aver/codegen/lean/

mod.rs

/// Lean 4 backend for the Aver transpiler.
///
/// Transpiles only pure core logic: functions without effects, type definitions,
/// verify blocks (as `example` proofs), and decision blocks (as comments).
/// Effectful functions and `main` are skipped.
mod builtins;
mod expr;
mod law_auto;
mod pattern;
mod shared;
mod toplevel;
mod types;

use std::collections::{HashMap, HashSet};

use crate::ast::{BinOp, Expr, FnBody, FnDef, MatchArm, Pattern, Stmt, TopLevel, VerifyKind};
use crate::call_graph;
use crate::codegen::{CodegenContext, ProjectOutput};

/// How verify blocks should be emitted in generated Lean.
#[derive(Clone, Copy, Debug, Eq, PartialEq)]
pub enum VerifyEmitMode {
    /// `example : lhs = rhs := by native_decide`
    NativeDecide,
    /// `example : lhs = rhs := by sorry`
    Sorry,
    /// Named theorem stubs:
    /// `theorem <fn>_verify_<n> : lhs = rhs := by`
    /// `  sorry`
    TheoremSkeleton,
}

/// Proof-mode recursion support class for emitted Lean definitions.
#[derive(Clone, Copy, Debug, Eq, PartialEq)]
pub enum RecursionPlan {
    /// Single-function recursion where first `Int` parameter decreases by 1.
    IntCountdown,
    /// Single-function structural recursion on first `List<_>` parameter.
    ListStructural,
    /// Single-function recursion where first `String` stays the same and second `Int`
    /// parameter strictly advances (`pos + k`, `k >= 1`).
    StringPosAdvance,
    /// Mutual recursion group where first `Int` parameter decreases by 1 across SCC calls.
    MutualIntCountdown,
    /// Mutual recursion group where first `String` is preserved and second `Int`
    /// either stays the same across rank-decreasing edges, or strictly advances.
    MutualStringPosAdvance { rank: usize },
    /// Generic mutual recursion plan using `sizeOf` on a selected parameter,
    /// plus rank for same-parameter edges.
    MutualSizeOfRanked {
        rank: usize,
        metric_param_index: usize,
    },
}

const LEAN_PRELUDE_HEADER: &str = r#"-- Generated by the Aver → Lean 4 transpiler
-- Pure core logic only (effectful functions are omitted)

-- Prelude: helper definitions for Aver builtins"#;

const LEAN_PRELUDE_FLOAT_COE: &str = r#"instance : Coe Int Float := ⟨fun n => Float.ofInt n⟩"#;

const LEAN_PRELUDE_FLOAT_DEC_EQ: &str = r#"private unsafe def Float.unsafeDecEq (a b : Float) : Decidable (a = b) :=
  if a == b then isTrue (unsafeCast ()) else isFalse (unsafeCast ())
@[implemented_by Float.unsafeDecEq]
private opaque Float.compDecEq (a b : Float) : Decidable (a = b)
instance : DecidableEq Float := Float.compDecEq"#;

const LEAN_PRELUDE_EXCEPT_DEC_EQ: &str = r#"instance [DecidableEq ε] [DecidableEq α] : DecidableEq (Except ε α)
  | .ok a, .ok b =>
    if h : a = b then isTrue (h ▸ rfl) else isFalse (by intro h'; cases h'; exact h rfl)
  | .error a, .error b =>
    if h : a = b then isTrue (h ▸ rfl) else isFalse (by intro h'; cases h'; exact h rfl)
  | .ok _, .error _ => isFalse (by intro h; cases h)
  | .error _, .ok _ => isFalse (by intro h; cases h)"#;

const LEAN_PRELUDE_EXCEPT_NS: &str = r#"namespace Except
def withDefault (r : Except ε α) (d : α) : α :=
  match r with
  | .ok v => v
  | .error _ => d
end Except"#;

const LEAN_PRELUDE_OPTION_TO_EXCEPT: &str = r#"def Option.toExcept (o : Option α) (e : ε) : Except ε α :=
  match o with
  | some v => .ok v
  | none => .error e"#;

const LEAN_PRELUDE_STRING_HADD: &str = r#"instance : HAdd String String String := ⟨String.append⟩"#;

const AVER_MAP_PRELUDE: &str = r#"namespace AverMap
def empty : List (α × β) := []
def get [BEq α] (m : List (α × β)) (k : α) : Option β :=
  match m with
  | [] => none
  | (k', v) :: rest => if k == k' then some v else AverMap.get rest k
def set [BEq α] (m : List (α × β)) (k : α) (v : β) : List (α × β) :=
  let rec go : List (α × β) → List (α × β)
    | [] => [(k, v)]
    | (k', v') :: rest => if k == k' then (k, v) :: rest else (k', v') :: go rest
  go m
def has [BEq α] (m : List (α × β)) (k : α) : Bool :=
  m.any (fun p => p.1 == k)
def remove [BEq α] (m : List (α × β)) (k : α) : List (α × β) :=
  m.filter (fun p => !(p.1 == k))
def keys (m : List (α × β)) : List α := m.map Prod.fst
def values (m : List (α × β)) : List β := m.map Prod.snd
def entries (m : List (α × β)) : List (α × β) := m
def len (m : List (α × β)) : Nat := m.length
def fromList (entries : List (α × β)) : List (α × β) := entries

private theorem any_set_go_self [BEq α] (k : α) (v : β) :
    ∀ (m : List (α × β)), List.any (AverMap.set.go k v m) (fun p => p.1 == k) = true := by
  intro m
  induction m with
  | nil =>
      simp [AverMap.set.go, List.any, beq_self_eq_true]
  | cons p tl ih =>
      simp only [AverMap.set.go]
      split <;> simp_all [List.any, beq_self_eq_true]

theorem has_set_self [BEq α] (m : List (α × β)) (k : α) (v : β) :
    AverMap.has (AverMap.set m k v) k = true := by
  simp [AverMap.has, AverMap.set]
  exact any_set_go_self k v m

private theorem get_set_go_self [BEq α] (k : α) (v : β) :
    ∀ (m : List (α × β)), AverMap.get (AverMap.set.go k v m) k = some v := by
  intro m
  induction m with
  | nil =>
      simp [AverMap.set.go, AverMap.get, beq_self_eq_true]
  | cons p tl ih =>
      simp only [AverMap.set.go]
      split
      · simp [AverMap.get, beq_self_eq_true]
      · simp [AverMap.get, beq_self_eq_true, ih]

theorem get_set_self [BEq α] (m : List (α × β)) (k : α) (v : β) :
    AverMap.get (AverMap.set m k v) k = some v := by
  simp [AverMap.set]
  exact get_set_go_self k v m
end AverMap"#;

const LEAN_PRELUDE_AVER_LIST: &str = r#"namespace AverList
private def insertSorted [Ord α] (x : α) : List α → List α
  | [] => [x]
  | y :: ys =>
    if compare x y == Ordering.lt || compare x y == Ordering.eq then
      x :: y :: ys
    else
      y :: insertSorted x ys
def sort [Ord α] (xs : List α) : List α :=
  xs.foldl (fun acc x => insertSorted x acc) []
end AverList"#;

const LEAN_PRELUDE_STRING_HELPERS: &str = r#"def String.charAt (s : String) (i : Int) : Option String :=
  if i < 0 then none
  else (s.toList.get? i.toNat).map Char.toString
def String.slice (s : String) (start stop : Int) : String :=
  let startN := if start < 0 then 0 else start.toNat
  let stopN := if stop < 0 then 0 else stop.toNat
  let chars := s.toList
  String.mk ((chars.drop startN).take (stopN - startN))
private def trimFloatTrailingZerosChars (chars : List Char) : List Char :=
  let noZeros := (chars.reverse.dropWhile (fun c => c == '0')).reverse
  match noZeros.reverse with
  | '.' :: rest => rest.reverse
  | _ => noZeros
private def normalizeFloatString (s : String) : String :=
  if s.toList.any (fun c => c == '.') then
    String.mk (trimFloatTrailingZerosChars s.toList)
  else s
def String.fromInt (n : Int) : String := toString n
def String.fromFloat (f : Float) : String := normalizeFloatString (toString f)
def String.chars (s : String) : List String := s.toList.map Char.toString
namespace AverString
def split (s delim : String) : List String :=
  if delim.isEmpty then
    "" :: (s.toList.map Char.toString) ++ [""]
  else
    s.splitOn delim
end AverString"#;

const LEAN_PRELUDE_NUMERIC_PARSE: &str = r#"def Int.fromString (s : String) : Except String Int :=
  match s.toInt? with
  | some n => .ok n
  | none => .error ("Invalid integer: " ++ s)

private def charDigitsToNat (cs : List Char) : Nat :=
  cs.foldl (fun acc c => acc * 10 + (c.toNat - '0'.toNat)) 0

private def parseExpPart : List Char → (Bool × List Char)
  | '-' :: rest => (true, rest.takeWhile Char.isDigit)
  | '+' :: rest => (false, rest.takeWhile Char.isDigit)
  | rest => (false, rest.takeWhile Char.isDigit)

def Float.fromString (s : String) : Except String Float :=
  let chars := s.toList
  let (neg, chars) := match chars with
    | '-' :: rest => (true, rest)
    | _ => (false, chars)
  let intPart := chars.takeWhile Char.isDigit
  let rest := chars.dropWhile Char.isDigit
  let (fracPart, rest) := match rest with
    | '.' :: rest => (rest.takeWhile Char.isDigit, rest.dropWhile Char.isDigit)
    | _ => ([], rest)
  let (expNeg, expDigits) := match rest with
    | 'e' :: rest => parseExpPart rest
    | 'E' :: rest => parseExpPart rest
    | _ => (false, [])
  if intPart.isEmpty && fracPart.isEmpty then .error ("Invalid float: " ++ s)
  else
    let mantissa := charDigitsToNat (intPart ++ fracPart)
    let fracLen : Int := fracPart.length
    let expVal : Int := charDigitsToNat expDigits
    let shift : Int := (if expNeg then -expVal else expVal) - fracLen
    let f := if shift >= 0 then Float.ofScientific mantissa false shift.toNat
             else Float.ofScientific mantissa true ((-shift).toNat)
    .ok (if neg then -f else f)"#;

const LEAN_PRELUDE_CHAR_BYTE: &str = r#"def Char.toCode (s : String) : Int :=
  match s.toList.head? with
  | some c => (c.toNat : Int)
  | none => panic! "Char.toCode: string is empty"
def Char.fromCode (n : Int) : Option String :=
  if n < 0 || n > 1114111 then none
  else if n >= 55296 && n <= 57343 then none
  else some (Char.toString (Char.ofNat n.toNat))

def hexDigit (n : Int) : String :=
  match n with
  | 0 => "0" | 1 => "1" | 2 => "2" | 3 => "3"
  | 4 => "4" | 5 => "5" | 6 => "6" | 7 => "7"
  | 8 => "8" | 9 => "9" | 10 => "a" | 11 => "b"
  | 12 => "c" | 13 => "d" | 14 => "e" | 15 => "f"
  | _ => "?"

