The core idea is to replace the current map-based type representations with a system centered around **canonicalized type descriptors (`Tilly.Type.Descr`)**, where each descriptor internally uses **Binary Decision Diagrams (BDDs)** to represent sets of values for different kinds of types (integers, atoms, pairs, etc.).

Here's a plan for adaptation:

** overarching concerns:

- lets use bare maps instead of structs. Structs are closed, and I want to keep the option of adding new fields later by the user of the compiler 

**I. Foundational BDD and Type Descriptor Infrastructure (New Modules)**

This phase focuses on building the core components described in `set_types.md`. These will mostly be new modules.

1.  **`Tilly.BDD.Node` (New):**
    *   Define the Elixir tagged tuples for BDD nodes: `false`, `true`, `{:leaf, leaf_value_id}`, `{:split, element_id, p_child_id, i_child_id, n_child_id}`.
    *   include smart constructors 
2.  **`Tilly.BDD.Store` (New):**
    *   Implement the hash-consing mechanism for BDD nodes.
    *   This store will be part of the compiler `ctx` map.
    *   Key function: `get_or_intern_node(typing_ctx, logical_structure_tuple) :: {new_typing_ctx, node_id}`.
3.  **`Tilly.BDD.ElementProtocol` and `Tilly.BDD.LeafProtocol` (New):**
    *   Define these protocols. Implementations will be provided for basic elements (e.g., atoms, integers for splitting) and basic leaves (e.g., booleans for simple set membership).
4.  **`Tilly.BDD.Ops` (New):**
    *   Implement core BDD operations: `union_bdds`, `intersection_bdds`, `negation_bdd`, `difference_bdd`.
    *   These functions will take BDD node IDs and the `typing_ctx`, returning a new BDD node ID.
    *   Implement smart constructors for `Split` and `Leaf` nodes that use the `Tilly.BDD.Store` and apply simplification rules.
5.  **`Tilly.Type.Descr` (New):**
    *   Define the Elixir struct. It will hold IDs of canonical BDDs for each basic kind (e.g., `:atoms_bdd_id`, `:integers_bdd_id`, `:pairs_bdd_id`, etc., mirroring CDuce's `descr` fields).
6.  **`Tilly.Type.Store` (New or Replaces `Til.Typer.Interner` logic for types):**
    *   Manages the interning of `Tilly.Type.Descr` structs. A `Descr` is canonical if its constituent BDD IDs are canonical and the combination is unique.
    *   This store will also be part of the `typing_ctx`.
7.  **`Tilly.Type.Ops` (New):**
    *   Implement `union_types(descr1_id, descr2_id, typing_ctx)`, `intersection_types`, `negation_type`. These operate on `Descr` IDs by performing field-wise BDD operations using `Tilly.BDD.Ops`, then interning the resulting `Descr`.

**II. Adapting Existing Typer Modules**

This phase involves refactoring existing modules to use the new infrastructure. The `typing_ctx` will need to be threaded through all relevant type-checking functions.

1.  **`Til.Typer.Types` (Major Refactor):**
    *   Functions like `get_primitive_type(:integer)` will now use the new infrastructure to construct/retrieve an interned `Tilly.Type.Descr` ID for the integer type (e.g., a `Descr` where `integers_bdd_id` points to a "true" BDD for integers, and others are "false").
    *   The concept of predefined type *maps* will be replaced by predefined canonical `Descr` IDs.
2.  **`Til.Typer.Interner` (Major Refactor/Integration with `Tilly.Type.Store` and `Tilly.BDD.Store`):**
    *   Its role in interning type *maps* will be replaced. The new stores will handle BDD node and `Descr` interning.
    *   `populate_known_types` will pre-populate the `typing_ctx` with canonical `Descr` IDs for base types like `any`, `integer`, `atom`, `nothing`.
3.  **`Til.Typer` and `Til.Typer.ExpressionTyper` (Significant Refactor):**
    *   `infer_type_for_node_ast` (in `ExpressionTyper` or similar):
        *   For literals (e.g., `123`, `:foo`), it will construct the corresponding `Descr` ID (e.g., an integer `Descr` with a BDD representing only `123`).
        *   For operations that combine types (e.g., if an `if` expression's branches have types A and B, the result is `A | B`), it will use `Tilly.Type.Ops.union_types`.
    *   `resolve_type_specifier_node`:
        *   For basic type names (`Integer`, `Atom`), it will fetch their canonical `Descr` IDs.
        *   For type expressions like `(or TypeA TypeB)`, it will recursively resolve `TypeA` and `TypeB` to `Descr` IDs, then use `Tilly.Type.Ops.union_types`. Similarly for `(and ...)` and `(not ...)`.
    *   The `type_id` field in AST nodes will now store the ID of an interned `Tilly.Type.Descr`.
4.  **`Til.Typer.SubtypeChecker` (Complete Rewrite):**
    *   `is_subtype?(descr_a_id, descr_b_id, typing_ctx)` will be implemented as:
        1.  `descr_not_b_id = Tilly.Type.Ops.negation_type(descr_b_id, typing_ctx)`.
        2.  `intersection_id = Tilly.Type.Ops.intersection_types(descr_a_id, descr_not_b_id, typing_ctx)`.
        3.  `is_empty_type(intersection_id, typing_ctx)`.
    *   `is_empty_type(descr_id, typing_ctx)` checks if all BDDs within the `Descr` are the canonical `False` BDD.

