>
+        let varName := varName.simpMacroScopes
+        return {
+          name := toString varName,
+        }
+      | .ldecl _ _ varName _ _ _ _ => do
+        return {
+          name := toString varName,
+        }
+    let ppVar (localDecl : LocalDecl) : MetaM Commands.Variable := do
+      match localDecl with
+      | .cdecl _ _ varName type _ _ =>
+        let varName := varName.simpMacroScopes
+        let type ← instantiateMVars type
+        return {
+          name := toString varName,
+          isInaccessible? := .some varName.isInaccessibleUserName
+          type? := .some (← serialize_expression options type)
+        }
+      | .ldecl _ _ varName type val _ _ => do
+        let varName := varName.simpMacroScopes
+        let type ← instantiateMVars type
+        let value? ← if showLetValues then
+          let val ← instantiateMVars val
+          pure $ .some (← serialize_expression options val)
+        else
+          pure $ .none
+        return {
+          name := toString varName,
+          isInaccessible? := .some varName.isInaccessibleUserName
+          type? := .some (← serialize_expression options type)
+          value? := value?
+        }
+    let vars ← lctx.foldlM (init := []) fun acc (localDecl : LocalDecl) => do
+      let skip := !ppAuxDecls && localDecl.isAuxDecl ||
+        !ppImplDetailHyps && localDecl.isImplementationDetail
+      if skip then
+        return acc
+      else
+        let nameOnly := options.proofVariableDelta && (parentDecl?.map
+          (λ decl => decl.lctx.find? localDecl.fvarId |>.isSome) |>.getD false)
+        let var ← match nameOnly with
+          | true => ppVarNameOnly localDecl
+          | false => ppVar localDecl
+        return var::acc
+    return {
+      caseName? := match mvarDecl.userName with
+        | Name.anonymous => .none
+        | name => .some <| toString name,
+      isConversion := "| " == (Meta.getGoalPrefix mvarDecl)
+      target := (← serialize_expression options (← instantiateMVars mvarDecl.type)),
+      vars := vars.reverse.toArray
+    }
+
+
+
+end Pantograph

Pantograph/Symbols.lean

@@ -0,0 +1,38 @@
+/-
+ - Manages the visibility status of symbols
+ -/
+import Lean.Declaration
+
+namespace Pantograph
+
+def str_to_name (s: String): Lean.Name :=
+  (s.splitOn ".").foldl Lean.Name.str Lean.Name.anonymous
+
+def is_symbol_unsafe_or_internal (n: Lean.Name) (info: Lean.ConstantInfo): Bool :=
+  let nameDeduce: Bool := match n.getRoot with
+  | .str _ name => name.startsWith "_" ∨ name == "Lean"
+  | _ => true
+  let stemDeduce: Bool := match n with
+  | .anonymous => true
+  | .str _ name => name.startsWith "_"
+  | .num _ _ => true
+  nameDeduce ∨ stemDeduce ∨ info.isUnsafe
+
+def to_compact_symbol_name (n: Lean.Name) (info: Lean.ConstantInfo): String :=
+  let pref := match info with
+  | .axiomInfo  _ => "axiom"
+  | .defnInfo   _ => "defn"
+  | .thmInfo    _ => "thm"
+  | .opaqueInfo _ => "opaque"
+  | .quotInfo   _ => "quot"
+  | .inductInfo _ => "induct"
+  | .ctorInfo   _ => "ctor"
+  | .recInfo    _ => "rec"
+  s!"{pref}|{toString n}"
+
+def to_filtered_symbol (n: Lean.Name) (info: Lean.ConstantInfo): Option String :=
+  if is_symbol_unsafe_or_internal n info
+  then Option.none
+  else Option.some <| to_compact_symbol_name n info
+
+end Pantograph