def byteToHex (code : Int) : String :=
  hexDigit (code / 16) ++ hexDigit (code % 16)

namespace AverByte
private def hexValue (c : Char) : Option Int :=
  match c with
  | '0' => some 0  | '1' => some 1  | '2' => some 2  | '3' => some 3
  | '4' => some 4  | '5' => some 5  | '6' => some 6  | '7' => some 7
  | '8' => some 8  | '9' => some 9  | 'a' => some 10 | 'b' => some 11
  | 'c' => some 12 | 'd' => some 13 | 'e' => some 14 | 'f' => some 15
  | 'A' => some 10 | 'B' => some 11 | 'C' => some 12 | 'D' => some 13
  | 'E' => some 14 | 'F' => some 15
  | _ => none
def toHex (n : Int) : Except String String :=
  if n < 0 || n > 255 then
    .error ("Byte.toHex: " ++ toString n ++ " is out of range 0-255")
  else
    .ok (byteToHex n)
def fromHex (s : String) : Except String Int :=
  match s.toList with
  | [hi, lo] =>
    match hexValue hi, hexValue lo with
    | some h, some l => .ok (h * 16 + l)
    | _, _ => .error ("Byte.fromHex: invalid hex '" ++ s ++ "'")
  | _ => .error ("Byte.fromHex: expected exactly 2 hex chars, got '" ++ s ++ "'")
end AverByte"#;

fn pure_fns<'a>(ctx: &'a CodegenContext) -> Vec<&'a FnDef> {
    ctx.modules
        .iter()
        .flat_map(|m| m.fn_defs.iter())
        .chain(ctx.fn_defs.iter())
        .filter(|fd| toplevel::is_pure_fn(fd))
        .collect()
}

fn recursive_pure_fn_names(ctx: &CodegenContext) -> HashSet<String> {
    let pure_names: HashSet<String> = pure_fns(ctx)
        .into_iter()
        .map(|fd| fd.name.clone())
        .collect();
    let mut callgraph_items = ctx.items.clone();
    for module in &ctx.modules {
        for fd in &module.fn_defs {
            callgraph_items.push(TopLevel::FnDef(fd.clone()));
        }
    }
    call_graph::find_recursive_fns(&callgraph_items)
        .into_iter()
        .filter(|name| pure_names.contains(name))
        .collect()
}

fn verify_counter_key(vb: &crate::ast::VerifyBlock) -> String {
    match &vb.kind {
        VerifyKind::Cases => format!("fn:{}", vb.fn_name),
        VerifyKind::Law(law) => format!("law:{}::{}", vb.fn_name, law.name),
    }
}

fn expr_to_dotted_name(expr: &Expr) -> Option<String> {
    match expr {
        Expr::Ident(name) => Some(name.clone()),
        Expr::Attr(obj, field) => expr_to_dotted_name(obj).map(|p| format!("{}.{}", p, field)),
        _ => None,
    }
}

fn call_matches(name: &str, target: &str) -> bool {
    name == target || name.rsplit('.').next() == Some(target)
}

fn call_is_in_set(name: &str, targets: &HashSet<String>) -> bool {
    call_matches_any(name, targets)
}

fn canonical_callee_name(name: &str, targets: &HashSet<String>) -> Option<String> {
    if targets.contains(name) {
        return Some(name.to_string());
    }
    name.rsplit('.')
        .next()
        .filter(|last| targets.contains(*last))
        .map(ToString::to_string)
}

fn call_matches_any(name: &str, targets: &HashSet<String>) -> bool {
    if targets.contains(name) {
        return true;
    }
    match name.rsplit('.').next() {
        Some(last) => targets.contains(last),
        None => false,
    }
}

fn is_int_minus_one(expr: &Expr, param_name: &str) -> bool {
    match expr {
        Expr::BinOp(BinOp::Sub, left, right) => {
            matches!(left.as_ref(), Expr::Ident(id) if id == param_name)
                && matches!(right.as_ref(), Expr::Literal(crate::ast::Literal::Int(1)))
        }
        Expr::FnCall(callee, args) => {
            let Some(name) = expr_to_dotted_name(callee) else {
                return false;
            };
            (name == "Int.sub" || name == "int.sub")
                && args.len() == 2
                && matches!(&args[0], Expr::Ident(id) if id == param_name)
                && matches!(&args[1], Expr::Literal(crate::ast::Literal::Int(1)))
        }
        _ => false,
    }
}

fn collect_calls_from_expr<'a>(expr: &'a Expr, out: &mut Vec<(String, Vec<&'a Expr>)>) {
    match expr {
        Expr::FnCall(callee, args) => {
            if let Some(name) = expr_to_dotted_name(callee) {
                out.push((name, args.iter().collect()));
            }
            collect_calls_from_expr(callee, out);
            for arg in args {
                collect_calls_from_expr(arg, out);
            }
        }
        Expr::TailCall(boxed) => {
            let (name, args) = boxed.as_ref();
            out.push((name.clone(), args.iter().collect()));
            for arg in args {
                collect_calls_from_expr(arg, out);
            }
        }
        Expr::Attr(obj, _) => collect_calls_from_expr(obj, out),
        Expr::BinOp(_, left, right) => {
            collect_calls_from_expr(left, out);
            collect_calls_from_expr(right, out);
        }
        Expr::Match { subject, arms, .. } => {
            collect_calls_from_expr(subject, out);
            for arm in arms {
                collect_calls_from_expr(&arm.body, out);
            }
        }
        Expr::Pipe(left, right) => {
            collect_calls_from_expr(left, out);
            collect_calls_from_expr(right, out);
        }
        Expr::Constructor(_, inner) => {
            if let Some(inner) = inner {
                collect_calls_from_expr(inner, out);
            }
        }
        Expr::ErrorProp(inner) => collect_calls_from_expr(inner, out),
        Expr::InterpolatedStr(parts) => {
            for p in parts {
                if let crate::ast::StrPart::Parsed(e) = p {
                    collect_calls_from_expr(e, out);
                }
            }
        }
        Expr::List(items) | Expr::Tuple(items) => {
            for item in items {
                collect_calls_from_expr(item, out);
            }
        }
        Expr::MapLiteral(entries) => {
            for (k, v) in entries {
                collect_calls_from_expr(k, out);
                collect_calls_from_expr(v, out);
            }
        }
        Expr::RecordCreate { fields, .. } => {
            for (_, v) in fields {
                collect_calls_from_expr(v, out);
            }
        }
        Expr::RecordUpdate { base, updates, .. } => {
            collect_calls_from_expr(base, out);
            for (_, v) in updates {
                collect_calls_from_expr(v, out);
            }
        }
        Expr::Literal(_) | Expr::Ident(_) | Expr::Resolved(_) => {}
    }
}

fn collect_calls_from_body<'a>(body: &'a FnBody) -> Vec<(String, Vec<&'a Expr>)> {
    let mut out = Vec::new();
    match body {
        FnBody::Expr(expr) => collect_calls_from_expr(expr, &mut out),
        FnBody::Block(stmts) => {
            for stmt in stmts {
                match stmt {
                    Stmt::Binding(_, _, expr) | Stmt::Expr(expr) => {
                        collect_calls_from_expr(expr, &mut out)
                    }
                }
            }
        }
    }
    out
}

fn collect_list_tail_binders_from_expr(
    expr: &Expr,
    list_param_name: &str,
    tails: &mut HashSet<String>,
) {
    match expr {
        Expr::Match { subject, arms, .. } => {
            if matches!(subject.as_ref(), Expr::Ident(id) if id == list_param_name) {
                for MatchArm { pattern, .. } in arms {
                    if let Pattern::Cons(_, tail) = pattern {
                        tails.insert(tail.clone());
                    }
                }
            }
            for arm in arms {
                collect_list_tail_binders_from_expr(&arm.body, list_param_name, tails);
            }
            collect_list_tail_binders_from_expr(subject, list_param_name, tails);
        }
        Expr::FnCall(callee, args) => {
            collect_list_tail_binders_from_expr(callee, list_param_name, tails);
            for arg in args {
                collect_list_tail_binders_from_expr(arg, list_param_name, tails);
            }
        }
        Expr::TailCall(boxed) => {
            let (_, args) = boxed.as_ref();
            for arg in args {
                collect_list_tail_binders_from_expr(arg, list_param_name, tails);
            }
        }
        Expr::Attr(obj, _) => collect_list_tail_binders_from_expr(obj, list_param_name, tails),
        Expr::BinOp(_, left, right) | Expr::Pipe(left, right) => {
            collect_list_tail_binders_from_expr(left, list_param_name, tails);
            collect_list_tail_binders_from_expr(right, list_param_name, tails);
        }
        Expr::Constructor(_, inner) => {
            if let Some(inner) = inner {
                collect_list_tail_binders_from_expr(inner, list_param_name, tails);
            }
        }
        Expr::ErrorProp(inner) => {
            collect_list_tail_binders_from_expr(inner, list_param_name, tails)
        }
        Expr::InterpolatedStr(parts) => {
            for p in parts {
                if let crate::ast::StrPart::Parsed(e) = p {
                    collect_list_tail_binders_from_expr(e, list_param_name, tails);
                }
            }
        }
        Expr::List(items) | Expr::Tuple(items) => {
            for item in items {
                collect_list_tail_binders_from_expr(item, list_param_name, tails);
            }
        }
        Expr::MapLiteral(entries) => {
            for (k, v) in entries {
                collect_list_tail_binders_from_expr(k, list_param_name, tails);
                collect_list_tail_binders_from_expr(v, list_param_name, tails);
            }
        }
        Expr::RecordCreate { fields, .. } => {
            for (_, v) in fields {
                collect_list_tail_binders_from_expr(v, list_param_name, tails);
            }
        }
        Expr::RecordUpdate { base, updates, .. } => {
            collect_list_tail_binders_from_expr(base, list_param_name, tails);
            for (_, v) in updates {
                collect_list_tail_binders_from_expr(v, list_param_name, tails);
            }
        }
        Expr::Literal(_) | Expr::Ident(_) | Expr::Resolved(_) => {}
    }
}

fn collect_list_tail_binders(fd: &FnDef, list_param_name: &str) -> HashSet<String> {
    let mut tails = HashSet::new();
    match fd.body.as_ref() {
        FnBody::Expr(expr) => {
            collect_list_tail_binders_from_expr(expr, list_param_name, &mut tails)
        }
        FnBody::Block(stmts) => {
            for stmt in stmts {
                match stmt {
                    Stmt::Binding(_, _, expr) | Stmt::Expr(expr) => {
                        collect_list_tail_binders_from_expr(expr, list_param_name, &mut tails)
                    }
                }
            }
        }
    }
    tails
}

fn supports_single_int_countdown(fd: &FnDef) -> bool {
    let Some((param_name, param_ty)) = fd.params.first() else {
        return false;
    };
    if param_ty != "Int" {
        return false;
    }
    let recursive_calls: Vec<Option<&Expr>> = collect_calls_from_body(fd.body.as_ref())
        .into_iter()
        .filter(|(name, _)| call_matches(name, &fd.name))
        .map(|(_, args)| args.first().copied())
        .collect();
    if recursive_calls.is_empty() {
        return false;
    }
    recursive_calls
        .into_iter()
        .all(|arg0| arg0.is_some_and(|e| is_int_minus_one(e, param_name)))
}

fn supports_single_list_structural(fd: &FnDef) -> bool {
    let Some((param_name, param_ty)) = fd.params.first() else {
        return false;
    };
    if !(param_ty.starts_with("List<") || param_ty == "List") {
        return false;
    }

    let tails = collect_list_tail_binders(fd, param_name);
    if tails.is_empty() {
        return false;
    }

    let recursive_calls: Vec<Option<&Expr>> = collect_calls_from_body(fd.body.as_ref())
        .into_iter()
        .filter(|(name, _)| call_matches(name, &fd.name))
        .map(|(_, args)| args.first().copied())
        .collect();
    if recursive_calls.is_empty() {
        return false;
    }

    recursive_calls.into_iter().all(|arg0| {
        matches!(
            arg0,
            Some(Expr::Ident(id)) if tails.contains(id)
        )
    })
}

fn is_ident(expr: &Expr, name: &str) -> bool {
    matches!(expr, Expr::Ident(id) if id == name)
}

fn is_int_plus_positive(expr: &Expr, param_name: &str) -> bool {
    match expr {
        Expr::BinOp(BinOp::Add, left, right) => {
            matches!(left.as_ref(), Expr::Ident(id) if id == param_name)
                && matches!(right.as_ref(), Expr::Literal(crate::ast::Literal::Int(n)) if *n >= 1)
        }
        Expr::FnCall(callee, args) => {
            let Some(name) = expr_to_dotted_name(callee) else {
                return false;
            };
            (name == "Int.add" || name == "int.add")
                && args.len() == 2
                && matches!(&args[0], Expr::Ident(id) if id == param_name)
                && matches!(&args[1], Expr::Literal(crate::ast::Literal::Int(n)) if *n >= 1)
        }
        _ => false,
    }
}

fn is_skip_ws_advance(expr: &Expr, string_param: &str, pos_param: &str) -> bool {
    let Expr::FnCall(callee, args) = expr else {
        return false;
    };
    let Some(name) = expr_to_dotted_name(callee) else {
        return false;
    };
    if !call_matches(&name, "skipWs") || args.len() != 2 {
        return false;
    }
    is_ident(&args[0], string_param) && is_int_plus_positive(&args[1], pos_param)
}

fn is_skip_ws_same(expr: &Expr, string_param: &str, pos_param: &str) -> bool {
    let Expr::FnCall(callee, args) = expr else {
        return false;
    };
    let Some(name) = expr_to_dotted_name(callee) else {
        return false;
    };
    if !call_matches(&name, "skipWs") || args.len() != 2 {
        return false;
    }
    is_ident(&args[0], string_param) && is_ident(&args[1], pos_param)
}

fn is_string_pos_advance(expr: &Expr, string_param: &str, pos_param: &str) -> bool {
    is_int_plus_positive(expr, pos_param) || is_skip_ws_advance(expr, string_param, pos_param)
}

