defmodule Tilly.X.Type do
  @moduledoc """
  Core type system definitions for Tilly — a Lisp that transpiles to Elixir,
  using set-theoretic types represented as Ternary Decision Diagrams (TDDs).

  Supports:
    - Set-theoretic types (union, intersection, negation)
    - Structural polymorphism with `forall`
    - Type constraints (e.g., Enumerable(~a))
    - Structural map types
  """

  # === Monotype TDD Representation ===

  defmodule TDD do
    @moduledoc """
    Represents a ternary decision diagram node for types.
    """

    defstruct [:decision, :yes, :no, :maybe]

    @type t :: %__MODULE__{
            decision: Tilly.Type.Decision.t(),
            yes: TDD.t() | :any | :none,
            no: TDD.t() | :any | :none,
            maybe: TDD.t() | :any | :none
          }
  end

  # === Type Variable ===

  defmodule Var do
    @moduledoc """
    Represents a type variable in a polymorphic type.
    """

    defstruct [:name, constraints: []]

    @type t :: %__MODULE__{
            name: String.t(),
            constraints: [Tilly.Type.Constraint.t()]
          }
  end

  # === Structural Map Type ===

  defmodule TDDMap do
    @moduledoc """
    Structural representation of a map type, with per-key typing and optional openness.
    """

    defstruct fields: [], rest: nil

    @type t :: %__MODULE__{
            fields: [{TDD.t(), TDD.t()}],
            rest: TDD.t() | nil
          }
  end

  @doc """
  Checks if t1 is a subtype of t2 under the current substitution.
  t1 <: t2  iff  t1 & (not t2) == None
  """
  def is_subtype(raw_t1, raw_t2, sub) do
    # Use the apply_sub we defined/refined previously
    t1 = tdd_substitute(raw_t1, sub)
    t2 = tdd_substitute(raw_t2, sub)

    # Handle edge cases with Any and None for robustness
    cond do
      # None is a subtype of everything
      t1 == tdd_none() ->
        true

      # Everything is a subtype of Any
      t2 == tdd_any() ->
        true

      # Any is not a subtype of a specific type (unless that type is also Any)
      t1 == tdd_any() and t2 != tdd_any() ->
        false

      # A non-None type cannot be a subtype of None
      t2 == tdd_none() and t1 != tdd_none() ->
        false

      true ->
        # The core set-theoretic check: t1 \ t2 == None
        tdd_diff(t1, t2) == tdd_none()

        # Alternatively: Type.tdd_and(t1, t2) == t1 (but this can be tricky with complex TDDs if not canonical)
        # The difference check is generally more direct for subtyping.
    end
  end

  # === Type Decisions (Predicates) ===

  defmodule Decision do
    @moduledoc """
    A type-level decision predicate used in a TDD node.
    """

    @type t ::
            :is_atom
            | :is_integer
            | :is_float
            | :is_binary
            | :is_list
            | :is_tuple
            | :is_map
            | :is_function
            | :is_pid
            | :is_reference
            | {:literal, term()}
            | {:tuple_len, pos_integer()}
            | {:key, TDD.t()}
            | {:has_struct_key, atom()}
            | {:var, String.t()}
  end

  # === Type Constraints (structural predicates) ===

  defmodule Constraint do
    @moduledoc """
    Represents a structural constraint on a type variable,
    similar to a typeclass in Haskell or trait in Rust, but structural.
    """

    defstruct [:kind, :arg]

    @type kind ::
            :enumerable
            | :collectable
            | :struct_with_keys
            | :custom

    @type t :: %__MODULE__{
            kind: kind(),
            arg: String.t() | TDD.t() | any()
          }
  end

  # === Polymorphic Types (forall + constraints) ===

  defmodule PolyTDD do
    @moduledoc """
    Represents a polymorphic type with optional structural constraints.
    """

    defstruct [:vars, :body]

    @type t :: %__MODULE__{
            vars: [Var.t()],
            body: TDD.t()
          }
  end

