scripts/AlphaRenaming.lean

/-
  Alpha-Renaming using Lean 4 Meta-programming

  This module performs variable renaming at the AST/Syntax level,
  which is more robust than Python string manipulation:
    1. Correct handling of variable scopes (shadowing)
    2. No accidental replacement in string literals
    3. Guaranteed syntactic correctness
-/

import Lean
import Lean.Elab.Command
import Lean.Parser

open Lean Elab Command Meta

namespace AlphaRenaming

-- Variable renaming map type
abbrev RenameMap := Std.HashMap Name Name

-- Candidate names for renaming (Greek letters first, then Latin)
def greekNames : Array Name := #[
  .mkSimple "α", .mkSimple "β", .mkSimple "γ", .mkSimple "δ",
  .mkSimple "ε", .mkSimple "ζ", .mkSimple "η", .mkSimple "θ",
  .mkSimple "ι", .mkSimple "κ", .mkSimple "μ", .mkSimple "ν",
  .mkSimple "ξ", .mkSimple "ο", .mkSimple "ρ", .mkSimple "σ",
  .mkSimple "τ", .mkSimple "υ", .mkSimple "φ", .mkSimple "χ",
  .mkSimple "ψ", .mkSimple "ω"
]

def latinNames : Array Name := #[
  .mkSimple "a", .mkSimple "b", .mkSimple "c", .mkSimple "d",
  .mkSimple "e", .mkSimple "f", .mkSimple "g", .mkSimple "i",
  .mkSimple "j", .mkSimple "k", .mkSimple "l", .mkSimple "m",
  .mkSimple "o", .mkSimple "p", .mkSimple "q", .mkSimple "r",
  .mkSimple "s", .mkSimple "t", .mkSimple "u", .mkSimple "v",
  .mkSimple "w"
]

def allCandidates : Array Name := greekNames ++ latinNames

-- Generate an unused variable name
def generateNewName (original : Name) (used : Std.HashSet Name) (suffix : Nat := 0) : Name :=
  let rec findUnused (idx : Nat) : Name :=
    if h : idx < allCandidates.size then
      let candidate := allCandidates[idx]
      if used.contains candidate then findUnused (idx + 1)
      else candidate
    else
      -- All candidates exhausted, add suffix
      .mkSimple s!"{original}_{suffix + idx}"
  findUnused 0

-- Collect all identifiers from syntax tree
partial def collectIdents (stx : Syntax) : Array Name :=
  match stx with
  | .ident _ _ val _ => #[val]
  | .node _ _ args => args.foldl (fun acc arg => acc ++ collectIdents arg) #[]
  | _ => #[]

-- Apply renaming to syntax tree
partial def applyRenaming (stx : Syntax) (renameMap : RenameMap) : Syntax :=
  match stx with
  | .ident info _rawVal val preresolved =>
    match renameMap[val]? with
    | some newName =>
      let newStr := newName.toString
      let newRawVal : Substring.Raw := ⟨newStr, ⟨0⟩, ⟨newStr.length⟩⟩
      .ident info newRawVal newName preresolved
    | none => stx
  | .node info kind args =>
    let newArgs := args.map (applyRenaming · renameMap)
    .node info kind newArgs
  | _ => stx

-- Extract variable names from binders (skip hypothesis names)
def extractBinderNames (binder : Syntax) : Array Name :=
  let idents := binder.getArgs.filter (·.isIdent)
  idents.foldl (fun acc ident =>
    match ident with
    | .ident _ _ val _ =>
      let nameStr := val.toString
      -- Skip hypothesis names like h₀, h₁, hn, hx
      if nameStr.startsWith "h" && nameStr.length > 1 then acc
      else if nameStr == "h" then acc
      else acc.push val
    | _ => acc
  ) #[]

-- Generate complete rename mapping for all variables
def generateRenameMap (varNames : Array Name) (_seed : Nat := 0) : RenameMap :=
  let initUsed : Std.HashSet Name := varNames.foldl (fun acc name => acc.insert name) {}
  let ((renameMap, _), _) := varNames.foldl (fun ((map, used), idx) name =>
    let newName := generateNewName name used idx
    ((map.insert name newName, used.insert newName), idx + 1))
    (({}, initUsed), 0)
  renameMap