#[derive(Clone, Copy, Debug, Eq, PartialEq)]
enum StringPosEdge {
    Same,
    Advance,
}

fn classify_string_pos_edge(
    expr: &Expr,
    string_param: &str,
    pos_param: &str,
) -> Option<StringPosEdge> {
    if is_ident(expr, pos_param) || is_skip_ws_same(expr, string_param, pos_param) {
        return Some(StringPosEdge::Same);
    }
    if is_string_pos_advance(expr, string_param, pos_param) {
        return Some(StringPosEdge::Advance);
    }
    if let Expr::FnCall(callee, args) = expr {
        let name = expr_to_dotted_name(callee)?;
        if call_matches(&name, "skipWs") && args.len() == 2 && is_ident(&args[0], string_param) {
            if matches!(&args[1], Expr::Ident(id) if id != pos_param) {
                return Some(StringPosEdge::Advance);
            }
        }
    }
    if matches!(expr, Expr::Ident(id) if id != pos_param) {
        return Some(StringPosEdge::Advance);
    }
    None
}

fn ranks_from_same_edges(
    names: &HashSet<String>,
    same_edges: &HashMap<String, HashSet<String>>,
) -> Option<HashMap<String, usize>> {
    let mut indegree: HashMap<String, usize> = names.iter().map(|n| (n.clone(), 0)).collect();
    for outs in same_edges.values() {
        for to in outs {
            if let Some(entry) = indegree.get_mut(to) {
                *entry += 1;
            } else {
                return None;
            }
        }
    }

    let mut queue: Vec<String> = indegree
        .iter()
        .filter_map(|(name, &deg)| (deg == 0).then_some(name.clone()))
        .collect();
    queue.sort();
    let mut topo = Vec::new();
    while let Some(node) = queue.pop() {
        topo.push(node.clone());
        let outs = same_edges.get(&node).cloned().unwrap_or_default();
        let mut newly_zero = Vec::new();
        for to in outs {
            if let Some(entry) = indegree.get_mut(&to) {
                *entry -= 1;
                if *entry == 0 {
                    newly_zero.push(to);
                }
            } else {
                return None;
            }
        }
        newly_zero.sort();
        queue.extend(newly_zero);
    }

    if topo.len() != names.len() {
        return None;
    }

    let n = topo.len();
    let mut ranks = HashMap::new();
    for (idx, name) in topo.into_iter().enumerate() {
        ranks.insert(name, n - idx);
    }
    Some(ranks)
}

fn supports_single_string_pos_advance(fd: &FnDef) -> bool {
    let Some((string_param, string_ty)) = fd.params.first() else {
        return false;
    };
    let Some((pos_param, pos_ty)) = fd.params.get(1) else {
        return false;
    };
    if string_ty != "String" || pos_ty != "Int" {
        return false;
    }

    let recursive_calls: Vec<(Option<&Expr>, Option<&Expr>)> =
        collect_calls_from_body(fd.body.as_ref())
            .into_iter()
            .filter(|(name, _)| call_matches(name, &fd.name))
            .map(|(_, args)| (args.first().copied(), args.get(1).copied()))
            .collect();
    if recursive_calls.is_empty() {
        return false;
    }

    recursive_calls.into_iter().all(|(arg0, arg1)| {
        arg0.is_some_and(|e| is_ident(e, string_param))
            && arg1.is_some_and(|e| is_string_pos_advance(e, string_param, pos_param))
    })
}

fn supports_mutual_int_countdown(component: &[&FnDef]) -> bool {
    if component.len() < 2 {
        return false;
    }
    if component
        .iter()
        .any(|fd| !matches!(fd.params.first(), Some((_, t)) if t == "Int"))
    {
        return false;
    }
    let names: HashSet<String> = component.iter().map(|fd| fd.name.clone()).collect();
    let mut any_intra = false;
    for fd in component {
        let param_name = &fd.params[0].0;
        for (callee, args) in collect_calls_from_body(fd.body.as_ref()) {
            if !call_is_in_set(&callee, &names) {
                continue;
            }
            any_intra = true;
            let Some(arg0) = args.first().copied() else {
                return false;
            };
            if !is_int_minus_one(arg0, param_name) {
                return false;
            }
        }
    }
    any_intra
}

fn supports_mutual_string_pos_advance(component: &[&FnDef]) -> Option<HashMap<String, usize>> {
    if component.len() < 2 {
        return None;
    }
    if component.iter().any(|fd| {
        !matches!(fd.params.first(), Some((_, t)) if t == "String")
            || !matches!(fd.params.get(1), Some((_, t)) if t == "Int")
    }) {
        return None;
    }

    let names: HashSet<String> = component.iter().map(|fd| fd.name.clone()).collect();
    let mut same_edges: HashMap<String, HashSet<String>> =
        names.iter().map(|n| (n.clone(), HashSet::new())).collect();
    let mut any_intra = false;

    for fd in component {
        let string_param = &fd.params[0].0;
        let pos_param = &fd.params[1].0;
        for (callee_raw, args) in collect_calls_from_body(fd.body.as_ref()) {
            let Some(callee) = canonical_callee_name(&callee_raw, &names) else {
                continue;
            };
            any_intra = true;

            let Some(arg0) = args.first().copied() else {
                return None;
            };
            let Some(arg1) = args.get(1).copied() else {
                return None;
            };

            if !is_ident(arg0, string_param) {
                return None;
            }

            match classify_string_pos_edge(arg1, string_param, pos_param) {
                Some(StringPosEdge::Same) => {
                    if let Some(edges) = same_edges.get_mut(&fd.name) {
                        edges.insert(callee);
                    } else {
                        return None;
                    }
                }
                Some(StringPosEdge::Advance) => {}
                None => return None,
            }
        }
    }

    if !any_intra {
        return None;
    }

    ranks_from_same_edges(&names, &same_edges)
}

fn metric_param_index_for_fn(fd: &FnDef) -> usize {
    if fd.params.len() >= 2
        && fd.params[0].1 == "String"
        && (fd.params[1].1 == "Int"
            || fd.params[1].1 == "List"
            || fd.params[1].1.starts_with("List<"))
    {
        return 1;
    }
    0
}

fn supports_mutual_sizeof_ranked(component: &[&FnDef]) -> Option<HashMap<String, (usize, usize)>> {
    if component.len() < 2 {
        return None;
    }
    let names: HashSet<String> = component.iter().map(|fd| fd.name.clone()).collect();
    let metric_idx: HashMap<String, usize> = component
        .iter()
        .map(|fd| (fd.name.clone(), metric_param_index_for_fn(fd)))
        .collect();
    if component.iter().any(|fd| {
        let idx = metric_idx.get(&fd.name).copied().unwrap_or(usize::MAX);
        idx >= fd.params.len()
    }) {
        return None;
    }

    let mut same_edges: HashMap<String, HashSet<String>> =
        names.iter().map(|n| (n.clone(), HashSet::new())).collect();
    let mut any_intra = false;
    for fd in component {
        let caller_metric_idx = metric_idx.get(&fd.name).copied()?;
        let caller_metric_param = &fd.params[caller_metric_idx].0;
        for (callee_raw, args) in collect_calls_from_body(fd.body.as_ref()) {
            let Some(callee) = canonical_callee_name(&callee_raw, &names) else {
                continue;
            };
            any_intra = true;
            let callee_metric_idx = metric_idx.get(&callee).copied()?;
            let Some(metric_arg) = args.get(callee_metric_idx).copied() else {
                return None;
            };
            if is_ident(metric_arg, caller_metric_param) {
                if let Some(edges) = same_edges.get_mut(&fd.name) {
                    edges.insert(callee);
                } else {
                    return None;
                }
            }
        }
    }
    if !any_intra {
        return None;
    }

    let ranks = ranks_from_same_edges(&names, &same_edges)?;
    let mut out = HashMap::new();
    for fd in component {
        let rank = ranks.get(&fd.name).copied()?;
        let idx = metric_idx.get(&fd.name).copied()?;
        out.insert(fd.name.clone(), (rank, idx));
    }
    Some(out)
}

fn proof_mode_recursion_analysis(
    ctx: &CodegenContext,
) -> (HashMap<String, RecursionPlan>, Vec<String>) {
    let mut plans = HashMap::new();
    let mut issues = Vec::new();

    let all_pure = pure_fns(ctx);
    let recursive_names = recursive_pure_fn_names(ctx);
    let components = call_graph::ordered_fn_components(&all_pure);

    for component in components {
        if component.is_empty() {
            continue;
        }
        let is_recursive_component =
            component.len() > 1 || recursive_names.contains(&component[0].name);
        if !is_recursive_component {
            continue;
        }

        if component.len() > 1 {
            if supports_mutual_int_countdown(&component) {
                for fd in &component {
                    plans.insert(fd.name.clone(), RecursionPlan::MutualIntCountdown);
                }
            } else if let Some(ranks) = supports_mutual_string_pos_advance(&component) {
                for fd in &component {
                    if let Some(rank) = ranks.get(&fd.name).copied() {
                        plans.insert(
                            fd.name.clone(),
                            RecursionPlan::MutualStringPosAdvance { rank },
                        );
                    } else {
                        issues.push(format!(
                            "internal proof-mode error: missing mutual String+pos rank for function '{}'",
                            fd.name
                        ));
                    }
                }
            } else if let Some(rank_idx) = supports_mutual_sizeof_ranked(&component) {
                for fd in &component {
                    if let Some((rank, metric_param_index)) = rank_idx.get(&fd.name).copied() {
                        plans.insert(
                            fd.name.clone(),
                            RecursionPlan::MutualSizeOfRanked {
                                rank,
                                metric_param_index,
                            },
                        );
                    } else {
                        issues.push(format!(
                            "internal proof-mode error: missing mutual sizeOf plan for function '{}'",
                            fd.name
                        ));
                    }
                }
            } else {
                let names = component
                    .iter()
                    .map(|fd| fd.name.clone())
                    .collect::<Vec<_>>()
                    .join(", ");
                issues.push(format!(
                    "unsupported mutual recursion group (supported: Int countdown on first param, String+pos advance, or ranked-sizeOf mutual plan): {}",
                    names
                ));
            }
            continue;
        }

        let fd = component[0];
        if supports_single_int_countdown(fd) {
            plans.insert(fd.name.clone(), RecursionPlan::IntCountdown);
        } else if supports_single_list_structural(fd) {
            plans.insert(fd.name.clone(), RecursionPlan::ListStructural);
        } else if supports_single_string_pos_advance(fd) {
            plans.insert(fd.name.clone(), RecursionPlan::StringPosAdvance);
        } else {
            issues.push(format!(
                "recursive function '{}' is outside proof subset (supported: Int countdown, List structural, String+pos advance, or supported mutual recursion class)",
                fd.name
            ));
        }
    }

    (plans, issues)
}

/// Strict proof-mode gate for Lean transpilation.
///
/// Returns human-readable blockers that would force generated Lean to rely on
/// non-proof recursion fallback (`partial`).
pub fn proof_mode_issues(ctx: &CodegenContext) -> Vec<String> {
    let (_plans, issues) = proof_mode_recursion_analysis(ctx);
    issues
}

/// Transpile an Aver program to a Lean 4 project.
pub fn transpile(ctx: &CodegenContext) -> ProjectOutput {
    transpile_with_verify_mode(ctx, VerifyEmitMode::NativeDecide)
}

/// Proof-mode transpilation.
///
/// Uses recursion plans validated by `proof_mode_issues` and emits supported
/// recursive functions without `partial`, adding `termination_by` scaffolding.
pub fn transpile_for_proof_mode(
    ctx: &CodegenContext,
    verify_mode: VerifyEmitMode,
) -> ProjectOutput {
    let (plans, _issues) = proof_mode_recursion_analysis(ctx);

    let mut sections = Vec::new();
    sections.push(generate_prelude());
    sections.push(String::new());

