<!--
An iteration/rewrite of the previous module proposal. Moved walkthrough and formalism before concepts. Rewrote major parts in every section (especially intro) to make it easier to approach. Added sections to discuss important topics.

Motivation
Objectives
Overview
Walkthrough
    Symbols of a module
    How importing modules use symbols
Formalism
    Layout of the codebase
    Individual module information
    Resolving names of exported declarations
    Providing additional information for importers
    Resolving names for compilation
Concepts
    Handling unboxed types
    C macros are not exportable
    Import ordering does not matter
    Forward declarations are unnecessary
    Explicit transitive module dependencies
    Exporting inline functions
    Generating multiple module interfaces
    Modules use `import` instead of `#include`
    Cyclic modules
    Other kinds of symbols
    Implementing module namespaces
Porting existing C code
Handling initialization order
Why C++20 modules failed (and why we will succeed)
-->

# Modules proposal (v5, reorganize)

## Motivation

This proposal adds a module system to Cforall, an extension to the C programming language. However, most of the information discussed can be used to create a module system in C or another system programming language.

**Why do we need modules?** It's worth noting that not all programming languages have modules (C being the obvious example here). In truth, modules don't tend to increase a language's expressive power, as its features can usually be emulated by other code structures. Where modules become really useful is when managing a codebase with multiple collaborators. Modules have the practical benefit of helping us focus only on the parts of the program we're working on. They also help us avoid accidentally relying on implementation details by restricting what can be accessed by other code, thereby keeping a codebase easier to extend and maintain.

But **isn't a C translation unit a module?** (a c translation unit is a `.c` file after preprocessing) It has `static` and `extern`, but there isn't a good way to analyze which symbols are used where in the program. A symbol defined in `foo.c` can be declared in `foo.h`, but that symbol can also be declared in `unrelated.c`. Calling a C translation unit a module is like saying a struct is well-defined, even if it can only be used if some arbitrary set of functions is called. We don't consider it a module because it doesn't provide a way to control which modules use its symbols. **We argue that C translation units, with some access control, can be considered a module.**

*Some paragraphs of this proposal are italicized - this is to indicate it is specific to Cforall, or my working thoughts. The rest of this proposal is applicable to systems programming languages in general.*

## Objectives

Let's clarify what we're trying to achieve with our modules. The term "module" is as abused as "polymorphism" in programming languages, which makes it challenging to determine what we're working towards with a module system for C. Here are our 3 main objectives:

1. **Make C translation units into modules**
2. **Remove the need for .h files**
3. **Modules should "own" their contents**

First, to make C translation units into modules, our proposed modules should not require fundamental architectural changes to an existing C project in order to use it. Crucially, there needs to be a way to represent forward declarations of other modules' contents.

Second, most modern languages don't require an additioanl file just to link symbols between files (Object Oriented languages have interfaces, but they are not required). We would like developers to only need to declare a symbol once, and leave symbol discovery to the module system.

Third, it should not be confusing as to which module's symbols are visible at a given time, because a module's symbols should only be visible if said module allows them to be. Ideally, such symbols are only visible if said module exports them and a module imports said module (we will find there are special cases where we need to leak some information).

Our key guiding principle which will help us achieve these goals is to **decouple symbol exports from each other**. This means that it should be possible to export a symbol's implementation details without leaking the implementation details of any other symbol. This allows our module system to have full control over what symbols are visible within a module, which enables us to perform our advanced analysis.

Other topics that will be dicussed include module friendship, backwards compatibility and interactions with Cforall features. Some topics are highly complex and are pulled into separate sections, such as handling initialization order and importing existing standard libraries.

## Overview

A key guiding principle behind this proposal is the idea that symbol exports are decoupled. This means that exporting a symbol should only provide enough functionality for the importer to use it, and nothing more. We try to take this even further: **only the statement in which a symbol is defined is allowed to export its implementation details,** as opposed to having one export implicitly exporting another's details. This means importers only get what they need (and nothing more) and exporters have full control over who has access to their details. To explain by example:

```
// module A
module;
export struct Inner {int a; int b;};

// module B
module;
import A;
export struct Outer {int i; struct Inner f1;};
export struct Outer constructOuter() { /* implementation omitted */ }

// module C
module;
import B;
export struct Outer o = constructOuter();
int x1 = o.i;
struct Inner x2 = o.f1;
int x3 = o.f1.a;  // error, must import definition of struct Inner to use
```

Module C can access the fields of `struct Outer`, but it cannot access the fields of `struct Inner` because it did not import module A. Note that module C can access the name `struct Inner`, because the type system requires the type of `x2` to be written out. Additionally, any module that imports module C does not receive the implementation details of `struct Outer` or `struct Inner`.

The fact that importing an individual symbol is well-defined here forms the basis of our module system. This is because it allows us to reason about individual symbols, without having to consider everything within a module. This greatly simplifies our proofs of correctness. This also makes it trivial to get order-agnostic imports, enables us to make modules cyclic and allows us to remove the need for forward declarations. In our setup, a module file is simply a convenient way to manage symbol scope and package symbols to be exported together.

This module system currently allows 3 kinds of symbols to be exported:
* Types (ie. `struct` and `typedef` statements)
* Functions
* Variables (ie. global variables)

As shown above, sometimes type names need to be visible even if they are not explicitly imported, in order to enable full functionality of other symbols. However, the type must be imported in order to access a type's fields. As for functions and variables, they must be imported in order to be visible or used. Importing an inline function should appear no different than a non-inline function - the only difference being more compilation dependencies and more information available to the optimizer.