Pantograph/Tactic.lean

@@ -0,0 +1,102 @@
+import Lean
+
+import Pantograph.Symbols
+import Pantograph.Serial
+
+/-
+The proof state manipulation system
+
+A proof state is launched by providing
+1. Environment: `Environment`
+2. Expression: `Expr`
+The expression becomes the first meta variable in the saved tactic state
+`Elab.Tactic.SavedState`.
+From this point on, any proof which extends
+`Elab.Term.Context` and
+-/
+
+def Lean.MessageLog.getErrorMessages (log : MessageLog) : MessageLog :=
+  {
+    msgs := log.msgs.filter fun m => match m.severity with | MessageSeverity.error => true | _ => false
+  }
+
+
+namespace Pantograph
+open Lean
+
+structure GoalState where
+  mvarId: MVarId
+  savedState : Elab.Tactic.SavedState
+
+abbrev M := Elab.TermElabM
+
+def GoalState.create (expr: Expr): M GoalState := do
+  let expr ← instantiateMVars expr
+  let goal := (← Meta.mkFreshExprMVar expr (kind := MetavarKind.synthetic))
+  let savedStateMonad: Elab.Tactic.TacticM Elab.Tactic.SavedState := MonadBacktrack.saveState
+  let savedState ← savedStateMonad { elaborator := .anonymous } |>.run' { goals := [goal.mvarId!]}
+  return {
+    savedState := savedState,
+    mvarId := goal.mvarId!
+  }
+
+def execute_tactic (state: Elab.Tactic.SavedState) (goal: MVarId) (tactic: String) :
+    M (Except (Array String) (Elab.Tactic.SavedState × List MVarId)):= do
+  let tacticM (stx: Syntax):  Elab.Tactic.TacticM (Except (Array String) (Elab.Tactic.SavedState × List MVarId)) := do
+    state.restore
+    Elab.Tactic.setGoals [goal]
+    try
+      Elab.Tactic.evalTactic stx
+      if (← getThe Core.State).messages.hasErrors then
+        let messages := (← getThe Core.State).messages.getErrorMessages |>.toList.toArray
+        let errors ← (messages.map Message.data).mapM fun md => md.toString
+        return .error errors
+      else
+        return .ok (← MonadBacktrack.saveState, ← Elab.Tactic.getUnsolvedGoals)
+    catch exception =>
+      return .error #[← exception.toMessageData.toString]
+  match Parser.runParserCategory
+    (env := ← MonadEnv.getEnv)
+    (catName := `tactic)
+    (input := tactic)
+    (fileName := "<stdin>") with
+  | Except.error err => return .error #[err]
+  | Except.ok stx    => tacticM stx { elaborator := .anonymous } |>.run' state.tactic
+
+/-- Response for executing a tactic -/
+inductive TacticResult where
+  -- Goes to next state
+  | success (goals: Array (GoalState × Commands.Goal))
+  -- Fails with messages
+  | failure (messages: Array String)
+
+namespace TacticResult
+
+def is_success: TacticResult → Bool
+  | .success _ => true
+  | .failure _ => false
+
+end TacticResult
+
+/-- Execute tactic on given state -/
+def GoalState.execute (goal: GoalState) (tactic: String):
+    Commands.OptionsT M TacticResult := do
+  let options ← read
+  match (← execute_tactic (state := goal.savedState) (goal := goal.mvarId) (tactic := tactic)) with
+  | .error errors =>
+    return .failure errors
+  | .ok (nextState, nextGoals) =>
+    if nextGoals.isEmpty then
+      return .success #[]
+    else
+      let nextGoals: List GoalState := nextGoals.map fun mvarId => { mvarId, savedState := nextState }
+      let parentDecl? := (← MonadMCtx.getMCtx).findDecl? goal.mvarId
+      let goals ← nextGoals.mapM fun nextGoal => do
+        match (← MonadMCtx.getMCtx).findDecl? nextGoal.mvarId with
+        | .some mvarDecl =>
+          let serializedGoal ← serialize_goal options mvarDecl (parentDecl? := parentDecl?)
+          return (nextGoal, serializedGoal)
+        | .none => throwError nextGoal.mvarId
+      return .success goals.toArray
+
+end Pantograph

Pantograph/Version.lean

@@ -0,0 +1,5 @@
+namespace Pantograph
+
+def version := "0.2.5"
+
+end Pantograph