    // Reuse the same type emission as standard mode.
    for module in &ctx.modules {
        for td in &module.type_defs {
            sections.push(toplevel::emit_type_def(td));
            if toplevel::is_recursive_type_def(td) {
                sections.push(toplevel::emit_recursive_decidable_eq(
                    toplevel::type_def_name(td),
                ));
            }
            sections.push(String::new());
        }
    }
    for td in &ctx.type_defs {
        sections.push(toplevel::emit_type_def(td));
        if toplevel::is_recursive_type_def(td) {
            sections.push(toplevel::emit_recursive_decidable_eq(
                toplevel::type_def_name(td),
            ));
        }
        sections.push(String::new());
    }

    emit_pure_functions_proof(ctx, &plans, &mut sections);

    for item in &ctx.items {
        if let TopLevel::Decision(db) = item {
            sections.push(toplevel::emit_decision(db));
            sections.push(String::new());
        }
    }

    let mut verify_case_counters: HashMap<String, usize> = HashMap::new();
    for item in &ctx.items {
        if let TopLevel::Verify(vb) = item {
            let key = verify_counter_key(vb);
            let start_idx = *verify_case_counters.get(&key).unwrap_or(&0);
            let (emitted, next_idx) = toplevel::emit_verify_block(vb, ctx, verify_mode, start_idx);
            verify_case_counters.insert(key, next_idx);
            sections.push(emitted);
            sections.push(String::new());
        }
    }

    let lean_source = sections.join("\n");
    let project_name = capitalize_first(&ctx.project_name);
    let lakefile = generate_lakefile(&project_name);
    let toolchain = generate_toolchain();
    ProjectOutput {
        files: vec![
            ("lakefile.lean".to_string(), lakefile),
            ("lean-toolchain".to_string(), toolchain),
            (format!("{}.lean", project_name), lean_source),
        ],
    }
}

/// Transpile an Aver program to a Lean 4 project with configurable verify proof mode.
///
/// - `NativeDecide` emits `example ... := by native_decide`
/// - `Sorry` emits `example ... := by sorry`
/// - `TheoremSkeleton` emits named theorem skeletons with `sorry`
pub fn transpile_with_verify_mode(
    ctx: &CodegenContext,
    verify_mode: VerifyEmitMode,
) -> ProjectOutput {
    let mut sections = Vec::new();

    // Prelude
    sections.push(generate_prelude());
    sections.push(String::new());

    // Detect recursive functions for `partial` annotation
    let recursive_fns = call_graph::find_recursive_fns(&ctx.items);

    // Module type definitions (from depends)
    for module in &ctx.modules {
        for td in &module.type_defs {
            sections.push(toplevel::emit_type_def(td));
            // #18: Recursive types need unsafe DecidableEq instance
            if toplevel::is_recursive_type_def(td) {
                sections.push(toplevel::emit_recursive_decidable_eq(
                    toplevel::type_def_name(td),
                ));
            }
            sections.push(String::new());
        }
    }

    // Type definitions
    for td in &ctx.type_defs {
        sections.push(toplevel::emit_type_def(td));
        // #18: Recursive types need unsafe DecidableEq instance
        if toplevel::is_recursive_type_def(td) {
            sections.push(toplevel::emit_recursive_decidable_eq(
                toplevel::type_def_name(td),
            ));
        }
        sections.push(String::new());
    }

    // Emit pure functions in SCC-topological order:
    // callees first, then callers; SCCs as `mutual` blocks.
    emit_pure_functions(ctx, &recursive_fns, &mut sections);

    // Decision blocks (as comments)
    for item in &ctx.items {
        if let TopLevel::Decision(db) = item {
            sections.push(toplevel::emit_decision(db));
            sections.push(String::new());
        }
    }

    // Verify blocks → proof items (`native_decide` by default, optional `sorry`/theorem stubs).
    let mut verify_case_counters: HashMap<String, usize> = HashMap::new();
    for item in &ctx.items {
        if let TopLevel::Verify(vb) = item {
            let key = verify_counter_key(vb);
            let start_idx = *verify_case_counters.get(&key).unwrap_or(&0);
            let (emitted, next_idx) = toplevel::emit_verify_block(vb, ctx, verify_mode, start_idx);
            verify_case_counters.insert(key, next_idx);
            sections.push(emitted);
            sections.push(String::new());
        }
    }

    let lean_source = sections.join("\n");

    // Project files
    let project_name = capitalize_first(&ctx.project_name);
    let lakefile = generate_lakefile(&project_name);
    let toolchain = generate_toolchain();

    ProjectOutput {
        files: vec![
            ("lakefile.lean".to_string(), lakefile),
            ("lean-toolchain".to_string(), toolchain),
            (format!("{}.lean", project_name), lean_source),
        ],
    }
}

fn emit_pure_functions(
    ctx: &CodegenContext,
    recursive_fns: &HashSet<String>,
    sections: &mut Vec<String>,
) {
    let all_fns: Vec<&FnDef> = ctx
        .modules
        .iter()
        .flat_map(|m| m.fn_defs.iter())
        .chain(ctx.fn_defs.iter())
        .filter(|fd| toplevel::is_pure_fn(fd))
        .collect();
    if all_fns.is_empty() {
        return;
    }

    let components = call_graph::ordered_fn_components(&all_fns);
    for fns in components {
        if fns.is_empty() {
            continue;
        }

        // Multi-node SCC => emit `mutual ... end`.
        if fns.len() > 1 {
            sections.push(toplevel::emit_mutual_group(&fns, ctx));
            sections.push(String::new());
            continue;
        }

        // Singleton SCC => regular `def` (recursive singletons still get `partial`
        // via `recursive_fns` in emit_fn_def).
        if let Some(code) = toplevel::emit_fn_def(fns[0], recursive_fns, ctx) {
            sections.push(code);
            sections.push(String::new());
        }
    }
}

fn emit_pure_functions_proof(
    ctx: &CodegenContext,
    plans: &HashMap<String, RecursionPlan>,
    sections: &mut Vec<String>,
) {
    let all_fns: Vec<&FnDef> = pure_fns(ctx);
    if all_fns.is_empty() {
        return;
    }

    let components = call_graph::ordered_fn_components(&all_fns);
    for fns in components {
        if fns.is_empty() {
            continue;
        }
        if fns.len() > 1 {
            sections.push(toplevel::emit_mutual_group_proof(&fns, ctx, plans));
            sections.push(String::new());
            continue;
        }

        if let Some(code) =
            toplevel::emit_fn_def_proof(fns[0], plans.get(&fns[0].name).copied(), ctx)
        {
            sections.push(code);
            sections.push(String::new());
        }
    }
}

fn generate_prelude() -> String {
    [
        LEAN_PRELUDE_HEADER,
        LEAN_PRELUDE_FLOAT_COE,
        LEAN_PRELUDE_FLOAT_DEC_EQ,
        LEAN_PRELUDE_EXCEPT_DEC_EQ,
        LEAN_PRELUDE_EXCEPT_NS,
        LEAN_PRELUDE_OPTION_TO_EXCEPT,
        LEAN_PRELUDE_STRING_HADD,
        AVER_MAP_PRELUDE,
        LEAN_PRELUDE_AVER_LIST,
        LEAN_PRELUDE_STRING_HELPERS,
        LEAN_PRELUDE_NUMERIC_PARSE,
        LEAN_PRELUDE_CHAR_BYTE,
    ]
    .join("\n\n")
}

fn generate_lakefile(project_name: &str) -> String {
    format!(
        r#"import Lake
open Lake DSL

package «{}» where
  version := v!"0.1.0"

@[default_target]
lean_lib «{}» where
  srcDir := "."
"#,
        project_name.to_lowercase(),
        project_name
    )
}

fn generate_toolchain() -> String {
    "leanprover/lean4:v4.15.0\n".to_string()
}

fn capitalize_first(s: &str) -> String {
    let mut chars = s.chars();
    match chars.next() {
        None => String::new(),
        Some(c) => c.to_uppercase().to_string() + chars.as_str(),
    }
}

#[cfg(test)]
mod tests {
    use super::{
        VerifyEmitMode, generate_prelude, proof_mode_issues, transpile, transpile_for_proof_mode,
        transpile_with_verify_mode,
    };
    use crate::ast::{
        BinOp, Expr, FnBody, FnDef, Literal, MatchArm, Pattern, Stmt, TopLevel, TypeDef,
        TypeVariant, VerifyBlock, VerifyGiven, VerifyGivenDomain, VerifyKind, VerifyLaw,
    };
    use crate::codegen::CodegenContext;
    use std::collections::{HashMap, HashSet};
    use std::rc::Rc;

    fn empty_ctx() -> CodegenContext {
        CodegenContext {
            items: vec![],
            fn_sigs: HashMap::new(),
            memo_fns: HashSet::new(),
            memo_safe_types: HashSet::new(),
            type_defs: vec![],
            fn_defs: vec![],
            project_name: "verify_mode".to_string(),
            modules: vec![],
            module_prefixes: HashSet::new(),
        }
    }

    fn empty_ctx_with_verify_case() -> CodegenContext {
        let mut ctx = empty_ctx();
        ctx.items.push(TopLevel::Verify(VerifyBlock {
            fn_name: "f".to_string(),
            line: 1,
            cases: vec![(
                Expr::Literal(Literal::Int(1)),
                Expr::Literal(Literal::Int(1)),
            )],
            kind: VerifyKind::Cases,
        }));
        ctx
    }

    fn empty_ctx_with_two_verify_blocks_same_fn() -> CodegenContext {
        let mut ctx = empty_ctx();
        ctx.items.push(TopLevel::Verify(VerifyBlock {
            fn_name: "f".to_string(),
            line: 1,
            cases: vec![(
                Expr::Literal(Literal::Int(1)),
                Expr::Literal(Literal::Int(1)),
            )],
            kind: VerifyKind::Cases,
        }));
        ctx.items.push(TopLevel::Verify(VerifyBlock {
            fn_name: "f".to_string(),
            line: 2,
            cases: vec![(
                Expr::Literal(Literal::Int(2)),
                Expr::Literal(Literal::Int(2)),
            )],
            kind: VerifyKind::Cases,
        }));
        ctx
    }

    fn empty_ctx_with_verify_law() -> CodegenContext {
        let mut ctx = empty_ctx();
        let add = FnDef {
            name: "add".to_string(),
            line: 1,
            params: vec![
                ("a".to_string(), "Int".to_string()),
                ("b".to_string(), "Int".to_string()),
            ],
            return_type: "Int".to_string(),
            effects: vec![],
            desc: None,
            body: Rc::new(FnBody::Expr(Expr::BinOp(
                BinOp::Add,
                Box::new(Expr::Ident("a".to_string())),
                Box::new(Expr::Ident("b".to_string())),
            ))),
            resolution: None,
        };
        ctx.fn_defs.push(add.clone());
        ctx.items.push(TopLevel::FnDef(add));
        ctx.items.push(TopLevel::Verify(VerifyBlock {
            fn_name: "add".to_string(),
            line: 1,
            cases: vec![
                (
                    Expr::FnCall(
                        Box::new(Expr::Ident("add".to_string())),
                        vec![
                            Expr::Literal(Literal::Int(1)),
                            Expr::Literal(Literal::Int(2)),
                        ],
                    ),
                    Expr::FnCall(
                        Box::new(Expr::Ident("add".to_string())),
                        vec![
                            Expr::Literal(Literal::Int(2)),
                            Expr::Literal(Literal::Int(1)),
                        ],
                    ),
                ),
                (
                    Expr::FnCall(
                        Box::new(Expr::Ident("add".to_string())),
                        vec![
                            Expr::Literal(Literal::Int(2)),
                            Expr::Literal(Literal::Int(3)),
                        ],
                    ),
                    Expr::FnCall(
                        Box::new(Expr::Ident("add".to_string())),
                        vec![
                            Expr::Literal(Literal::Int(3)),
                            Expr::Literal(Literal::Int(2)),
                        ],
                    ),
                ),
            ],
            kind: VerifyKind::Law(VerifyLaw {
                name: "commutative".to_string(),
                givens: vec![
                    VerifyGiven {
                        name: "a".to_string(),
                        type_name: "Int".to_string(),
                        domain: VerifyGivenDomain::IntRange { start: 1, end: 2 },
                    },
                    VerifyGiven {
                        name: "b".to_string(),
                        type_name: "Int".to_string(),
                        domain: VerifyGivenDomain::Explicit(vec![
                            Expr::Literal(Literal::Int(2)),
                            Expr::Literal(Literal::Int(3)),
                        ]),
                    },
                ],
                lhs: Expr::FnCall(
                    Box::new(Expr::Ident("add".to_string())),
                    vec![Expr::Ident("a".to_string()), Expr::Ident("b".to_string())],
                ),
                rhs: Expr::FnCall(
                    Box::new(Expr::Ident("add".to_string())),
                    vec![Expr::Ident("b".to_string()), Expr::Ident("a".to_string())],
                ),
            }),
        }));
        ctx
    }