  # === Constants for base types ===

  @doc "A TDD representing the universal type (any value)"
  def tdd_any, do: :any

  @doc "A TDD representing the empty type (no values)"
  def tdd_none, do: :none

  @doc "Creates a TDD for a literal value"
  def tdd_literal(value) do
    %TDD{
      decision: {:literal, value},
      yes: :any,
      no: :none,
      maybe: :none
    }
  end

  @doc "Creates a TDD for a base predicate (e.g., is_atom)"
  def tdd_pred(pred) when is_atom(pred) do
    %TDD{
      decision: pred,
      yes: :any,
      no: :none,
      maybe: :none
    }
  end

  @doc "Creates a TDD for a type variable reference"
  def tdd_var(name) when is_binary(name) do
    %TDD{
      decision: {:var, name},
      yes: :any,
      no: :none,
      maybe: :none
    }
  end

  @doc """
  Performs type variable substitution in a TDD,
  replacing variables found in the given `env` map.
  """
  def tdd_substitute(:any, _env), do: :any
  def tdd_substitute(:none, _env), do: :none

  def tdd_substitute(%TDD{decision: {:var, name}}, env) when is_map(env) do
    Map.get(env, name, %TDD{decision: {:var, name}, yes: :any, no: :none, maybe: :none})
  end

  def tdd_substitute(%TDD{} = tdd, env) do
    %TDD{
      decision: tdd.decision,
      yes: tdd_substitute(tdd.yes, env),
      no: tdd_substitute(tdd.no, env),
      maybe: tdd_substitute(tdd.maybe, env)
    }
  end

  @doc """
  Performs substitution in a polymorphic type, replacing all vars
  in `vars` with given TDDs from `env`.
  """
  def poly_substitute(%PolyTDD{vars: vars, body: body}, env) do
    var_names = Enum.map(vars, & &1.name)
    restricted_env = Map.take(env, var_names)
    tdd_substitute(body, restricted_env)
  end

  # === Constraints ===

  @doc """
  Checks whether a TDD satisfies a built-in structural constraint,
  such as Enumerable or String.Chars.
  """
  def satisfies_constraint?(tdd, %Constraint{kind: :enumerable}) do
    tdd_is_of_kind?(tdd, [:list, :map, :bitstring])
  end

  def satisfies_constraint?(tdd, %Constraint{kind: :string_chars}) do
    tdd_is_of_kind?(tdd, [:bitstring, :atom])
  end

  def satisfies_constraint?(_tdd, %Constraint{kind: :custom}) do
    raise "Custom constraints not implemented yet"
  end

  # Default fallback: constraint not recognized
  def satisfies_constraint?(_tdd, %Constraint{kind: kind}) do
    raise ArgumentError, "Unknown constraint kind: #{inspect(kind)}"
  end

  @doc """
  Checks if a TDD is semantically a subtype of any of the specified kinds.
  Used to approximate constraint satisfaction structurally.
  """
  def tdd_is_of_kind?(:any, _), do: true
  def tdd_is_of_kind?(:none, _), do: false

  def tdd_is_of_kind?(%TDD{decision: pred} = tdd, kinds) do
    if pred in kinds do
      # Decision directly confirms kind
      tdd.yes != :none
    else
      # Otherwise we conservatively say "no" unless the TDD is union-like
      false
    end
  end

  # === Decision  ===
  defmodule Decision do
    @moduledoc """
    A type-level decision predicate used in a TDD node.
    """

    @type t ::
            :is_atom
            | :is_integer
            | :is_float
            | :is_binary
            | :is_list
            | :is_tuple
            | :is_map
            # General "is a function"
            | :is_function
            | :is_pid
            | :is_reference
            | {:literal, term()}
            | {:tuple_len, pos_integer()}
            # Type of a map key (used in structural map checks)
            | {:key, TDD.t()}
            | {:has_struct_key, atom()}
            # A type variable name, e.g., "~a"
            | {:var, String.t()}
            # New
            | {:is_function_sig, param_types :: [TDD.t()], return_type :: TDD.t()}
  end