README.md

@@ -0,0 +1,110 @@
+# Pantograph
+
+An interaction system for Lean 4.
+
+![Pantograph](doc/icon.svg)
+
+## Installation
+
+Install `elan` and `lean4`. Then, execute
+``` sh
+lake build
+```
+Then, setup the `LEAN_PATH` environment variable so it contains the library path of lean libraries. The libraries must be built in advance. For example, if `mathlib4` is stored at `../lib/mathlib4`,
+``` sh
+LIB="../lib"
+LIB_MATHLIB="$LIB/mathlib4/lake-packages"
+export LEAN_PATH="$LIB/mathlib4/build/lib:$LIB_MATHLIB/aesop/build/lib:$LIB_MATHLIB/Qq/build/lib:$LIB_MATHLIB/std/build/lib"
+
+LEAN_PATH=$LEAN_PATH build/bin/pantograph $@
+```
+Note that `lean-toolchain` must be present in the `$PWD` in order to run Pantograph! This is because Pantograph taps into Lean's internals.
+
+## Usage
+
+``` sh
+build/bin/pantograph MODULES|LEAN_OPTIONS
+```
+
+The REPL loop accepts commands as single-line JSON inputs and outputs either an
+`Error:` (indicating malformed command) or a JSON return value indicating the
+result of a command execution.  The command can be passed in one of two formats
+```
+command { ... }
+{ "cmd": command, "payload": ... }
+```
+The list of available commands can be found in `Pantograph/Commands.lean` and below. An
+empty command aborts the REPL.
+
+The `Pantograph` executable must be run with a list of modules to import. It can
+also accept lean options of the form `--key=value` e.g. `--pp.raw=true`.
+
+Example: (~5k symbols)
+```
+$ build/bin/Pantograph Init
+lib.catalog
+lib.inspect {"name": "Nat.le_add_left"}
+```
+Example with `mathlib4` (~90k symbols, may stack overflow, see troubleshooting)
+```
+$ lake env build/bin/Pantograph Mathlib.Analysis.Seminorm
+lib.catalog
+```
+Example proving a theorem: (alternatively use `goal.start {"copyFrom": "Nat.add_comm"}`) to prime the proof
+```
+$ env build/bin/Pantograph Init
+goal.start {"expr": "∀ (n m : Nat), n + m = m + n"}
+goal.tactic {"goalId": 0, "tactic": "intro n m"}
+goal.tactic {"goalId": 1, "tactic": "assumption"}
+goal.delete {"goalIds": [0]}
+stat {}
+goal.tactic {"goalId": 1, "tactic": "rw [Nat.add_comm]"}
+stat
+```
+where the application of `assumption` should lead to a failure.
+
+## Commands
+
+See `Pantograph/Commands.lean` for a description of the parameters and return values in JSON.
+- `reset`: Delete all cached expressions and proof trees
+- `expr.echo {"expr": <expr>}`: Determine the type of an expression and round-trip it
+- `lib.catalog`: Display a list of all safe Lean symbols in the current context
+- `lib.inspect {"name": <name>, "value": <bool>}`: Show the type and package of a
+  given symbol; If value flag is set, the value is printed or hidden. By default
+  only the values of definitions are printed.
+- `options.set { key: value, ... }`: Set one or more options (not Lean options; those
+  have to be set via command line arguments.), for options, see `Pantograph/Commands.lean`
+- `options.print`: Display the current set of options
+- `goal.start {["name": <name>], ["expr": <expr>], ["copyFrom": <symbol>]}`: Start a new goal from a given expression or symbol
+- `goal.tactic {"goalId": <id>, "tactic": <tactic>}`: Execute a tactic string on a given goal
+- `goal.remove {"goalIds": [<id>]}"`: Remove a bunch of stored goals.
+- `stat`: Display resource usage
+
+## Errors
+
+When an error pertaining to the execution of a command happens, the returning JSON structure is
+
+``` json
+{ error: "type", desc: "description" }
+```
+Common error forms:
+* `command`: Indicates malformed command structure which results from either
+  invalid command or a malformed JSON structure that cannot be fed to an
+  individual command.
+* `index`: Indicates an invariant maintained by the output of one command and
+  input of another is broken. For example, attempting to query a symbol not
+  existing in the library or indexing into a non-existent proof state.
+
+## Troubleshooting
+
+If lean encounters stack overflow problems when printing catalog, execute this before running lean:
+```sh
+ulimit -s unlimited
+```
+
+## Testing
+
+The tests are based on `LSpec`. To run tests,
+``` sh
+test/all.sh
+```