    #[test]
    fn prelude_normalizes_float_string_format() {
        let prelude = generate_prelude();
        assert!(
            prelude.contains("private def normalizeFloatString (s : String) : String :="),
            "missing normalizeFloatString helper in prelude"
        );
        assert!(
            prelude.contains(
                "def String.fromFloat (f : Float) : String := normalizeFloatString (toString f)"
            ),
            "String.fromFloat should normalize Lean float formatting"
        );
    }

    #[test]
    fn prelude_validates_char_from_code_unicode_bounds() {
        let prelude = generate_prelude();
        assert!(
            prelude.contains("if n < 0 || n > 1114111 then none"),
            "Char.fromCode should reject code points above Unicode max"
        );
        assert!(
            prelude.contains("else if n >= 55296 && n <= 57343 then none"),
            "Char.fromCode should reject surrogate code points"
        );
    }

    #[test]
    fn prelude_includes_map_set_helper_lemmas() {
        let prelude = generate_prelude();
        assert!(
            prelude.contains("theorem has_set_self [BEq α]"),
            "missing AverMap.has_set_self helper theorem"
        );
        assert!(
            prelude.contains("theorem get_set_self [BEq α]"),
            "missing AverMap.get_set_self helper theorem"
        );
    }

    #[test]
    fn transpile_emits_native_decide_for_verify_by_default() {
        let out = transpile(&empty_ctx_with_verify_case());
        let lean = out
            .files
            .iter()
            .find_map(|(name, content)| (name == "Verify_mode.lean").then_some(content))
            .expect("expected generated Lean file");
        assert!(lean.contains("example : 1 = 1 := by native_decide"));
    }

    #[test]
    fn transpile_can_emit_sorry_for_verify_when_requested() {
        let out = transpile_with_verify_mode(&empty_ctx_with_verify_case(), VerifyEmitMode::Sorry);
        let lean = out
            .files
            .iter()
            .find_map(|(name, content)| (name == "Verify_mode.lean").then_some(content))
            .expect("expected generated Lean file");
        assert!(lean.contains("example : 1 = 1 := by sorry"));
    }

    #[test]
    fn transpile_can_emit_theorem_skeletons_for_verify() {
        let out = transpile_with_verify_mode(
            &empty_ctx_with_verify_case(),
            VerifyEmitMode::TheoremSkeleton,
        );
        let lean = out
            .files
            .iter()
            .find_map(|(name, content)| (name == "Verify_mode.lean").then_some(content))
            .expect("expected generated Lean file");
        assert!(lean.contains("theorem f_verify_1 : 1 = 1 := by"));
        assert!(lean.contains("  sorry"));
    }

    #[test]
    fn theorem_skeleton_numbering_is_global_per_function_across_verify_blocks() {
        let out = transpile_with_verify_mode(
            &empty_ctx_with_two_verify_blocks_same_fn(),
            VerifyEmitMode::TheoremSkeleton,
        );
        let lean = out
            .files
            .iter()
            .find_map(|(name, content)| (name == "Verify_mode.lean").then_some(content))
            .expect("expected generated Lean file");
        assert!(lean.contains("theorem f_verify_1 : 1 = 1 := by"));
        assert!(lean.contains("theorem f_verify_2 : 2 = 2 := by"));
    }

    #[test]
    fn transpile_emits_named_theorems_for_verify_law() {
        let out = transpile(&empty_ctx_with_verify_law());
        let lean = out
            .files
            .iter()
            .find_map(|(name, content)| (name == "Verify_mode.lean").then_some(content))
            .expect("expected generated Lean file");
        assert!(lean.contains("-- verify law add.commutative (2 cases)"));
        assert!(lean.contains("-- given a: Int = 1..2"));
        assert!(lean.contains("-- given b: Int = [2, 3]"));
        assert!(lean.contains(
            "theorem add_law_commutative : ∀ (a : Int) (b : Int), add a b = add b a := by"
        ));
        assert!(lean.contains("  intro a b"));
        assert!(lean.contains("  simp [add, Int.add_comm]"));
        assert!(lean.contains(
            "theorem add_law_commutative_sample_1 : add 1 2 = add 2 1 := by native_decide"
        ));
        assert!(lean.contains(
            "theorem add_law_commutative_sample_2 : add 2 3 = add 3 2 := by native_decide"
        ));
    }

    #[test]
    fn transpile_auto_proves_reflexive_law_with_rfl() {
        let mut ctx = empty_ctx();
        ctx.items.push(TopLevel::Verify(VerifyBlock {
            fn_name: "idLaw".to_string(),
            line: 1,
            cases: vec![(
                Expr::Literal(Literal::Int(1)),
                Expr::Literal(Literal::Int(1)),
            )],
            kind: VerifyKind::Law(VerifyLaw {
                name: "reflexive".to_string(),
                givens: vec![VerifyGiven {
                    name: "x".to_string(),
                    type_name: "Int".to_string(),
                    domain: VerifyGivenDomain::IntRange { start: 1, end: 2 },
                }],
                lhs: Expr::Ident("x".to_string()),
                rhs: Expr::Ident("x".to_string()),
            }),
        }));
        let out = transpile(&ctx);
        let lean = out
            .files
            .iter()
            .find_map(|(name, content)| (name == "Verify_mode.lean").then_some(content))
            .expect("expected generated Lean file");
        assert!(lean.contains("theorem idLaw_law_reflexive : ∀ (x : Int), x = x := by"));
        assert!(lean.contains("  intro x"));
        assert!(lean.contains("  rfl"));
    }

    #[test]
    fn transpile_auto_proves_identity_law_for_int_add_wrapper() {
        let mut ctx = empty_ctx_with_verify_law();
        ctx.items.push(TopLevel::Verify(VerifyBlock {
            fn_name: "add".to_string(),
            line: 10,
            cases: vec![(
                Expr::FnCall(
                    Box::new(Expr::Ident("add".to_string())),
                    vec![
                        Expr::Literal(Literal::Int(1)),
                        Expr::Literal(Literal::Int(0)),
                    ],
                ),
                Expr::Literal(Literal::Int(1)),
            )],
            kind: VerifyKind::Law(VerifyLaw {
                name: "identityZero".to_string(),
                givens: vec![VerifyGiven {
                    name: "a".to_string(),
                    type_name: "Int".to_string(),
                    domain: VerifyGivenDomain::Explicit(vec![
                        Expr::Literal(Literal::Int(0)),
                        Expr::Literal(Literal::Int(1)),
                    ]),
                }],
                lhs: Expr::FnCall(
                    Box::new(Expr::Ident("add".to_string())),
                    vec![Expr::Ident("a".to_string()), Expr::Literal(Literal::Int(0))],
                ),
                rhs: Expr::Ident("a".to_string()),
            }),
        }));
        let out = transpile(&ctx);
        let lean = out
            .files
            .iter()
            .find_map(|(name, content)| (name == "Verify_mode.lean").then_some(content))
            .expect("expected generated Lean file");
        assert!(lean.contains("theorem add_law_identityZero : ∀ (a : Int), add a 0 = a := by"));
        assert!(lean.contains("  intro a"));
        assert!(lean.contains("  simp [add]"));
    }

    #[test]
    fn transpile_auto_proves_associative_law_for_int_add_wrapper() {
        let mut ctx = empty_ctx_with_verify_law();
        ctx.items.push(TopLevel::Verify(VerifyBlock {
            fn_name: "add".to_string(),
            line: 20,
            cases: vec![(
                Expr::FnCall(
                    Box::new(Expr::Ident("add".to_string())),
                    vec![
                        Expr::FnCall(
                            Box::new(Expr::Ident("add".to_string())),
                            vec![
                                Expr::Literal(Literal::Int(1)),
                                Expr::Literal(Literal::Int(2)),
                            ],
                        ),
                        Expr::Literal(Literal::Int(3)),
                    ],
                ),
                Expr::FnCall(
                    Box::new(Expr::Ident("add".to_string())),
                    vec![
                        Expr::Literal(Literal::Int(1)),
                        Expr::FnCall(
                            Box::new(Expr::Ident("add".to_string())),
                            vec![
                                Expr::Literal(Literal::Int(2)),
                                Expr::Literal(Literal::Int(3)),
                            ],
                        ),
                    ],
                ),
            )],
            kind: VerifyKind::Law(VerifyLaw {
                name: "associative".to_string(),
                givens: vec![
                    VerifyGiven {
                        name: "a".to_string(),
                        type_name: "Int".to_string(),
                        domain: VerifyGivenDomain::Explicit(vec![Expr::Literal(Literal::Int(1))]),
                    },
                    VerifyGiven {
                        name: "b".to_string(),
                        type_name: "Int".to_string(),
                        domain: VerifyGivenDomain::Explicit(vec![Expr::Literal(Literal::Int(2))]),
                    },
                    VerifyGiven {
                        name: "c".to_string(),
                        type_name: "Int".to_string(),
                        domain: VerifyGivenDomain::Explicit(vec![Expr::Literal(Literal::Int(3))]),
                    },
                ],
                lhs: Expr::FnCall(
                    Box::new(Expr::Ident("add".to_string())),
                    vec![
                        Expr::FnCall(
                            Box::new(Expr::Ident("add".to_string())),
                            vec![Expr::Ident("a".to_string()), Expr::Ident("b".to_string())],
                        ),
                        Expr::Ident("c".to_string()),
                    ],
                ),
                rhs: Expr::FnCall(
                    Box::new(Expr::Ident("add".to_string())),
                    vec![
                        Expr::Ident("a".to_string()),
                        Expr::FnCall(
                            Box::new(Expr::Ident("add".to_string())),
                            vec![Expr::Ident("b".to_string()), Expr::Ident("c".to_string())],
                        ),
                    ],
                ),
            }),
        }));
        let out = transpile(&ctx);
        let lean = out
            .files
            .iter()
            .find_map(|(name, content)| (name == "Verify_mode.lean").then_some(content))
            .expect("expected generated Lean file");
        assert!(lean.contains(
            "theorem add_law_associative : ∀ (a : Int) (b : Int) (c : Int), add (add a b) c = add a (add b c) := by"
        ));
        assert!(lean.contains("  intro a b c"));
        assert!(lean.contains("  simp [add, Int.add_assoc]"));
    }

    #[test]
    fn transpile_auto_proves_sub_laws() {
        let mut ctx = empty_ctx();
        let sub = FnDef {
            name: "sub".to_string(),
            line: 1,
            params: vec![
                ("a".to_string(), "Int".to_string()),
                ("b".to_string(), "Int".to_string()),
            ],
            return_type: "Int".to_string(),
            effects: vec![],
            desc: None,
            body: Rc::new(FnBody::Expr(Expr::BinOp(
                BinOp::Sub,
                Box::new(Expr::Ident("a".to_string())),
                Box::new(Expr::Ident("b".to_string())),
            ))),
            resolution: None,
        };
        ctx.fn_defs.push(sub.clone());
        ctx.items.push(TopLevel::FnDef(sub));

        ctx.items.push(TopLevel::Verify(VerifyBlock {
            fn_name: "sub".to_string(),
            line: 10,
            cases: vec![(
                Expr::FnCall(
                    Box::new(Expr::Ident("sub".to_string())),
                    vec![
                        Expr::Literal(Literal::Int(2)),
                        Expr::Literal(Literal::Int(0)),
                    ],
                ),
                Expr::Literal(Literal::Int(2)),
            )],
            kind: VerifyKind::Law(VerifyLaw {
                name: "rightIdentity".to_string(),
                givens: vec![VerifyGiven {
                    name: "a".to_string(),
                    type_name: "Int".to_string(),
                    domain: VerifyGivenDomain::Explicit(vec![Expr::Literal(Literal::Int(2))]),
                }],
                lhs: Expr::FnCall(
                    Box::new(Expr::Ident("sub".to_string())),
                    vec![Expr::Ident("a".to_string()), Expr::Literal(Literal::Int(0))],
                ),
                rhs: Expr::Ident("a".to_string()),
            }),
        }));
        ctx.items.push(TopLevel::Verify(VerifyBlock {
            fn_name: "sub".to_string(),
            line: 20,
            cases: vec![(
                Expr::FnCall(
                    Box::new(Expr::Ident("sub".to_string())),
                    vec![
                        Expr::Literal(Literal::Int(2)),
                        Expr::Literal(Literal::Int(1)),
                    ],
                ),
                Expr::BinOp(
                    BinOp::Sub,
                    Box::new(Expr::Literal(Literal::Int(0))),
                    Box::new(Expr::FnCall(
                        Box::new(Expr::Ident("sub".to_string())),
                        vec![
                            Expr::Literal(Literal::Int(1)),
                            Expr::Literal(Literal::Int(2)),
                        ],
                    )),
                ),
            )],
            kind: VerifyKind::Law(VerifyLaw {
                name: "antiCommutative".to_string(),
                givens: vec![
                    VerifyGiven {
                        name: "a".to_string(),
                        type_name: "Int".to_string(),
                        domain: VerifyGivenDomain::Explicit(vec![Expr::Literal(Literal::Int(2))]),
                    },
                    VerifyGiven {
                        name: "b".to_string(),
                        type_name: "Int".to_string(),
                        domain: VerifyGivenDomain::Explicit(vec![Expr::Literal(Literal::Int(1))]),
                    },
                ],
                lhs: Expr::FnCall(
                    Box::new(Expr::Ident("sub".to_string())),
                    vec![Expr::Ident("a".to_string()), Expr::Ident("b".to_string())],
                ),
                rhs: Expr::BinOp(
                    BinOp::Sub,
                    Box::new(Expr::Literal(Literal::Int(0))),
                    Box::new(Expr::FnCall(
                        Box::new(Expr::Ident("sub".to_string())),
                        vec![Expr::Ident("b".to_string()), Expr::Ident("a".to_string())],
                    )),
                ),
            }),
        }));