  @doc "Creates a TDD for a specific function signature"
  def tdd_function_sig(param_types, return_type)
      when is_list(param_types) and (is_struct(return_type, TDD) or return_type in [:any, :none]) do
    %TDD{
      decision: {:is_function_sig, param_types, return_type},
      # A value matches if it's a function of this signature
      yes: :any,
      no: :none,
      # Maybe it's some other function
      maybe: %TDD{decision: :is_function, yes: :any, no: :none, maybe: :none}
    }
  end

  # ... (existing tdd_or, tdd_and, tdd_not, tdd_diff) ...

  @doc """
  Performs type variable substitution in a TDD,
  replacing variables found in the given `env` map (var_name -> TDD).
  """
  def tdd_substitute(:any, _env), do: :any
  def tdd_substitute(:none, _env), do: :none

  def tdd_substitute(%TDD{decision: {:var, name}} = tdd, env) when is_map(env) do
    # If var 'name' is in env, substitute it. Otherwise, keep the var.
    Map.get(env, name, tdd)
  end

  def tdd_substitute(%TDD{decision: {:is_function_sig, params, ret_type}} = tdd, env) do
    # Substitute within the signature parts
    substituted_params = Enum.map(params, &tdd_substitute(&1, env))
    substituted_ret_type = tdd_substitute(ret_type, env)

    # Reconstruct the TDD node, keeping yes/no/maybe branches as they are fixed for this predicate.
    # Note: If canonicalization (mk_tdd) were used, this would go through it.
    %TDD{tdd | decision: {:is_function_sig, substituted_params, substituted_ret_type}}
  end

  def tdd_substitute(%TDD{decision: {:key, key_type_tdd}} = tdd, env) do
    # Substitute within the key type TDD
    substituted_key_type = tdd_substitute(key_type_tdd, env)
    %TDD{tdd | decision: {:key, substituted_key_type}}
  end

  # Generic case for other decisions: substitute in branches
  def tdd_substitute(%TDD{} = tdd, env) do
    %TDD{
      # Assume decision itself doesn't contain substitutable vars unless handled above
      decision: tdd.decision,
      yes: tdd_substitute(tdd.yes, env),
      no: tdd_substitute(tdd.no, env),
      maybe: tdd_substitute(tdd.maybe, env)
    }
  end

  @doc """
  Performs substitution in a polymorphic type's body,
  using the provided `env` (var_name -> TDD).
  This substitutes *free* variables in the PolyTDD's body, not its quantified variables.
  To instantiate quantified variables, use `Tilly.Inference.instantiate/3`.
  """
  def poly_substitute_free_vars(%PolyTDD{vars: _quantified_vars, body: body} = poly_tdd, env) do
    # We only substitute variables in the body that are NOT the quantified ones.
    # `env` should ideally not contain keys that are names of quantified variables of this PolyTDD.
    # For simplicity, if env has a quantified var name, it will be shadowed by the quantified var itself.
    # A more robust approach might filter env based on quantified_vars.
    substituted_body = tdd_substitute(body, env)
    %PolyTDD{poly_tdd | body: substituted_body}
  end

  @doc "Finds all free type variable names in a TDD."
  def free_vars(:any), do: MapSet.new()
  def free_vars(:none), do: MapSet.new()

  def free_vars(%TDD{decision: {:var, name}}) do
    MapSet.new([name])
  end

  def free_vars(%TDD{decision: {:is_function_sig, params, ret_type}}) do
    param_fvs = Enum.map(params, &free_vars/1) |> Enum.reduce(MapSet.new(), &MapSet.union/2)
    ret_fvs = free_vars(ret_type)
    MapSet.union(param_fvs, ret_fvs)
    # Note: yes/no/maybe branches for this node are typically :any/:none or simple predicates,
    # but if they could contain vars, they'd need to be included.
    # Current tdd_function_sig has fixed branches.
  end

  def free_vars(%TDD{decision: {:key, key_type_tdd}}) do
    free_vars(key_type_tdd)
    # Similar note about yes/no/maybe branches.
  end

  def free_vars(%TDD{yes: yes, no: no, maybe: maybe}) do
    MapSet.union(free_vars(yes), MapSet.union(free_vars(no), free_vars(maybe)))
  end