Test/Integration.lean

@@ -0,0 +1,93 @@
+/- Integration test for the REPL
+ -/
+import LSpec
+import Pantograph
+namespace Pantograph.Test
+open Pantograph
+
+def subroutine_named_step (name cmd: String) (payload: List (String × Lean.Json))
+    (expected: Lean.Json): MainM LSpec.TestSeq := do
+  let result ← execute { cmd := cmd, payload := Lean.Json.mkObj payload }
+  return LSpec.test name (toString result = toString expected)
+def subroutine_step (cmd: String) (payload: List (String × Lean.Json))
+    (expected: Lean.Json): MainM LSpec.TestSeq := subroutine_named_step cmd cmd payload expected
+
+def subroutine_runner (steps: List (MainM LSpec.TestSeq)): IO LSpec.TestSeq := do
+  -- Setup the environment for execution
+  let env ← Lean.importModules
+    (imports := [{module := Lean.Name.str .anonymous "Init", runtimeOnly := false }])
+    (opts := {})
+    (trustLevel := 1)
+  let context: Context := {
+    imports := ["Init"]
+  }
+  let coreContext: Lean.Core.Context := {
+    currNamespace := Lean.Name.str .anonymous "Aniva"
+    openDecls := [],
+    fileName := "<Test>",
+    fileMap := { source := "", positions := #[0], lines := #[1] },
+    options := Lean.Options.empty
+  }
+  let commands: MainM LSpec.TestSeq :=
+    steps.foldlM (λ suite step => do
+      let result ← step
+      return suite ++ result) LSpec.TestSeq.done
+  try
+    let termElabM := commands.run context |>.run' {}
+    let metaM := termElabM.run' (ctx := {
+      declName? := some "_pantograph",
+      errToSorry := false
+    })
+    let coreM := metaM.run'
+    return Prod.fst $ (← coreM.toIO coreContext { env := env })
+  catch ex =>
+    return LSpec.check s!"Uncaught IO exception: {ex.toString}" false
+
+def test_option_modify : IO LSpec.TestSeq :=
+  let pp? := Option.some "∀ (n : Nat), n + 1 = Nat.succ n"
+  let sexp? := Option.some "(:forall n (:c Nat) ((((:c Eq) (:c Nat)) (((((((:c HAdd.hAdd) (:c Nat)) (:c Nat)) (:c Nat)) (((:c instHAdd) (:c Nat)) (:c instAddNat))) 0) ((((:c OfNat.ofNat) (:c Nat)) (:lit 1)) ((:c instOfNatNat) (:lit 1))))) ((:c Nat.succ) 0)))"
+  let module? := Option.some "Init.Data.Nat.Basic"
+  let options: Commands.Options := {}
+  subroutine_runner [
+    subroutine_step "lib.inspect"
+      [("name", .str "Nat.add_one")]
+     (Lean.toJson ({
+       type := { pp? }, module? }:
+      Commands.LibInspectResult)),
+    subroutine_step "options.set"
+      [("printExprAST", .bool true)]
+     (Lean.toJson ({ }:
+      Commands.OptionsSetResult)),
+    subroutine_step "lib.inspect"
+      [("name", .str "Nat.add_one")]
+     (Lean.toJson ({
+       type := { pp?, sexp? }, module? }:
+      Commands.LibInspectResult)),
+    subroutine_step "options.print"
+      []
+     (Lean.toJson ({ options with printExprAST := true }:
+      Commands.OptionsPrintResult))
+  ]
+def test_malformed_command : IO LSpec.TestSeq :=
+  let invalid := "invalid"
+  subroutine_runner [
+    subroutine_named_step "Invalid command" invalid
+      [("name", .str "Nat.add_one")]
+     (Lean.toJson ({
+       error := "command", desc := s!"Unknown command {invalid}"}:
+      Commands.InteractionError)),
+    subroutine_named_step "JSON Deserialization" "expr.echo"
+      [(invalid, .str "Random garbage data")]
+     (Lean.toJson ({
+       error := "command", desc := s!"Unable to parse json: Pantograph.Commands.ExprEcho.expr: String expected"}:
+      Commands.InteractionError))
+  ]
+
+def test_integration: IO LSpec.TestSeq := do
+
+  return LSpec.group "Integration" $
+    (LSpec.group "Option modify" (← test_option_modify)) ++
+    (LSpec.group "Malformed command" (← test_malformed_command))
+
+
+end Pantograph.Test

Test/Main.lean

@@ -0,0 +1,18 @@
+import LSpec
+import Test.Integration
+import Test.Proofs
+import Test.Serial
+
+open Pantograph.Test
+
+unsafe def main := do
+  Lean.enableInitializersExecution
+  Lean.initSearchPath (← Lean.findSysroot)
+
+  let suites := [
+    test_integration,
+    test_proofs,
+    test_serial
+  ]
+  let all ← suites.foldlM (λ acc m => do pure $ acc ++ (← m)) LSpec.TestSeq.done
+  LSpec.lspecIO $ all