-- Protected keywords and identifiers that should NOT be renamed
def keywords : Std.HashSet Name :=
  let s : Std.HashSet Name := {}
  -- Lean keywords
  s.insert (.mkSimple "theorem")
  |>.insert (.mkSimple "lemma")
  |>.insert (.mkSimple "def")
  |>.insert (.mkSimple "by")
  |>.insert (.mkSimple "sorry")
  |>.insert (.mkSimple "rfl")
  -- Type names
  |>.insert (.mkSimple "ℕ")
  |>.insert (.mkSimple "ℤ")
  |>.insert (.mkSimple "ℚ")
  |>.insert (.mkSimple "ℝ")
  |>.insert (.mkSimple "ℂ")
  |>.insert (.mkSimple "Nat")
  |>.insert (.mkSimple "Int")
  |>.insert (.mkSimple "Rat")
  |>.insert (.mkSimple "Real")
  |>.insert (.mkSimple "Finset")
  |>.insert (.mkSimple "List")
  |>.insert (.mkSimple "Set")
  |>.insert (.mkSimple "Prop")
  |>.insert (.mkSimple "Type")
  -- Common library functions
  |>.insert (.mkSimple "range")
  |>.insert (.mkSimple "sum")
  |>.insert (.mkSimple "prod")
  |>.insert (.mkSimple "card")
  |>.insert (.mkSimple "gcd")
  |>.insert (.mkSimple "abs")
  |>.insert (.mkSimple "min")
  |>.insert (.mkSimple "max")
  |>.insert (.mkSimple "log")
  |>.insert (.mkSimple "exp")
  |>.insert (.mkSimple "sin")
  |>.insert (.mkSimple "cos")
  |>.insert (.mkSimple "tan")
  |>.insert (.mkSimple "mod")
  |>.insert (.mkSimple "div")
  |>.insert (.mkSimple "lcm")
  |>.insert (.mkSimple "id")
  |>.insert (.mkSimple "fun")
  |>.insert (.mkSimple "Even")
  |>.insert (.mkSimple "Odd")
  -- Struct field accessors (to avoid x.field issues)
  |>.insert (.mkSimple "num")
  |>.insert (.mkSimple "den")
  |>.insert (.mkSimple "re")
  |>.insert (.mkSimple "im")
  |>.insert (.mkSimple "fst")
  |>.insert (.mkSimple "snd")
  |>.insert (.mkSimple "val")
  |>.insert (.mkSimple "toNat")
  |>.insert (.mkSimple "toInt")
  |>.insert (.mkSimple "toRat")
  |>.insert (.mkSimple "floor")
  |>.insert (.mkSimple "ceil")
  |>.insert (.mkSimple "natAbs")
  |>.insert (.mkSimple "succ")
  |>.insert (.mkSimple "pred")
  -- Variables commonly used with field access (S.card, z.im, m.num, etc.)
  |>.insert (.mkSimple "S")
  |>.insert (.mkSimple "T")
  |>.insert (.mkSimple "A")
  |>.insert (.mkSimple "B")
  |>.insert (.mkSimple "f")
  |>.insert (.mkSimple "g")
  |>.insert (.mkSimple "z")
  |>.insert (.mkSimple "w")
  |>.insert (.mkSimple "m")
  |>.insert (.mkSimple "q")
  |>.insert (.mkSimple "p")
  |>.insert (.mkSimple "d")

-- Check if name is a hypothesis name (h₀, h₁, hn, hx, etc.)
def isHypothesisName (n : Name) : Bool :=
  let s := n.toString
  if s.length == 1 then false
  else if s.startsWith "h" then
    let rest := s.drop 1
    rest.all (fun c => c.isDigit || c == '_' || (c.isAlpha && c.isLower) ||
                       "₀₁₂₃₄₅₆₇₈₉".toList.contains c)
  else false

-- Main alpha-renaming function for theorem propositions
def alphaRenameTheorem (declStx : Syntax) : MetaM Syntax := do
  let allIdents := collectIdents declStx

  -- Filter: short names that are likely variables
  let varCandidates := allIdents.filter (fun n =>
    !keywords.contains n &&
    n.toString.length <= 3 &&
    !isHypothesisName n
  )

  -- Deduplicate
  let uniqueVars := varCandidates.foldl (fun acc n =>
    if acc.contains n then acc else acc.push n) #[]

  let renameMap := generateRenameMap uniqueVars
  return applyRenaming declStx renameMap

-- Command: alpha-rename and print result
elab "#alpha_rename " thm:term : command => do
  let renamedStx ← liftTermElabM <| alphaRenameTheorem thm
  logInfo m!"Renamed:\n{renamedStx}"

-- Command: alpha-rename with ID markers for Python parsing
elab "#alpha_rename_id " "[" id:ident "]" thm:term : command => do
  let renamedStx ← liftTermElabM <| alphaRenameTheorem thm
  let idStr := id.getId.toString
  logInfo m!"[RENAMED:{idStr}]\n{renamedStx}\n[/RENAMED:{idStr}]"

end AlphaRenaming

-- Example usage
section Examples
#alpha_rename (∀ (n : Nat), n + 0 = n)
end Examples