  # Helper for PolyTDD free vars (vars free in body that are not quantified)
  def free_vars_in_poly_tdd_body(%PolyTDD{vars: quantified_vars_list, body: body}) do
    quantified_names = Enum.map(quantified_vars_list, & &1.name) |> MapSet.new()
    body_fvs = free_vars(body)
    MapSet.difference(body_fvs, quantified_names)
  end
end

defmodule Tilly.Inference do
  alias Tilly.Type
  alias Tilly.Type.{TDD, Var, PolyTDD, Constraint}

  @typedoc "Type environment: maps variable names (atoms) to their types (TDD or PolyTDD)"
  @type type_env :: %{atom() => TDD.t() | PolyTDD.t()}

  @typedoc "Substitution map: maps type variable names (strings) to TDDs"
  @type substitution :: %{String.t() => TDD.t()}

  @typedoc "Constraints collected during inference: {type_var_name, constraint}"
  @type collected_constraints :: [{String.t(), Constraint.t()}]

  @typedoc """
  Result of inference for an expression:
  - inferred_type: The TDD or PolyTDD type of the expression.
  - var_counter: The updated counter for generating fresh type variables.
  - substitution: The accumulated substitution map.
  - constraints: Constraints that need to be satisfied.
  """
  @type infer_result ::
          {inferred_type :: TDD.t() | PolyTDD.t(), var_counter :: non_neg_integer(),
           substitution :: substitution(), constraints :: collected_constraints()}

  # --- Helper for Fresh Type Variables ---
  defmodule FreshVar do
    @doc "Generates a new type variable name and increments the counter."
    @spec next(non_neg_integer()) :: {String.t(), non_neg_integer()}
    def next(counter) do
      new_var_name = "~t" <> Integer.to_string(counter)
      {new_var_name, counter + 1}
    end
  end

  # --- Core Inference Function ---

  @doc "Infers the type of a Tilly expression."
  @spec infer(
          expr :: term(),
          env :: type_env(),
          var_counter :: non_neg_integer(),
          sub :: substitution()
        ) ::
          infer_result()
  def infer({:lit, val}, _env, var_counter, sub) do
    type =
      cond do
        # More precise: Type.tdd_literal(val)
        is_atom(val) -> Type.tdd_pred(:is_atom)
        # Type.tdd_literal(val)
        is_integer(val) -> Type.tdd_pred(:is_integer)
        # Type.tdd_literal(val)
        is_float(val) -> Type.tdd_pred(:is_float)
        # Type.tdd_literal(val)
        is_binary(val) -> Type.tdd_pred(:is_binary)
        # Add other literals as needed
        # Fallback for other kinds of literals
        true -> Type.tdd_literal(val)
      end

    {type, var_counter, sub, []}
  end

  def infer({:var, name}, env, var_counter, sub) when is_atom(name) do
    case Map.get(env, name) do
      nil ->
        raise "Unbound variable: #{name}"

      %TDD{} = tdd_type ->
        {Type.tdd_substitute(tdd_type, sub), var_counter, sub, []}

      %PolyTDD{} = poly_type ->
        {instantiated_type, new_var_counter, new_constraints} =
          instantiate(poly_type, var_counter)