Test/Proofs.lean

@@ -0,0 +1,252 @@
+import LSpec
+import Pantograph.Tactic
+import Pantograph.Serial
+
+namespace Pantograph.Test
+open Pantograph
+open Lean
+
+inductive Start where
+  | copy (name: String) -- Start from some name in the environment
+  | expr (expr: String) -- Start from some expression
+
+abbrev TestM := StateRefT LSpec.TestSeq (ReaderT Commands.Options M)
+
+deriving instance DecidableEq, Repr for Commands.Expression
+deriving instance DecidableEq, Repr for Commands.Variable
+deriving instance DecidableEq, Repr for Commands.Goal
+
+def add_test (test: LSpec.TestSeq): TestM Unit := do
+  set $ (← get) ++ test
+
+def start_proof (start: Start): TestM (Option GoalState) := do
+  let env ← Lean.MonadEnv.getEnv
+  match start with
+  | .copy name =>
+    let cInfo? := str_to_name name |> env.find?
+    add_test $ LSpec.check s!"Symbol exists {name}" cInfo?.isSome
+    match cInfo? with
+    | .some cInfo =>
+      let goal ← GoalState.create (expr := cInfo.type)
+      return Option.some goal
+    | .none =>
+      return Option.none
+  | .expr expr =>
+    let syn? := syntax_from_str env expr
+    add_test $ LSpec.check s!"Parsing {expr}" (syn?.isOk)
+    match syn? with
+    | .error error =>
+      IO.println error
+      return Option.none
+    | .ok syn =>
+      let expr? ← syntax_to_expr syn
+      add_test $ LSpec.check s!"Elaborating" expr?.isOk
+      match expr? with
+      | .error error =>
+        IO.println error
+        return Option.none
+      | .ok expr =>
+        let goal ← GoalState.create (expr := expr)
+        return Option.some goal
+
+def assert_unreachable (message: String): LSpec.TestSeq := LSpec.check message false
+
+def build_goal (nameType: List (String × String)) (target: String): Commands.Goal :=
+  {
+    target := { pp? := .some target},
+    vars := (nameType.map fun x => ({
+      name := x.fst,
+      type? := .some { pp? := .some x.snd },
+      isInaccessible? := .some false
+    })).toArray
+  }
+-- Like `build_goal` but allow certain variables to be elided.
+def build_goal_selective (nameType: List (String × Option String)) (target: String): Commands.Goal :=
+  {
+    target := { pp? := .some target},
+    vars := (nameType.map fun x => ({
+      name := x.fst,
+      type? := x.snd.map (λ type => { pp? := type }),
+      isInaccessible? := x.snd.map (λ _ => false)
+    })).toArray
+  }
+
+
+-- Individual test cases
+example: ∀ (a b: Nat), a + b = b + a := by
+  intro n m
+  rw [Nat.add_comm]
+def proof_nat_add_comm: TestM Unit := do
+  let goal? ← start_proof (.copy "Nat.add_comm")
+  add_test $ LSpec.check "Start goal" goal?.isSome
+  if let .some goal := goal? then
+    if let .success #[(goal, sGoal)] ← goal.execute "intro n m" then
+      let sGoal1e: Commands.Goal := build_goal [("n", "Nat"), ("m", "Nat")] "n + m = m + n"
+      add_test $ LSpec.check "intro n m" (sGoal = sGoal1e)
+
+      if let .failure #[message] ← goal.execute "assumption" then
+        add_test $ LSpec.check "assumption" (message = "tactic 'assumption' failed\nn m : Nat\n⊢ n + m = m + n")
+      else
+        add_test $ assert_unreachable "assumption"
+
+      if let .success #[] ← goal.execute "rw [Nat.add_comm]" then
+        return ()
+      else