        let out = transpile(&ctx);
        let lean = out
            .files
            .iter()
            .find_map(|(name, content)| (name == "Verify_mode.lean").then_some(content))
            .expect("expected generated Lean file");
        assert!(lean.contains("theorem sub_law_rightIdentity : ∀ (a : Int), sub a 0 = a := by"));
        assert!(lean.contains("  simp [sub]"));
        assert!(lean.contains(
            "theorem sub_law_antiCommutative : ∀ (a : Int) (b : Int), sub a b = (-sub b a) := by"
        ));
        assert!(lean.contains("  simp [sub, sub_eq_add_neg, add_comm, add_left_comm, add_assoc]"));
    }

    #[test]
    fn transpile_auto_proves_unary_wrapper_equivalence_law() {
        let mut ctx = empty_ctx();
        let add = FnDef {
            name: "add".to_string(),
            line: 1,
            params: vec![
                ("a".to_string(), "Int".to_string()),
                ("b".to_string(), "Int".to_string()),
            ],
            return_type: "Int".to_string(),
            effects: vec![],
            desc: None,
            body: Rc::new(FnBody::Expr(Expr::BinOp(
                BinOp::Add,
                Box::new(Expr::Ident("a".to_string())),
                Box::new(Expr::Ident("b".to_string())),
            ))),
            resolution: None,
        };
        let add_one = FnDef {
            name: "addOne".to_string(),
            line: 2,
            params: vec![("n".to_string(), "Int".to_string())],
            return_type: "Int".to_string(),
            effects: vec![],
            desc: None,
            body: Rc::new(FnBody::Expr(Expr::BinOp(
                BinOp::Add,
                Box::new(Expr::Ident("n".to_string())),
                Box::new(Expr::Literal(Literal::Int(1))),
            ))),
            resolution: None,
        };
        ctx.fn_defs.push(add.clone());
        ctx.fn_defs.push(add_one.clone());
        ctx.items.push(TopLevel::FnDef(add));
        ctx.items.push(TopLevel::FnDef(add_one));
        ctx.items.push(TopLevel::Verify(VerifyBlock {
            fn_name: "addOne".to_string(),
            line: 3,
            cases: vec![(
                Expr::FnCall(
                    Box::new(Expr::Ident("addOne".to_string())),
                    vec![Expr::Literal(Literal::Int(2))],
                ),
                Expr::FnCall(
                    Box::new(Expr::Ident("add".to_string())),
                    vec![
                        Expr::Literal(Literal::Int(2)),
                        Expr::Literal(Literal::Int(1)),
                    ],
                ),
            )],
            kind: VerifyKind::Law(VerifyLaw {
                name: "identityViaAdd".to_string(),
                givens: vec![VerifyGiven {
                    name: "n".to_string(),
                    type_name: "Int".to_string(),
                    domain: VerifyGivenDomain::Explicit(vec![Expr::Literal(Literal::Int(2))]),
                }],
                lhs: Expr::FnCall(
                    Box::new(Expr::Ident("addOne".to_string())),
                    vec![Expr::Ident("n".to_string())],
                ),
                rhs: Expr::FnCall(
                    Box::new(Expr::Ident("add".to_string())),
                    vec![Expr::Ident("n".to_string()), Expr::Literal(Literal::Int(1))],
                ),
            }),
        }));
        let out = transpile(&ctx);
        let lean = out
            .files
            .iter()
            .find_map(|(name, content)| (name == "Verify_mode.lean").then_some(content))
            .expect("expected generated Lean file");
        assert!(
            lean.contains(
                "theorem addOne_law_identityViaAdd : ∀ (n : Int), addOne n = add n 1 := by"
            )
        );
        assert!(lean.contains("  simp [addOne, add]"));
    }

    #[test]
    fn transpile_auto_proves_direct_map_set_laws() {
        let mut ctx = empty_ctx();

        let map_set = |m: Expr, k: Expr, v: Expr| {
            Expr::FnCall(
                Box::new(Expr::Attr(
                    Box::new(Expr::Ident("Map".to_string())),
                    "set".to_string(),
                )),
                vec![m, k, v],
            )
        };
        let map_has = |m: Expr, k: Expr| {
            Expr::FnCall(
                Box::new(Expr::Attr(
                    Box::new(Expr::Ident("Map".to_string())),
                    "has".to_string(),
                )),
                vec![m, k],
            )
        };
        let map_get = |m: Expr, k: Expr| {
            Expr::FnCall(
                Box::new(Expr::Attr(
                    Box::new(Expr::Ident("Map".to_string())),
                    "get".to_string(),
                )),
                vec![m, k],
            )
        };
        let some = |v: Expr| {
            Expr::FnCall(
                Box::new(Expr::Attr(
                    Box::new(Expr::Ident("Option".to_string())),
                    "Some".to_string(),
                )),
                vec![v],
            )
        };

        ctx.items.push(TopLevel::Verify(VerifyBlock {
            fn_name: "map".to_string(),
            line: 1,
            cases: vec![(
                map_has(
                    map_set(
                        Expr::Ident("m".to_string()),
                        Expr::Ident("k".to_string()),
                        Expr::Ident("v".to_string()),
                    ),
                    Expr::Ident("k".to_string()),
                ),
                Expr::Literal(Literal::Bool(true)),
            )],
            kind: VerifyKind::Law(VerifyLaw {
                name: "setHasKey".to_string(),
                givens: vec![
                    VerifyGiven {
                        name: "m".to_string(),
                        type_name: "Map<String, Int>".to_string(),
                        domain: VerifyGivenDomain::Explicit(vec![Expr::FnCall(
                            Box::new(Expr::Attr(
                                Box::new(Expr::Ident("Map".to_string())),
                                "empty".to_string(),
                            )),
                            vec![],
                        )]),
                    },
                    VerifyGiven {
                        name: "k".to_string(),
                        type_name: "String".to_string(),
                        domain: VerifyGivenDomain::Explicit(vec![Expr::Literal(Literal::Str(
                            "a".to_string(),
                        ))]),
                    },
                    VerifyGiven {
                        name: "v".to_string(),
                        type_name: "Int".to_string(),
                        domain: VerifyGivenDomain::Explicit(vec![Expr::Literal(Literal::Int(1))]),
                    },
                ],
                lhs: map_has(
                    map_set(
                        Expr::Ident("m".to_string()),
                        Expr::Ident("k".to_string()),
                        Expr::Ident("v".to_string()),
                    ),
                    Expr::Ident("k".to_string()),
                ),
                rhs: Expr::Literal(Literal::Bool(true)),
            }),
        }));

        ctx.items.push(TopLevel::Verify(VerifyBlock {
            fn_name: "map".to_string(),
            line: 2,
            cases: vec![(
                map_get(
                    map_set(
                        Expr::Ident("m".to_string()),
                        Expr::Ident("k".to_string()),
                        Expr::Ident("v".to_string()),
                    ),
                    Expr::Ident("k".to_string()),
                ),
                some(Expr::Ident("v".to_string())),
            )],
            kind: VerifyKind::Law(VerifyLaw {
                name: "setGetKey".to_string(),
                givens: vec![
                    VerifyGiven {
                        name: "m".to_string(),
                        type_name: "Map<String, Int>".to_string(),
                        domain: VerifyGivenDomain::Explicit(vec![Expr::FnCall(
                            Box::new(Expr::Attr(
                                Box::new(Expr::Ident("Map".to_string())),
                                "empty".to_string(),
                            )),
                            vec![],
                        )]),
                    },
                    VerifyGiven {
                        name: "k".to_string(),
                        type_name: "String".to_string(),
                        domain: VerifyGivenDomain::Explicit(vec![Expr::Literal(Literal::Str(
                            "a".to_string(),
                        ))]),
                    },
                    VerifyGiven {
                        name: "v".to_string(),
                        type_name: "Int".to_string(),
                        domain: VerifyGivenDomain::Explicit(vec![Expr::Literal(Literal::Int(1))]),
                    },
                ],
                lhs: map_get(
                    map_set(
                        Expr::Ident("m".to_string()),
                        Expr::Ident("k".to_string()),
                        Expr::Ident("v".to_string()),
                    ),
                    Expr::Ident("k".to_string()),
                ),
                rhs: some(Expr::Ident("v".to_string())),
            }),
        }));

        let out = transpile(&ctx);
        let lean = out
            .files
            .iter()
            .find_map(|(name, content)| (name == "Verify_mode.lean").then_some(content))
            .expect("expected generated Lean file");
        assert!(lean.contains("simpa using AverMap.has_set_self m k v"));
        assert!(lean.contains("simpa using AverMap.get_set_self m k v"));
    }

    #[test]
    fn transpile_auto_proves_map_update_laws() {
        let mut ctx = empty_ctx();

        let map_get = |m: Expr, k: Expr| {
            Expr::FnCall(
                Box::new(Expr::Attr(
                    Box::new(Expr::Ident("Map".to_string())),
                    "get".to_string(),
                )),
                vec![m, k],
            )
        };
        let map_set = |m: Expr, k: Expr, v: Expr| {
            Expr::FnCall(
                Box::new(Expr::Attr(
                    Box::new(Expr::Ident("Map".to_string())),
                    "set".to_string(),
                )),
                vec![m, k, v],
            )
        };
        let map_has = |m: Expr, k: Expr| {
            Expr::FnCall(
                Box::new(Expr::Attr(
                    Box::new(Expr::Ident("Map".to_string())),
                    "has".to_string(),
                )),
                vec![m, k],
            )
        };
        let option_some = |v: Expr| {
            Expr::FnCall(
                Box::new(Expr::Attr(
                    Box::new(Expr::Ident("Option".to_string())),
                    "Some".to_string(),
                )),
                vec![v],
            )
        };
        let option_with_default = |opt: Expr, def: Expr| {
            Expr::FnCall(
                Box::new(Expr::Attr(
                    Box::new(Expr::Ident("Option".to_string())),
                    "withDefault".to_string(),
                )),
                vec![opt, def],
            )
        };

        let add_one = FnDef {
            name: "addOne".to_string(),
            line: 1,
            params: vec![("n".to_string(), "Int".to_string())],
            return_type: "Int".to_string(),
            effects: vec![],
            desc: None,
            body: Rc::new(FnBody::Expr(Expr::BinOp(
                BinOp::Add,
                Box::new(Expr::Ident("n".to_string())),
                Box::new(Expr::Literal(Literal::Int(1))),
            ))),
            resolution: None,
        };
        ctx.fn_defs.push(add_one.clone());
        ctx.items.push(TopLevel::FnDef(add_one));