        # Apply current substitution to the instantiated type
        # (in case fresh vars from instantiation are already in sub from elsewhere)
        final_type = Type.tdd_substitute(instantiated_type, sub)
        {final_type, new_var_counter, sub, new_constraints}
    end
  end

  def infer({:fn, param_atoms, body_expr}, env, var_counter, sub) when is_list(param_atoms) do
    # 1. Create fresh type variables for parameters
    {param_tdd_vars, extended_env, counter_after_params} =
      Enum.reduce(param_atoms, {[], env, var_counter}, fn param_name,
                                                          {vars_acc, env_acc, c_acc} ->
        {fresh_var_name, next_c} = FreshVar.next(c_acc)
        param_tdd_var = Type.tdd_var(fresh_var_name)
        {[param_tdd_var | vars_acc], Map.put(env_acc, param_name, param_tdd_var), next_c}
      end)

    param_types = Enum.reverse(param_tdd_vars)

    # 2. Infer body with extended environment and current substitution
    {body_type_raw, counter_after_body, sub_after_body, body_constraints} =
      infer(body_expr, extended_env, counter_after_params, sub)

    # 3. Apply the substitution from body inference to parameter types
    #    This is because unification within the body might refine what the param types can be.
    final_param_types = Enum.map(param_types, &Type.tdd_substitute(&1, sub_after_body))
    # Already applied in infer usually
    final_body_type = Type.tdd_substitute(body_type_raw, sub_after_body)

    # 4. Construct function type
    fun_type = Type.tdd_function_sig(final_param_types, final_body_type)
    {fun_type, counter_after_body, sub_after_body, body_constraints}
  end

  def infer({:app, fun_expr, arg_exprs}, env, var_counter, sub) when is_list(arg_exprs) do
    # 1. Infer function expression
    {fun_type_raw, c1, s1, fun_constraints} = infer(fun_expr, env, var_counter, sub)
    # Apply substitutions so far
    fun_type_template = Type.tdd_substitute(fun_type_raw, s1)

    # 2. Infer argument expressions
    {arg_types_raw, c2, s2, args_constraints_lists} =
      Enum.map_reduce(arg_exprs, {c1, s1}, fn arg_expr, {c_acc, s_acc} ->
        {arg_t, next_c, next_s, arg_c} = infer(arg_expr, env, c_acc, s_acc)
        # Pass along type and its constraints
        {{arg_t, arg_c}, {next_c, next_s}}
      end)

    actual_arg_types = Enum.map(arg_types_raw, fn {t, _cs} -> Type.tdd_substitute(t, s2) end)
    all_arg_constraints = Enum.flat_map(arg_types_raw, fn {_t, cs} -> cs end) ++ fun_constraints

    # 3. Unify/Match function type with arguments
    #    `fun_type_template` is the type of the function (e.g., {:var, "~f"} or an actual fn_sig)
    #    `s2` is the current global substitution.
    {return_type_final, c3, s3, unification_constraints} =
      unify_apply(fun_type_template, actual_arg_types, c2, s2)

    {return_type_final, c3, s3, all_arg_constraints ++ unification_constraints}
  end

  def infer({:let, [{var_name, val_expr}], body_expr}, env, var_counter, sub) do
    # 1. Infer the type of the value expression
    {val_type_raw, c1, s1, val_constraints} = infer(val_expr, env, var_counter, sub)

    # 2. Apply current substitution and generalize the value's type
    #    Generalization happens *before* adding to env, over variables free in val_type but not env.
    #    The substitution `s1` contains all refinements up to this point.
    val_type_substituted = Type.tdd_substitute(val_type_raw, s1)
    generalized_val_type = generalize(val_type_substituted, env, s1)

    # 3. Extend environment and infer body
    extended_env = Map.put(env, var_name, generalized_val_type)
    # Use s1 for body too
    {body_type_raw, c2, s2, body_constraints} = infer(body_expr, extended_env, c1, s1)

    # The final substitution s2 incorporates s1 and any changes from body.
    # The final body_type is already substituted by s2.
    {body_type_raw, c2, s2, val_constraints ++ body_constraints}
  end