+        add_test $ assert_unreachable "rw [Nat.add_comm]"
+    else
+      add_test $ assert_unreachable "intro n m"
+def proof_nat_add_comm_manual: TestM Unit := do
+  let goal? ← start_proof (.expr "∀ (a b: Nat), a + b = b + a")
+  add_test $ LSpec.check "Start goal" goal?.isSome
+  if let .some goal := goal? then
+    if let .success #[(goal, sGoal)] ← goal.execute "intro n m" then
+      let sGoal1e: Commands.Goal := build_goal [("n", "Nat"), ("m", "Nat")] "n + m = m + n"
+      add_test $ LSpec.check "intro n m" (sGoal = sGoal1e)
+
+      if let .failure #[message] ← goal.execute "assumption" then
+        add_test $ LSpec.check "assumption" (message = "tactic 'assumption' failed\nn m : Nat\n⊢ n + m = m + n")
+      else
+        add_test $ assert_unreachable "assumption"
+
+      if let .success #[] ← goal.execute "rw [Nat.add_comm]" then
+        return ()
+      else
+        add_test $ assert_unreachable "rw [Nat.add_comm]"
+    else
+      add_test $ assert_unreachable "intro n m"
+
+
+-- Two ways to write the same theorem
+example: ∀ (p q: Prop), p ∨ q → q ∨ p := by
+  intro p q h
+  cases h
+  apply Or.inr
+  assumption
+  apply Or.inl
+  assumption
+example: ∀ (p q: Prop), p ∨ q → q ∨ p := by
+  intro p q h
+  cases h
+  . apply Or.inr
+    assumption
+  . apply Or.inl
+    assumption
+def proof_or_comm: TestM Unit := do
+  let typeProp: Commands.Expression := { pp? := .some "Prop" }
+  let branchGoal (caseName name: String): Commands.Goal := {
+    caseName? := .some caseName,
+    target := { pp? := .some "q ∨ p" },
+    vars := #[
+      { name := "p", type? := .some typeProp, isInaccessible? := .some false },
+      { name := "q", type? := .some typeProp, isInaccessible? := .some false },
+      { name := "h✝", type? := .some { pp? := .some name }, isInaccessible? := .some true }
+    ]
+  }
+  let goal? ← start_proof (.expr "∀ (p q: Prop), p ∨ q → q ∨ p")
+  add_test $ LSpec.check "Start goal" goal?.isSome
+  if let .some goal := goal? then
+    if let .success #[(goal, sGoal)] ← goal.execute "intro p q h" then
+      let sGoal1e := build_goal [("p", "Prop"), ("q", "Prop"), ("h", "p ∨ q")] "q ∨ p"
+      add_test $ LSpec.check "intro p q h" (sGoal = sGoal1e)
+
+      if let .success #[(goal1, sGoal1), (goal2, sGoal2)] ← goal.execute "cases h" then
+        add_test $ LSpec.check "cases h/1" (sGoal1 = branchGoal "inl" "p")
+        if let .success #[(goal, _)] ← goal1.execute "apply Or.inr" then
+          if let .success #[] ← goal.execute "assumption" then
+            return ()
+          else
+            add_test $ assert_unreachable "assumption"
+        else
+          add_test $ assert_unreachable "apply Or.inr"
+
+
+        add_test $ LSpec.check "cases h/2" (sGoal2 = branchGoal "inr" "q")
+        if let .success #[(goal, _)] ← goal2.execute "apply Or.inl" then
+          if let .success #[] ← goal.execute "assumption" then
+            return ()
+          else
+            add_test $ assert_unreachable "assumption"
+        else
+          add_test $ assert_unreachable "apply Or.inl"
+
+      else
+        add_test $ assert_unreachable "cases h"
+    else
+      add_test $ assert_unreachable "intro p q h"
+
+example (w x y z : Nat) (p : Nat → Prop)