        let inc_count = FnDef {
            name: "incCount".to_string(),
            line: 2,
            params: vec![
                ("counts".to_string(), "Map<String, Int>".to_string()),
                ("word".to_string(), "String".to_string()),
            ],
            return_type: "Map<String, Int>".to_string(),
            effects: vec![],
            desc: None,
            body: Rc::new(FnBody::Block(vec![
                Stmt::Binding(
                    "current".to_string(),
                    None,
                    map_get(
                        Expr::Ident("counts".to_string()),
                        Expr::Ident("word".to_string()),
                    ),
                ),
                Stmt::Expr(Expr::Match {
                    subject: Box::new(Expr::Ident("current".to_string())),
                    arms: vec![
                        MatchArm {
                            pattern: Pattern::Constructor(
                                "Some".to_string(),
                                vec!["n".to_string()],
                            ),
                            body: Box::new(map_set(
                                Expr::Ident("counts".to_string()),
                                Expr::Ident("word".to_string()),
                                Expr::BinOp(
                                    BinOp::Add,
                                    Box::new(Expr::Ident("n".to_string())),
                                    Box::new(Expr::Literal(Literal::Int(1))),
                                ),
                            )),
                        },
                        MatchArm {
                            pattern: Pattern::Constructor("None".to_string(), vec![]),
                            body: Box::new(map_set(
                                Expr::Ident("counts".to_string()),
                                Expr::Ident("word".to_string()),
                                Expr::Literal(Literal::Int(1)),
                            )),
                        },
                    ],
                    line: 2,
                }),
            ])),
            resolution: None,
        };
        ctx.fn_defs.push(inc_count.clone());
        ctx.items.push(TopLevel::FnDef(inc_count));

        ctx.items.push(TopLevel::Verify(VerifyBlock {
            fn_name: "incCount".to_string(),
            line: 10,
            cases: vec![(
                map_has(
                    Expr::FnCall(
                        Box::new(Expr::Ident("incCount".to_string())),
                        vec![
                            Expr::Ident("counts".to_string()),
                            Expr::Ident("word".to_string()),
                        ],
                    ),
                    Expr::Ident("word".to_string()),
                ),
                Expr::Literal(Literal::Bool(true)),
            )],
            kind: VerifyKind::Law(VerifyLaw {
                name: "keyPresent".to_string(),
                givens: vec![
                    VerifyGiven {
                        name: "counts".to_string(),
                        type_name: "Map<String, Int>".to_string(),
                        domain: VerifyGivenDomain::Explicit(vec![Expr::FnCall(
                            Box::new(Expr::Attr(
                                Box::new(Expr::Ident("Map".to_string())),
                                "empty".to_string(),
                            )),
                            vec![],
                        )]),
                    },
                    VerifyGiven {
                        name: "word".to_string(),
                        type_name: "String".to_string(),
                        domain: VerifyGivenDomain::Explicit(vec![Expr::Literal(Literal::Str(
                            "a".to_string(),
                        ))]),
                    },
                ],
                lhs: map_has(
                    Expr::FnCall(
                        Box::new(Expr::Ident("incCount".to_string())),
                        vec![
                            Expr::Ident("counts".to_string()),
                            Expr::Ident("word".to_string()),
                        ],
                    ),
                    Expr::Ident("word".to_string()),
                ),
                rhs: Expr::Literal(Literal::Bool(true)),
            }),
        }));

        ctx.items.push(TopLevel::Verify(VerifyBlock {
            fn_name: "incCount".to_string(),
            line: 20,
            cases: vec![(
                map_get(
                    Expr::FnCall(
                        Box::new(Expr::Ident("incCount".to_string())),
                        vec![
                            Expr::Ident("counts".to_string()),
                            Expr::Literal(Literal::Str("a".to_string())),
                        ],
                    ),
                    Expr::Literal(Literal::Str("a".to_string())),
                ),
                option_some(Expr::FnCall(
                    Box::new(Expr::Ident("addOne".to_string())),
                    vec![option_with_default(
                        map_get(
                            Expr::Ident("counts".to_string()),
                            Expr::Literal(Literal::Str("a".to_string())),
                        ),
                        Expr::Literal(Literal::Int(0)),
                    )],
                )),
            )],
            kind: VerifyKind::Law(VerifyLaw {
                name: "existingKeyIncrements".to_string(),
                givens: vec![VerifyGiven {
                    name: "counts".to_string(),
                    type_name: "Map<String, Int>".to_string(),
                    domain: VerifyGivenDomain::Explicit(vec![Expr::FnCall(
                        Box::new(Expr::Attr(
                            Box::new(Expr::Ident("Map".to_string())),
                            "empty".to_string(),
                        )),
                        vec![],
                    )]),
                }],
                lhs: map_get(
                    Expr::FnCall(
                        Box::new(Expr::Ident("incCount".to_string())),
                        vec![
                            Expr::Ident("counts".to_string()),
                            Expr::Literal(Literal::Str("a".to_string())),
                        ],
                    ),
                    Expr::Literal(Literal::Str("a".to_string())),
                ),
                rhs: option_some(Expr::FnCall(
                    Box::new(Expr::Ident("addOne".to_string())),
                    vec![option_with_default(
                        map_get(
                            Expr::Ident("counts".to_string()),
                            Expr::Literal(Literal::Str("a".to_string())),
                        ),
                        Expr::Literal(Literal::Int(0)),
                    )],
                )),
            }),
        }));

        let out = transpile(&ctx);
        let lean = out
            .files
            .iter()
            .find_map(|(name, content)| (name == "Verify_mode.lean").then_some(content))
            .expect("expected generated Lean file");
        assert!(
            lean.contains("cases h : AverMap.get counts word <;> simp [AverMap.has_set_self]"),
            "expected keyPresent auto-proof with has_set_self"
        );
        assert!(
            lean.contains("cases h : AverMap.get counts \"a\" <;> simp [AverMap.get_set_self, addOne, incCount]"),
            "expected existingKeyIncrements auto-proof with get_set_self"
        );
    }

    #[test]
    fn transpile_parenthesizes_negative_int_call_args_in_law_samples() {
        let mut ctx = empty_ctx();
        let add = FnDef {
            name: "add".to_string(),
            line: 1,
            params: vec![
                ("a".to_string(), "Int".to_string()),
                ("b".to_string(), "Int".to_string()),
            ],
            return_type: "Int".to_string(),
            effects: vec![],
            desc: None,
            body: Rc::new(FnBody::Expr(Expr::BinOp(
                BinOp::Add,
                Box::new(Expr::Ident("a".to_string())),
                Box::new(Expr::Ident("b".to_string())),
            ))),
            resolution: None,
        };
        ctx.fn_defs.push(add.clone());
        ctx.items.push(TopLevel::FnDef(add));
        ctx.items.push(TopLevel::Verify(VerifyBlock {
            fn_name: "add".to_string(),
            line: 1,
            cases: vec![(
                Expr::FnCall(
                    Box::new(Expr::Ident("add".to_string())),
                    vec![
                        Expr::Literal(Literal::Int(-2)),
                        Expr::Literal(Literal::Int(-1)),
                    ],
                ),
                Expr::FnCall(
                    Box::new(Expr::Ident("add".to_string())),
                    vec![
                        Expr::Literal(Literal::Int(-1)),
                        Expr::Literal(Literal::Int(-2)),
                    ],
                ),
            )],
            kind: VerifyKind::Law(VerifyLaw {
                name: "commutative".to_string(),
                givens: vec![
                    VerifyGiven {
                        name: "a".to_string(),
                        type_name: "Int".to_string(),
                        domain: VerifyGivenDomain::Explicit(vec![Expr::Literal(Literal::Int(-2))]),
                    },
                    VerifyGiven {
                        name: "b".to_string(),
                        type_name: "Int".to_string(),
                        domain: VerifyGivenDomain::Explicit(vec![Expr::Literal(Literal::Int(-1))]),
                    },
                ],
                lhs: Expr::FnCall(
                    Box::new(Expr::Ident("add".to_string())),
                    vec![Expr::Ident("a".to_string()), Expr::Ident("b".to_string())],
                ),
                rhs: Expr::FnCall(
                    Box::new(Expr::Ident("add".to_string())),
                    vec![Expr::Ident("b".to_string()), Expr::Ident("a".to_string())],
                ),
            }),
        }));

        let out = transpile(&ctx);
        let lean = out
            .files
            .iter()
            .find_map(|(name, content)| (name == "Verify_mode.lean").then_some(content))
            .expect("expected generated Lean file");
        assert!(lean.contains(
            "theorem add_law_commutative_sample_1 : add (-2) (-1) = add (-1) (-2) := by native_decide"
        ));
    }

    #[test]
    fn verify_law_numbering_is_scoped_per_law_name() {
        let mut ctx = empty_ctx();
        let f = FnDef {
            name: "f".to_string(),
            line: 1,
            params: vec![("x".to_string(), "Int".to_string())],
            return_type: "Int".to_string(),
            effects: vec![],
            desc: None,
            body: Rc::new(FnBody::Expr(Expr::Ident("x".to_string()))),
            resolution: None,
        };
        ctx.fn_defs.push(f.clone());
        ctx.items.push(TopLevel::FnDef(f));
        ctx.items.push(TopLevel::Verify(VerifyBlock {
            fn_name: "f".to_string(),
            line: 1,
            cases: vec![(
                Expr::Literal(Literal::Int(1)),
                Expr::Literal(Literal::Int(1)),
            )],
            kind: VerifyKind::Cases,
        }));
        ctx.items.push(TopLevel::Verify(VerifyBlock {
            fn_name: "f".to_string(),
            line: 2,
            cases: vec![(
                Expr::Literal(Literal::Int(2)),
                Expr::Literal(Literal::Int(2)),
            )],
            kind: VerifyKind::Law(VerifyLaw {
                name: "identity".to_string(),
                givens: vec![VerifyGiven {
                    name: "x".to_string(),
                    type_name: "Int".to_string(),
                    domain: VerifyGivenDomain::Explicit(vec![Expr::Literal(Literal::Int(2))]),
                }],
                lhs: Expr::Ident("x".to_string()),
                rhs: Expr::Ident("x".to_string()),
            }),
        }));
        let out = transpile_with_verify_mode(&ctx, VerifyEmitMode::TheoremSkeleton);
        let lean = out
            .files
            .iter()
            .find_map(|(name, content)| (name == "Verify_mode.lean").then_some(content))
            .expect("expected generated Lean file");
        assert!(lean.contains("theorem f_verify_1 : 1 = 1 := by"));
        assert!(lean.contains("theorem f_law_identity : ∀ (x : Int), x = x := by"));
        assert!(lean.contains("theorem f_law_identity_sample_1 : 2 = 2 := by"));
        assert!(!lean.contains("theorem f_law_identity_sample_2 : 2 = 2 := by"));
    }

    #[test]
    fn proof_mode_accepts_single_int_countdown_recursion() {
        let mut ctx = empty_ctx();
        let down = FnDef {
            name: "down".to_string(),
            line: 1,
            params: vec![("n".to_string(), "Int".to_string())],
            return_type: "Int".to_string(),
            effects: vec![],
            desc: None,
            body: Rc::new(FnBody::Expr(Expr::Match {
                subject: Box::new(Expr::Ident("n".to_string())),
                arms: vec![
                    MatchArm {
                        pattern: Pattern::Literal(Literal::Int(0)),
                        body: Box::new(Expr::Literal(Literal::Int(0))),
                    },
                    MatchArm {
                        pattern: Pattern::Wildcard,
                        body: Box::new(Expr::TailCall(Box::new((
                            "down".to_string(),
                            vec![Expr::BinOp(
                                BinOp::Sub,
                                Box::new(Expr::Ident("n".to_string())),
                                Box::new(Expr::Literal(Literal::Int(1))),
                            )],
                        )))),
                    },
                ],
                line: 1,
            })),
            resolution: None,
        };
        ctx.items.push(TopLevel::FnDef(down.clone()));
        ctx.fn_defs.push(down);

        let issues = proof_mode_issues(&ctx);
        assert!(
            issues.is_empty(),
            "expected Int countdown recursion to be accepted, got: {:?}",
            issues
        );

        let out = transpile_for_proof_mode(&ctx, VerifyEmitMode::NativeDecide);
        let lean = out
            .files
            .iter()
            .find_map(|(name, content)| (name == "Verify_mode.lean").then_some(content))
            .expect("expected generated Lean file");
        assert!(lean.contains("def down (n : Int) : Int :="));
        assert!(lean.contains("termination_by Int.natAbs n"));
        assert!(lean.contains("decreasing_by"));
    }

    #[test]
    fn proof_mode_accepts_single_list_structural_recursion() {
        let mut ctx = empty_ctx();
        let len = FnDef {
            name: "len".to_string(),
            line: 1,
            params: vec![("xs".to_string(), "List<Int>".to_string())],
            return_type: "Int".to_string(),
            effects: vec![],
            desc: None,
            body: Rc::new(FnBody::Expr(Expr::Match {
                subject: Box::new(Expr::Ident("xs".to_string())),
                arms: vec![
                    MatchArm {
                        pattern: Pattern::EmptyList,
                        body: Box::new(Expr::Literal(Literal::Int(0))),
                    },
                    MatchArm {
                        pattern: Pattern::Cons("h".to_string(), "t".to_string()),
                        body: Box::new(Expr::TailCall(Box::new((
                            "len".to_string(),
                            vec![Expr::Ident("t".to_string())],
                        )))),
                    },
                ],
                line: 1,
            })),
            resolution: None,
        };
        ctx.items.push(TopLevel::FnDef(len.clone()));
        ctx.fn_defs.push(len);

        let issues = proof_mode_issues(&ctx);
        assert!(
            issues.is_empty(),
            "expected List structural recursion to be accepted, got: {:?}",
            issues
        );
    }