  # --- Polymorphism: Instantiation and Generalization ---

  @doc "Instantiates a polymorphic type scheme by replacing quantified variables with fresh ones."
  def instantiate(%PolyTDD{vars: poly_vars_list, body: body_tdd}, var_counter) do
    # Create substitution map from quantified vars to fresh vars
    {substitution_to_fresh, new_var_counter, new_constraints} =
      Enum.reduce(poly_vars_list, {%{}, var_counter, []}, fn %Var{
                                                               name: q_name,
                                                               constraints: q_constraints
                                                             },
                                                             {sub_acc, c_acc, cons_acc} ->
        {fresh_name, next_c} = FreshVar.next(c_acc)
        fresh_tdd_var = Type.tdd_var(fresh_name)
        # Associate constraints of the quantified var with the new fresh var
        # Tie constraint to fresh var name
        fresh_var_constraints = Enum.map(q_constraints, &%Constraint{&1 | arg: fresh_name})
        {Map.put(sub_acc, q_name, fresh_tdd_var), next_c, cons_acc ++ fresh_var_constraints}
      end)

    instantiated_body = Type.tdd_substitute(body_tdd, substitution_to_fresh)
    {instantiated_body, new_var_counter, new_constraints}
  end

  @doc "Generalizes a TDD type into a PolyTDD if it has free variables not in the environment."
  def generalize(type_tdd, env, current_sub) do
    # Apply current substitution to resolve any vars in type_tdd that are already determined
    type_to_generalize = Type.tdd_substitute(type_tdd, current_sub)

    env_free_vars =
      env
      |> Map.values()
      |> Enum.map(&apply_sub_and_get_free_vars(&1, current_sub))
      |> Enum.reduce(MapSet.new(), &MapSet.union/2)

    type_free_vars_set = Type.free_vars(type_to_generalize)

    vars_to_quantify_names = MapSet.difference(type_free_vars_set, env_free_vars)

    if MapSet.size(vars_to_quantify_names) == 0 do
      # No variables to quantify, return as is
      type_to_generalize
    else
      quantified_vars_structs =
        Enum.map(MapSet.to_list(vars_to_quantify_names), fn var_name ->
          # For now, generalized variables have no attached constraints here.
          # Constraints arise from usage and are checked later.
          %Var{name: var_name, constraints: []}
        end)

      %PolyTDD{vars: quantified_vars_structs, body: type_to_generalize}
    end
  end

  defp apply_sub_and_get_free_vars(%TDD{} = tdd, sub) do
    Type.tdd_substitute(tdd, sub) |> Type.free_vars()
  end

  defp apply_sub_and_get_free_vars(%PolyTDD{} = poly_tdd, sub) do
    # For a PolyTDD in the env, we care about its free variables *after* substitution,
    # excluding its own quantified variables.
    # Substitutes free vars in body
    Type.poly_substitute_free_vars(poly_tdd, sub)
    |> Type.free_vars_in_poly_tdd_body()
  end

  # --- Unification (Simplified for now) ---

  @doc """
  Constrains variables in t1 and t2 to be compatible and updates the substitution.
  If t1 is Var(~a) and t2 is Type T, then ~a's bound becomes current_bound(~a) & T.
  If t1 and t2 are concrete, checks their intersection isn't None.
  Returns new substitution. Throws on error.
  """
  def constrain_and_update_sub(raw_t1, raw_t2, sub) do
    # IO.inspect({:constrain_start, raw_t1, raw_t2, sub}, label: "CONSTRAIN")
    t1 = tdd_substitute(raw_t1, sub)
    t2 = tdd_substitute(raw_t2, sub)
    # IO.inspect({:constrain_applied, t1, t2}, label: "CONSTRAIN")

    cond do
      # Identical or one is Any (Any & T = T, so effectively no new constraint on T if T is a var already refined from Any)
      t1 == t2 ->
        sub

      # Effectively constrains t2 if it's a var
      t1 == Type.tdd_any() ->
        constrain_var_with_type(t2, t1, sub)

      # Effectively constrains t1 if it's a var
      t2 == Type.tdd_any() ->
        constrain_var_with_type(t1, t2, sub)

      # Case 1: t1 is a variable
      %TDD{decision: {:var, v_name1}} = t1 ->
        update_var_bound(v_name1, t2, sub, raw_t1, raw_t2)