+        (h : p (x * y + z * w * x)) : p (x * w * z + y * x) := by
+  simp [Nat.add_assoc, Nat.add_comm, Nat.add_left_comm, Nat.mul_comm, Nat.mul_assoc, Nat.mul_left_comm] at *
+  assumption
+def proof_arith_1: TestM Unit := do
+  let goal? ← start_proof (.expr "∀ (w x y z : Nat) (p : Nat → Prop) (h : p (x * y + z * w * x)), p (x * w * z + y * x)")
+  add_test $ LSpec.check "Start goal" goal?.isSome
+  if let .some goal := goal? then
+    if let .success #[(goal, _)] ← goal.execute "intros" then
+      if let .success #[(goal, _)] ← goal.execute "simp [Nat.add_assoc, Nat.add_comm, Nat.add_left_comm, Nat.mul_comm, Nat.mul_assoc, Nat.mul_left_comm] at *" then
+        if let .success #[] ← goal.execute "assumption" then
+          return ()
+        else
+          add_test $ assert_unreachable "assumption"
+      else
+        add_test $ assert_unreachable "simp ..."
+    else
+      add_test $ assert_unreachable "intros"
+
+def proof_delta_variable: TestM Unit := withReader (fun _ => {proofVariableDelta := true}) do
+  let goal? ← start_proof (.expr "∀ (a b: Nat), a + b = b + a")
+  add_test $ LSpec.check "Start goal" goal?.isSome
+  if let .some goal := goal? then
+    if let .success #[(goal, sGoal)] ← goal.execute "intro n" then
+      let sGoal1e: Commands.Goal := build_goal_selective [("n", .some "Nat")] "∀ (b : Nat), n + b = b + n"
+      add_test $ LSpec.check "intro n" (sGoal = sGoal1e)
+
+      if let .success #[(_, sGoal)] ← goal.execute "intro m" then
+        let sGoal2e: Commands.Goal := build_goal_selective [("n", .none), ("m", .some "Nat")] "n + m = m + n"
+        add_test $ LSpec.check "intro m" (sGoal = sGoal2e)
+      else
+        add_test $ assert_unreachable "intro m"
+    else
+      add_test $ assert_unreachable "intro n"
+
+def proof_runner (env: Lean.Environment) (tests: TestM Unit): IO LSpec.TestSeq := do
+  let termElabM := tests.run LSpec.TestSeq.done |>.run {} -- with default options
+
+  let coreContext: Lean.Core.Context := {
+    currNamespace := str_to_name "Aniva",
+    openDecls := [],     -- No 'open' directives needed
+    fileName := "<Pantograph>",
+    fileMap := { source := "", positions := #[0], lines := #[1] }
+  }
+  let metaM := termElabM.run' (ctx := {
+    declName? := some "_pantograph",
+    errToSorry := false
+  })
+  let coreM := metaM.run'
+  match ← (coreM.run' coreContext { env := env }).toBaseIO with
+  | .error exception =>
+    return LSpec.test "Exception" (s!"internal exception #{← exception.toMessageData.toString}" = "")
+  | .ok (_, a) =>
+    return a
+
+def test_proofs : IO LSpec.TestSeq := do
+  let env: Lean.Environment ← Lean.importModules
+    (imports := ["Init"].map (λ str => { module := str_to_name str, runtimeOnly := false }))
+    (opts := {})
+    (trustLevel := 1)
+  let tests := [
+    ("Nat.add_comm", proof_nat_add_comm),
+    ("nat.add_comm manual", proof_nat_add_comm_manual),
+    ("Or.comm", proof_or_comm),
+    ("arithmetic 1", proof_arith_1),
+    ("delta variable", proof_delta_variable)
+  ]
+  let tests ← tests.foldlM (fun acc tests => do
+    let (name, tests) := tests
+    let tests ← proof_runner env tests
+    return acc ++ (LSpec.group name tests)) LSpec.TestSeq.done
+
+  return LSpec.group "Proofs" tests
+
+end Pantograph.Test
+