    #[test]
    fn proof_mode_accepts_single_string_pos_advance_recursion() {
        let mut ctx = empty_ctx();
        let skip_ws = FnDef {
            name: "skipWs".to_string(),
            line: 1,
            params: vec![
                ("s".to_string(), "String".to_string()),
                ("pos".to_string(), "Int".to_string()),
            ],
            return_type: "Int".to_string(),
            effects: vec![],
            desc: None,
            body: Rc::new(FnBody::Expr(Expr::Match {
                subject: Box::new(Expr::FnCall(
                    Box::new(Expr::Attr(
                        Box::new(Expr::Ident("String".to_string())),
                        "charAt".to_string(),
                    )),
                    vec![Expr::Ident("s".to_string()), Expr::Ident("pos".to_string())],
                )),
                arms: vec![
                    MatchArm {
                        pattern: Pattern::Constructor("Option.None".to_string(), vec![]),
                        body: Box::new(Expr::Ident("pos".to_string())),
                    },
                    MatchArm {
                        pattern: Pattern::Wildcard,
                        body: Box::new(Expr::TailCall(Box::new((
                            "skipWs".to_string(),
                            vec![
                                Expr::Ident("s".to_string()),
                                Expr::BinOp(
                                    BinOp::Add,
                                    Box::new(Expr::Ident("pos".to_string())),
                                    Box::new(Expr::Literal(Literal::Int(1))),
                                ),
                            ],
                        )))),
                    },
                ],
                line: 1,
            })),
            resolution: None,
        };
        ctx.items.push(TopLevel::FnDef(skip_ws.clone()));
        ctx.fn_defs.push(skip_ws);

        let issues = proof_mode_issues(&ctx);
        assert!(
            issues.is_empty(),
            "expected String+pos recursion to be accepted, got: {:?}",
            issues
        );

        let out = transpile_for_proof_mode(&ctx, VerifyEmitMode::NativeDecide);
        let lean = out
            .files
            .iter()
            .find_map(|(name, content)| (name == "Verify_mode.lean").then_some(content))
            .expect("expected generated Lean file");
        assert!(lean.contains("def skipWs (s : String) (pos : Int) : Int :="));
        assert!(lean.contains("termination_by ((s.data.length) - (pos.toNat))"));
        assert!(lean.contains("decreasing_by"));
    }

    #[test]
    fn proof_mode_accepts_mutual_int_countdown_recursion() {
        let mut ctx = empty_ctx();
        let even = FnDef {
            name: "even".to_string(),
            line: 1,
            params: vec![("n".to_string(), "Int".to_string())],
            return_type: "Bool".to_string(),
            effects: vec![],
            desc: None,
            body: Rc::new(FnBody::Expr(Expr::Match {
                subject: Box::new(Expr::Ident("n".to_string())),
                arms: vec![
                    MatchArm {
                        pattern: Pattern::Literal(Literal::Int(0)),
                        body: Box::new(Expr::Literal(Literal::Bool(true))),
                    },
                    MatchArm {
                        pattern: Pattern::Wildcard,
                        body: Box::new(Expr::TailCall(Box::new((
                            "odd".to_string(),
                            vec![Expr::BinOp(
                                BinOp::Sub,
                                Box::new(Expr::Ident("n".to_string())),
                                Box::new(Expr::Literal(Literal::Int(1))),
                            )],
                        )))),
                    },
                ],
                line: 1,
            })),
            resolution: None,
        };
        let odd = FnDef {
            name: "odd".to_string(),
            line: 2,
            params: vec![("n".to_string(), "Int".to_string())],
            return_type: "Bool".to_string(),
            effects: vec![],
            desc: None,
            body: Rc::new(FnBody::Expr(Expr::Match {
                subject: Box::new(Expr::Ident("n".to_string())),
                arms: vec![
                    MatchArm {
                        pattern: Pattern::Literal(Literal::Int(0)),
                        body: Box::new(Expr::Literal(Literal::Bool(false))),
                    },
                    MatchArm {
                        pattern: Pattern::Wildcard,
                        body: Box::new(Expr::TailCall(Box::new((
                            "even".to_string(),
                            vec![Expr::BinOp(
                                BinOp::Sub,
                                Box::new(Expr::Ident("n".to_string())),
                                Box::new(Expr::Literal(Literal::Int(1))),
                            )],
                        )))),
                    },
                ],
                line: 2,
            })),
            resolution: None,
        };
        ctx.items.push(TopLevel::FnDef(even.clone()));
        ctx.items.push(TopLevel::FnDef(odd.clone()));
        ctx.fn_defs.push(even);
        ctx.fn_defs.push(odd);

        let issues = proof_mode_issues(&ctx);
        assert!(
            issues.is_empty(),
            "expected mutual Int countdown recursion to be accepted, got: {:?}",
            issues
        );
    }

    #[test]
    fn proof_mode_accepts_mutual_string_pos_recursion_with_ranked_same_edges() {
        let mut ctx = empty_ctx();
        let f = FnDef {
            name: "f".to_string(),
            line: 1,
            params: vec![
                ("s".to_string(), "String".to_string()),
                ("pos".to_string(), "Int".to_string()),
            ],
            return_type: "Int".to_string(),
            effects: vec![],
            desc: None,
            body: Rc::new(FnBody::Expr(Expr::Match {
                subject: Box::new(Expr::BinOp(
                    BinOp::Gte,
                    Box::new(Expr::Ident("pos".to_string())),
                    Box::new(Expr::Literal(Literal::Int(3))),
                )),
                arms: vec![
                    MatchArm {
                        pattern: Pattern::Literal(Literal::Bool(true)),
                        body: Box::new(Expr::Ident("pos".to_string())),
                    },
                    MatchArm {
                        pattern: Pattern::Wildcard,
                        body: Box::new(Expr::TailCall(Box::new((
                            "g".to_string(),
                            vec![Expr::Ident("s".to_string()), Expr::Ident("pos".to_string())],
                        )))),
                    },
                ],
                line: 1,
            })),
            resolution: None,
        };
        let g = FnDef {
            name: "g".to_string(),
            line: 2,
            params: vec![
                ("s".to_string(), "String".to_string()),
                ("pos".to_string(), "Int".to_string()),
            ],
            return_type: "Int".to_string(),
            effects: vec![],
            desc: None,
            body: Rc::new(FnBody::Expr(Expr::Match {
                subject: Box::new(Expr::BinOp(
                    BinOp::Gte,
                    Box::new(Expr::Ident("pos".to_string())),
                    Box::new(Expr::Literal(Literal::Int(3))),
                )),
                arms: vec![
                    MatchArm {
                        pattern: Pattern::Literal(Literal::Bool(true)),
                        body: Box::new(Expr::Ident("pos".to_string())),
                    },
                    MatchArm {
                        pattern: Pattern::Wildcard,
                        body: Box::new(Expr::TailCall(Box::new((
                            "f".to_string(),
                            vec![
                                Expr::Ident("s".to_string()),
                                Expr::BinOp(
                                    BinOp::Add,
                                    Box::new(Expr::Ident("pos".to_string())),
                                    Box::new(Expr::Literal(Literal::Int(1))),
                                ),
                            ],
                        )))),
                    },
                ],
                line: 2,
            })),
            resolution: None,
        };
        ctx.items.push(TopLevel::FnDef(f.clone()));
        ctx.items.push(TopLevel::FnDef(g.clone()));
        ctx.fn_defs.push(f);
        ctx.fn_defs.push(g);

        let issues = proof_mode_issues(&ctx);
        assert!(
            issues.is_empty(),
            "expected mutual String+pos recursion to be accepted, got: {:?}",
            issues
        );

        let out = transpile_for_proof_mode(&ctx, VerifyEmitMode::NativeDecide);
        let lean = out
            .files
            .iter()
            .find_map(|(name, content)| (name == "Verify_mode.lean").then_some(content))
            .expect("expected generated Lean file");
        assert!(lean.contains("termination_by"));
        assert!(lean.contains("termination_by ((s.data.length) - (pos.toNat),"));
        assert!(lean.contains("decreasing_by"));
    }

    #[test]
    fn proof_mode_accepts_mutual_ranked_sizeof_recursion() {
        let mut ctx = empty_ctx();
        let f = FnDef {
            name: "f".to_string(),
            line: 1,
            params: vec![("xs".to_string(), "List<Int>".to_string())],
            return_type: "Int".to_string(),
            effects: vec![],
            desc: None,
            body: Rc::new(FnBody::Expr(Expr::TailCall(Box::new((
                "g".to_string(),
                vec![
                    Expr::Literal(Literal::Str("acc".to_string())),
                    Expr::Ident("xs".to_string()),
                ],
            ))))),
            resolution: None,
        };
        let g = FnDef {
            name: "g".to_string(),
            line: 2,
            params: vec![
                ("acc".to_string(), "String".to_string()),
                ("xs".to_string(), "List<Int>".to_string()),
            ],
            return_type: "Int".to_string(),
            effects: vec![],
            desc: None,
            body: Rc::new(FnBody::Expr(Expr::Match {
                subject: Box::new(Expr::Ident("xs".to_string())),
                arms: vec![
                    MatchArm {
                        pattern: Pattern::EmptyList,
                        body: Box::new(Expr::Literal(Literal::Int(0))),
                    },
                    MatchArm {
                        pattern: Pattern::Cons("h".to_string(), "t".to_string()),
                        body: Box::new(Expr::TailCall(Box::new((
                            "f".to_string(),
                            vec![Expr::Ident("t".to_string())],
                        )))),
                    },
                ],
                line: 2,
            })),
            resolution: None,
        };
        ctx.items.push(TopLevel::FnDef(f.clone()));
        ctx.items.push(TopLevel::FnDef(g.clone()));
        ctx.fn_defs.push(f);
        ctx.fn_defs.push(g);

        let issues = proof_mode_issues(&ctx);
        assert!(
            issues.is_empty(),
            "expected mutual ranked-sizeOf recursion to be accepted, got: {:?}",
            issues
        );

        let out = transpile_for_proof_mode(&ctx, VerifyEmitMode::NativeDecide);
        let lean = out
            .files
            .iter()
            .find_map(|(name, content)| (name == "Verify_mode.lean").then_some(content))
            .expect("expected generated Lean file");
        assert!(lean.contains("termination_by"));
        assert!(lean.contains("(sizeOf"));
        assert!(lean.contains("decreasing_by"));
    }

    #[test]
    fn proof_mode_rejects_recursive_pure_functions() {
        let mut ctx = empty_ctx();
        let recursive_fn = FnDef {
            name: "loop".to_string(),
            line: 1,
            params: vec![("n".to_string(), "Int".to_string())],
            return_type: "Int".to_string(),
            effects: vec![],
            desc: None,
            body: Rc::new(FnBody::Expr(Expr::FnCall(
                Box::new(Expr::Ident("loop".to_string())),
                vec![Expr::Ident("n".to_string())],
            ))),
            resolution: None,
        };
        ctx.items.push(TopLevel::FnDef(recursive_fn.clone()));
        ctx.fn_defs.push(recursive_fn);

        let issues = proof_mode_issues(&ctx);
        assert!(
            issues.iter().any(|i| i.contains("outside proof subset")),
            "expected recursive function blocker, got: {:?}",
            issues
        );
    }

    #[test]
    fn proof_mode_allows_recursive_types() {
        let mut ctx = empty_ctx();
        let recursive_type = TypeDef::Sum {
            name: "Node".to_string(),
            variants: vec![TypeVariant {
                name: "Cons".to_string(),
                fields: vec!["Node".to_string()],
            }],
            line: 1,
        };
        ctx.items.push(TopLevel::TypeDef(recursive_type.clone()));
        ctx.type_defs.push(recursive_type);

        let issues = proof_mode_issues(&ctx);
        assert!(
            issues
                .iter()
                .all(|i| !i.contains("recursive types require unsafe DecidableEq shim")),
            "did not expect recursive type blocker, got: {:?}",
            issues
        );
    }
}