      # Case 2: t2 is a variable (and t1 is not)
      %TDD{decision: {:var, v_name2}} = t2 ->
        # Note order for error message
        update_var_bound(v_name2, t1, sub, raw_t2, raw_t1)

      # Case 3: Both are function signatures (concrete)
      %TDD{decision: {:is_function_sig, params1, ret1}} = t1,
      %TDD{decision: {:is_function_sig, params2, ret2}} = t2 ->
        if length(params1) != length(params2) do
          raise "Type error (constrain): Function arity mismatch between #{inspect(t1)} and #{inspect(t2)}"
        end

        # For two function *types* to be compatible/substitutable, their parameters are contravariant, return is covariant.
        # However, if we are "unifying" them to be *the same type structure*, then params are covariant.
        # Let's assume for now `constrain_and_update_sub` implies they should be "equal or compatible via intersection".
        # This means their intersection should be non-None, and vars within them get constrained.

        sub_after_params =
          Enum.zip(params1, params2)
          |> Enum.reduce(sub, fn {p1, p2}, acc_sub ->
            # Params are "unified" directly
            constrain_and_update_sub(p1, p2, acc_sub)
          end)

        # Return types are "unified" directly
        constrain_and_update_sub(ret1, ret2, sub_after_params)

      # TODO: Add cases for Tuples, Lists, TDDMap
      # For tuples: length must match, then constrain_and_update_sub elements pairwise.
      # %TDD{decision: {:is_tuple, len1}, yes: elements_tdd1} ...
      # This requires TDDs to encode tuple elements more directly if we want to unify structurally.
      # Current TDD for tuple is just {:tuple_len, N} or general :is_tuple. We need richer TDDs for structural unification.
      # For now, this fallback will handle simple tuple predicates.

      # Case 4: Other concrete types.
      true ->
        intersection = tdd_and(t1, t2)

        if intersection == Type.tdd_none() do
          raise "Type error (constrain): Types #{inspect(t1)} (from #{inspect(raw_t1)}) and #{inspect(t2)} (from #{inspect(raw_t2)}) are incompatible (intersection is empty). Current sub: #{inspect(sub)}"
        end

        # If they are concrete and compatible, `sub` is unchanged at this level.
        sub
    end

    defp constrain_var_with_type(%TDD{decision: {:var, v_name}} = var_tdd, other_type, sub) do
      # raw_t1, raw_t2 are for error msg context
      update_var_bound(v_name, other_type, sub, var_tdd, other_type)
    end

    # No var, no sub change here
    defp constrain_var_with_type(_concrete_type, _other_type, sub), do: sub

    defp update_var_bound(v_name, constraining_type, sub, raw_var_form, raw_constraining_form) do
      # Default to Any
      current_bound_v = Map.get(sub, v_name, Type.tdd_any())
      new_bound_v = Type.tdd_and(current_bound_v, constraining_type)

      if new_bound_v == Type.tdd_none() do
        original_var_constraint_str =
          if raw_var_form != constraining_type,
            do: "(from unifying with #{inspect(raw_constraining_form)})",
            else: ""

        raise "Type error: Constraining variable #{v_name} with #{inspect(constraining_type)} #{original_var_constraint_str} results in an empty type. Previous bound: #{inspect(current_bound_v)}. Current sub: #{inspect(sub)}"
      end