Test/Serial.lean

@@ -0,0 +1,76 @@
+import LSpec
+import Pantograph.Serial
+import Pantograph.Symbols
+
+namespace Pantograph.Test
+
+open Pantograph
+open Lean
+
+deriving instance Repr, DecidableEq for Commands.BoundExpression
+
+def test_str_to_name: LSpec.TestSeq :=
+    LSpec.test "Symbol parsing" (Name.str (.str (.str .anonymous "Lean") "Meta") "run" = Pantograph.str_to_name "Lean.Meta.run")
+
+def test_expr_to_binder (env: Environment): IO LSpec.TestSeq := do
+  let entries: List (String × Commands.BoundExpression) := [
+    ("Nat.add_comm", { binders := #[("n", "Nat"), ("m", "Nat")], target := "n + m = m + n" }),
+    ("Nat.le_of_succ_le", { binders := #[("n", "Nat"), ("m", "Nat"), ("h", "Nat.succ n ≤ m")], target := "n ≤ m" })
+  ]
+  let coreM := entries.foldlM (λ suites (symbol, target) => do
+    let env ← MonadEnv.getEnv
+    let expr := str_to_name symbol |> env.find? |>.get! |>.type
+    let test := LSpec.check symbol ((← type_expr_to_bound expr) = target)
+    return LSpec.TestSeq.append suites test) LSpec.TestSeq.done |>.run'
+  let coreContext: Core.Context := {
+    currNamespace := Lean.Name.str .anonymous "Aniva"
+    openDecls := [],     -- No 'open' directives needed
+    fileName := "<Pantograph/Test>",
+    fileMap := { source := "", positions := #[0], lines := #[1] }
+  }
+  match ← (coreM.run' coreContext { env := env }).toBaseIO with
+  | .error exception =>
+    return LSpec.test "Exception" (s!"internal exception #{← exception.toMessageData.toString}" = "")
+  | .ok a            => return a
+
+def test_sexp_of_symbol (env: Environment): IO LSpec.TestSeq := do
+  let entries: List (String × String) := [
+    -- This one contains unhygienic variable names which must be suppressed
+    ("Nat.add", "(:forall :anon (:c Nat) (:forall :anon (:c Nat) (:c Nat)))"),
+    -- These ones are normal and easy
+    ("Nat.add_one", "(:forall n (:c Nat) ((((:c Eq) (:c Nat)) (((((((:c HAdd.hAdd) (:c Nat)) (:c Nat)) (:c Nat)) (((:c instHAdd) (:c Nat)) (:c instAddNat))) 0) ((((:c OfNat.ofNat) (:c Nat)) (:lit 1)) ((:c instOfNatNat) (:lit 1))))) ((:c Nat.succ) 0)))"),
+    ("Nat.le_of_succ_le", "(:forall n (:c Nat) (:forall m (:c Nat) (:forall h (((((:c LE.le) (:c Nat)) (:c instLENat)) ((:c Nat.succ) 1)) 0) (((((:c LE.le) (:c Nat)) (:c instLENat)) 2) 1)) :implicit) :implicit)"),
+    -- Handling of higher order types
+    ("Or", "(:forall a (:sort 0) (:forall b (:sort 0) (:sort 0)))"),
+    ("List", "(:forall α (:sort (+ u 1)) (:sort (+ u 1)))")
+  ]
+  let metaM: MetaM LSpec.TestSeq := entries.foldlM (λ suites (symbol, target) => do
+    let env ← MonadEnv.getEnv
+    let expr := str_to_name symbol |> env.find? |>.get! |>.type
+    let test := LSpec.check symbol ((← serialize_expression_ast expr) = target)
+    return LSpec.TestSeq.append suites test) LSpec.TestSeq.done |>.run'
+  let coreM := metaM.run'
+  let coreContext: Core.Context := {
+    currNamespace := Lean.Name.str .anonymous "Aniva"
+    openDecls := [],     -- No 'open' directives needed
+    fileName := "<Pantograph/Test>",
+    fileMap := { source := "", positions := #[0], lines := #[1] }
+  }
+  match ← (coreM.run' coreContext { env := env }).toBaseIO with
+  | .error exception =>
+    return LSpec.test "Exception" (s!"internal exception #{← exception.toMessageData.toString}" = "")
+  | .ok a            => return a
+
+
+def test_serial: IO LSpec.TestSeq := do
+  let env: Environment ← importModules
+    (imports := ["Init"].map (λ str => { module := str_to_name str, runtimeOnly := false }))
+    (opts := {})
+    (trustLevel := 1)
+
+  return LSpec.group "Serialisation" $
+    (LSpec.group "str_to_name" test_str_to_name) ++
+    (LSpec.group "Expression binder" (← test_expr_to_binder env)) ++
+    (LSpec.group "Sexp from symbol" (← test_sexp_of_symbol env))
+
+end Pantograph.Test

Test/all.sh

@@ -0,0 +1,3 @@
+#!/bin/bash
+
+lake build test && lake env build/bin/test

doc/icon.svg

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lake-manifest.json

@@ -0,0 +1,11 @@
+{"version": 5,
+ "packagesDir": "lake-packages",
+ "packages":
+ [{"git":
+   {"url": "https://github.com/lurk-lab/LSpec.git",
+    "subDir?": null,
+    "rev": "88f7d23e56a061d32c7173cea5befa4b2c248b41",
+    "opts": {},
+    "name": "LSpec",
+    "inputRev?": "88f7d23e56a061d32c7173cea5befa4b2c248b41",
+    "inherited": false}}]}

lakefile.lean

@@ -1,19 +1,24 @@
 import Lake
 open Lake DSL
 
-
+package pantograph
-package pantograph {
-  -- add package configuration options here
-}
-
-require mathlib from git
-  "https://github.com/leanprover-community/mathlib4.git" @  "8e5a00a8afc8913c0584cb85f37951995275fd87"
 
 lean_lib Pantograph {
-  -- add library configuration options here
 }
 
 @[default_target]
 lean_exe pantograph {
   root := `Main
+  -- Somehow solves the native symbol not found problem
+  supportInterpreter := true
+}
+
+require LSpec from git
+  "https://github.com/lurk-lab/LSpec.git" @ "88f7d23e56a061d32c7173cea5befa4b2c248b41"
+lean_lib Test {
+}
+lean_exe test {
+  root := `Test.Main
+  -- Somehow solves the native symbol not found problem
+  supportInterpreter := true
 }

lean-toolchain

@@ -1 +1 @@
-leanprover/lean4:nightly-2023-05-06
+leanprover/lean4:4.0.0