checkpoint discussion

.aider.chat.history.md

@@ -56997,3 +56997,20 @@ mix test
 > Tokens: 82k sent, 1.6k received. Cost: $0.12 message, $0.26 session.  
 > lib/tilly/bdd.ex  
 > Add file to the chat? (Y)es/(N)o/(D)on't ask again [Yes]: y  
+
+# aider chat started at 2025-06-15 02:19:36
+
+> Newer aider version v0.84.0 is available.  
+> /home/omnissiah/.local/share/uv/tools/aider-chat/bin/python -m pip install --upgrade --upgrade-strategy only-if-needed aider-chat  
+> Run pip install? (Y)es/(N)o [Yes]: n  
+> You can skip this check with --no-gitignore  
+> Add .aider* to .gitignore (recommended)? (Y)es/(N)o [Yes]: n  
+> /home/omnissiah/.local/bin/aider --watch-files --model openrouter/google/gemini-2.5-pro-preview --api-key openrouter=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 --editor n  
+> Error: Read-only file /home/omnissiah/git/pl/CONVENTIONS.md does not exist. Skipping.  
+> Aider v0.83.2  
+> Model: openrouter/google/gemini-2.5-pro-preview with whole edit format  
+> Git repo: .git with 60 files  
+> Repo-map: using 4096 tokens, auto refresh  
+
+#### /map-refresh  
+> The repo map has been refreshed, use /map to view it.  

.aider.input.history

@@ -4158,3 +4158,9 @@
 
 # 2025-06-13 18:48:07.920080
 +y
+
+# 2025-06-15 02:19:44.496228
++n
+
+# 2025-06-15 02:23:11.675263
++/map-refresh

lib/til/tdd.ex

@@ -0,0 +1,51 @@
+defmodule Tdd do
+  @moduledoc """
+  Ternary decision diagram, used for representing set-theoritic types, akin to cduce.
+  There are 2 types of nodes: 
+  - terminal nodes (true, false) 
+  - variable nodes 
+
+  variable nodes consist of:
+  - the variable being tested 
+  - yes: id of the node if the result of the test is true 
+  - no: id of the node if the result of the test is false 
+  - dc: id of the node if the result of the test is irrelevant for the current operation
+
+  the TDD needs to be ordered and reduced (ROBDD)
+  - 'ordered' if different variables appear in the same order on all paths from the root. 
+  - 'reduced' if the following two rules have been applied to its graph:
+    - Merge any isomorphic subgraphs.
+    - Eliminate any node whose two children are isomorphic.
+
+  Working notes:
+  - structure of the ordered variables:
+    Im thinking of structuring all possible types inside 1 TDD, in contrast to cduce, which uses a `desrc` structure that contains several TDDs (one for each domain, like ints, atoms, functions, etc.), and descr is a union between them.
+    For this, I need to come up with a variable structure that'll be ordered. 
+    My set types will need to represent types like: atoms, strings, ints, maps, tuples, functions, kinds? 
+    Moreso, those types themselves consist of smaller subsets of types like:
+    - int < 10 
+    - int in [1, 2, 3]
+    - string > "prefix_" 
+    - atom == false
+    - atom == false or atom == true or atom == nil
+    - map == %{"id" => string} and %{string => any | nil}
+    - etc.
+    Dont know how to represent them and make them ordered.
+  - node cache:
+     I don't yet know what it should contain, I suspect ids of nodes (TDDs) after reduction. This way a comparison between 2 types is just a pointer (id) check in the node cache. But not yet sure.
+  - reduction rules: not sure how to approach them 
+
+  """
+
+  def node(elem, yes, no, dc = _dont_care) do
+  end
+
+  def sum(one, two) do
+  end
+
+  def intersect(one, two) do
+  end
+
+  def negate(one, two) do
+  end
+end

lib/til/type.ex

@@ -0,0 +1,817 @@
+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