      Map.put(sub, v_name, new_bound_v)
    end

    @doc """
    Handles the application of a function type to actual argument types.
    `fun_type_template` is the (possibly variable) type of the function.
    `actual_arg_types` are the TDDs of the arguments.
    `var_counter` and `sub` are current state.
    Returns `{final_return_type, new_counter, new_sub, new_constraints}`.
    """
    def unify_apply(fun_type_template, actual_arg_types, var_counter, sub) do
      # Apply current substitutions to fun_type_template
      current_fun_type = Type.tdd_substitute(fun_type_template, sub)

      case current_fun_type do
        %TDD{decision: {:var, fun_var_name}} ->
          # Function is a type variable. We need to unify it with a newly minted function signature.
          {param_var_tds, c1} =
            Enum.map_reduce(actual_arg_types, var_counter, fn _arg, c_acc ->
              {fresh_name, next_c} = FreshVar.next(c_acc)
              {Type.tdd_var(fresh_name), next_c}
            end)

          {return_var_name, c2} = FreshVar.next(c1)
          return_var_tdd = Type.tdd_var(return_var_name)

          # The new signature that fun_var_name must conform to
          synthetic_fun_sig_tdd = Type.tdd_function_sig(param_var_tds, return_var_tdd)

          # Unify the function variable with this synthetic signature
          {s1, cons1} = unify(current_fun_type, synthetic_fun_sig_tdd, sub)

          # Now unify actual arguments with the fresh parameter type variables
          {s2, cons2_list} =
            Enum.zip(actual_arg_types, param_var_tds)
            |> Enum.reduce({s1, []}, fn {actual_arg_t, param_var_t}, {s_acc, c_acc_list} ->
              {next_s, next_cs} = unify(actual_arg_t, param_var_t, s_acc)
              {next_s, [next_cs | c_acc_list]}
            end)

          final_return_type = Type.tdd_substitute(return_var_tdd, s2)
          {final_return_type, c2, s2, cons1 ++ List.flatten(cons2_list)}

        %TDD{decision: {:is_function_sig, expected_param_types, expected_return_type}} ->
          # Function is a known signature.
          if length(actual_arg_types) != length(expected_param_types) do
            raise "Arity mismatch: expected #{length(expected_param_types)}, got #{length(actual_arg_types)}"
          end

          # Unify actual arguments with expected parameter types
          {s1, constraints_from_params_list} =
            Enum.zip(actual_arg_types, expected_param_types)
            |> Enum.reduce({sub, []}, fn {actual_arg_t, expected_param_t}, {s_acc, c_acc_list} ->
              {next_s, param_cs} = unify(actual_arg_t, expected_param_t, s_acc)
              {next_s, [param_cs | c_acc_list]}
            end)

          final_return_type = Type.tdd_substitute(expected_return_type, s1)
          {final_return_type, var_counter, s1, List.flatten(constraints_from_params_list)}

        other_type ->
          raise "Type error: expected a function, but got #{inspect(other_type)}"
      end
    end

    @doc "Top-level type checking function for a Tilly program (list of expressions)."
    def typecheck_program(exprs, initial_env \\ %{}) do
      # For a program, we can infer each top-level expression.
      # For `def`s, they would add to the environment.
      # For now, let's just infer a single expression.
      # A real program would involve modules, defs, etc.
      initial_var_counter = 0
      initial_substitution = %{}

      # This is a simplified entry point, inferring a single expression
      # A full program checker would iterate, manage top-level defs, etc.
      if is_list(exprs) and Enum.count(exprs) == 1 do
        [main_expr] = exprs

        {raw_type, _counter, final_sub, constraints} =
          infer(main_expr, initial_env, initial_var_counter, initial_substitution)

        final_type = Type.tdd_substitute(raw_type, final_sub)
        # Here, you would solve/check `constraints` using `final_sub`
        # For example:
        Enum.each(constraints, fn {var_name, constraint_obj} ->
          var_final_type = Map.get(final_sub, var_name, Type.tdd_var(var_name))

          unless Type.satisfies_constraint?(var_final_type, constraint_obj) do
            raise "Constraint #{inspect(constraint_obj)} not satisfied for #{var_name} (type #{inspect(var_final_type)})"
          end
        end)

        {:ok, final_type, final_sub}
      else
        # Placeholder for multi-expression program handling
        {:error, "Program must be a single expression for now"}
      end
    end
  end
end