**III. Handling Specific Type Kinds from `project.md`**

The existing type kinds in `project.md` need to be mapped to the new `Descr` model:

*   **Primitive Types:** `%{type_kind: :primitive, name: :integer}` becomes a canonical `Descr` ID where `integers_bdd_id` is "all integers" and other BDDs are empty.
*   **Literal Types:** `%{type_kind: :literal, value: 42}` becomes a `Descr` ID where `integers_bdd_id` represents only `42`.
*   **Union/Intersection/Negation Types:** These are no longer explicit `type_kind`s. They are results of operations in `Tilly.Type.Ops` combining other `Descr` objects.
*   **Function, List, Tuple, Map Types:**
    *   These will be represented by `Descr` objects where the corresponding BDD (e.g., `functions_bdd_id`, `pairs_bdd_id` for lists/tuples, `records_bdd_id` for maps) is non-empty.
    *   The structure of these BDDs will be more complex, as outlined in CDuce (e.g., BDDs whose leaves are other BDDs, or BDDs splitting on type variables/labels). This is a more advanced step.
    *   Initially, `list_type(element_descr_id)` might create a `Descr` where `pairs_bdd_id` points to a BDD representing pairs whose first element matches `element_descr_id` and second is recursively a list or nil.
    *   The detailed map type representation from `project.md` (`known_elements`, `index_signature`) will need to be encoded into the structure of the `records_bdd_id`. This will be a complex part, drawing heavily from how CDuce handles record types with BDDs.

**IV. Parser (`lib/til/parser.ex`)**

*   No immediate changes are required for the AST structure itself.
*   If new syntax for type operations (e.g., `(or Int Atom)`) is desired directly in source code (as opposed to only being used by `resolve_type_specifier_node`), the parser will need to be updated to produce AST nodes that `resolve_type_specifier_node` can interpret.

**V. Documentation (`project.md`)**

*   The "Type Representation" sections will need a complete overhaul to describe the new `Tilly.Type.Descr` and BDD-based system.

**Suggested Phased Approach:**

1.  **Phase 0: Core BDD Infrastructure:** Implement `Tilly.BDD.{Node, Store, Ops, Protocols}`. Focus on BDDs for simple sets first (e.g., sets of atoms, integers).
2.  **Phase 1: `Tilly.Type.Descr` and Basic Types:** Implement `Tilly.Type.Descr`, `Tilly.Type.Store`, and `Tilly.Type.Ops`. Implement construction of `Descr` IDs for primitives (`any`, `nothing`, `integer`, `atom`) and literals.
3.  **Phase 2: Typer Integration for Primitives:** Refactor `Til.Typer.Types`, `Til.Typer.Interner`, and parts of `Til.Typer.ExpressionTyper` to use the new system for primitive and literal types. Update `resolve_type_specifier_node` for basic type names and simple `(or)`, `(and)`, `(not)` forms.
4.  **Phase 3: Subtyping:** Implement the new `Til.Typer.SubtypeChecker`.
5.  **Phase 4: Constructed Types (Iterative):**
    *   Start with pairs/tuples, then lists. Design their BDD representations within `Tilly.Type.Descr`.
    *   Tackle records/maps. This will be challenging and require careful mapping of `project.md`'s map features to CDuce-style record BDDs.
    *   Address function types.
6.  **Phase 5: Advanced Features:** Polymorphism (type variables in BDDs), refinement types.

This is a substantial refactoring. The key is to build the BDD foundation correctly, as everything else will depend on it. The `typing_ctx` will become a critical piece of data passed throughout the type system.

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