# 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