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17
.aider.chat.history.md
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@ -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.

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.aider.input.history
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@ -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

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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

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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