Note that there is a distinction between "visible to the module" and "visible to the optimizer" that is different from regular C: Just because something is provided to the optimizer, doesn't mean the code in a module can access it. In contrast, regular C code would be like putting `export` on every exportable symbol and import statement (ie. transitive module dependency). In this proposal, "visible" refers to "visible to the module".

*This module system was in part inspired by the concept of weak and strong modules as described by [this article](https://thunderseethe.dev/posts/whats-in-a-module/) and the paper [Backpack: Retrofitting Haskell with Interfaces](https://plv.mpi-sws.org/backpack/). Put roughly, weak modules are dependent on other modules, while strong modules are dependent on module interfaces. Unfortunately, the concept of what is an interface and what is not is unclear in C (where header-only libraries exist), and certain aspects of systems programming require exposing certain details that would otherwise be hidden in other languages (eg. unboxed types). After multiple attempts of trying to figure out the key principle behind the distinction (as well as figure out if it can be implemented), I eventually reached the key insight of decoupling symbol exports.*

## Walkthrough

A module holds a collection of symbols to be exported. A module also uses imports to control what symbols are visible and how those symbols can be used. We will analyze:
* What are the kinds of symbols and what does the importing module see?
* How does the importing module disambiguate between symbols?

As stated in the overview, we wish to enforce that **only the statement in which a symbol is defined is allowed to export its implementation details.** This means that you cannot use a function or struct that is defined in another module unless that module exports it and you import said module (of course, it may be accessible using `extern "C"`). We will see certain cases where C forces this encapsulation to be somewhat broken (eg. types and inline functions), but we try to limit this "information leakage" as much as we can.

### Symbols of a module

Symbol definitions in our modules (ie. the symbols the module can export) are either types, functions or variables. While types can be defined in the same line as a variable (eg. `export struct {int i;} name = {5};`), we will make the simplifying assumption right now that this does not happen (in the example, both `name` and the anonymous struct would be exported together).

#### Types

We'll consider 3 kinds of types: builtins (eg. `int`), user-defined `struct` types, and aliases (ie. `typedef`). We defer discussion on pointers, references and arrays until the end of this section. We'll consider other user-defined types (eg. `union`) in Other kinds of symbols section.

Built-ins are provided by the compiler to every module, so we don't need to consider them. We treat aliases like a `struct` with one field, which is implicitly accessed, allowing us to only consider the `struct` case (note that exporting a `typedef` without exporting the underlying type produces different behaviour than what one may be used to).

Taking the most idealized version of our guiding principles, if we export `struct A` that has a `struct B` field (ie. not itself), then we should not export any information related to `struct B`. The importer will be able to access all fields in any `struct A` variable, but the `struct B` field is essentially an opaque type (if a module also wants to access its fields, it needs to import `struct B` too).

Unfortunately, this runs into problems. First, we have unboxed types (boxed types are implemented as a pointer to the actual object). This means we need to know the size and alignment of every field, so we know how large the struct is and the offsets of each field. Second, a very common pattern (so for practical purposes, we cannot ban it) is to initialize a variable with a field, which requires writing down the type name (eg. `struct Exported e; struct Field f = e.f1;`). So importers need to know the size, alignment and name of a field (we also need to consider move/copy constructors for Cforall types, but in C we simply copy bytes). A similar problem occurs when returning types from functions (eg. `export struct Unexported foo();`), which we will discuss in the Functions section.

How do we obtain this size/alignment/name information? We use compile-time reflection to crawl import modules as needed (see Formalism section for details and a proof of correctness). Our technique handles circular imports, as it should only fail if we encounter a type name ambiguity (eg. we import module `A` and `B` which both export `struct S`, and we need a `struct S`) or the type is infinitely recursive (eg. `struct A {struct B b;}; struct B {struct A a;};`). This means we could end up analyzing the entire codebase to determine a the size/alignment of a `struct`, but in practice this should not happen often (regular C also requires the type definitions of every field, so we are arguably not much worse).

Pointers and references are boxed values, so we know its size/alignment (so no need to analyze the underlying type). However, we still require modules to import the symbol in order to handle name disambiguation. Arrays may be parameterized by an integer whose value must be immediately available. This is important, as otherwise we can end up with cases such as `struct S {struct T t[sizeof(struct U)];};`, which may be difficult to resolve. In our case, we can simply leverage compile-time reflection to obtain the integer value, similar to the way we resolve field types.

#### Functions

Functions have the form `returnType name(parameterType, ...numberOfParameters) {...body}`. In order for importers to use this function, we need to provide the size, alignment and name of any types in its declaration. We use compile-time reflection to resolve the details (see Types section for details).

If we are exporting an inline function, we also need to provide the function body to the compiler/optimizer (though from the perspective of the module, symbol visibility is the same whether inline or non-inline). This also uses compile-time reflection in order to resolve the symbols within the function body (which is done within the context of the containing module, not the importing module).

*Cforall introduces a keyword called `forall`, which can be used to create polymorphic functions. This is currently implemented using a technique called "dictionary passing", similar to Haskell or Ocaml. This means there is only one instance of the polymorphic function, and callers need to pass any trait information as additional (hidden) parameters. This means we must provide trait information to the importer. Within a `forall` block we can also define polymorphic types, which can be used as the return value of a polymorphic function. In that case we need size/align/name information, and the first two are currently handled by calling a "layout function" at runtime (this could possibly be moved to happening at compile-time, but I don't believe it is). As such, we also need to provide the layout function to the importing module. So polymorphic functions can be made to work with our system, but we may need to relax some aspects of our guiding principles.*

#### Variables

Variables have the form `variableType name = expression;`. We make the simplifying assumption that only one name is defined at a time (ie. no `int a, b, c;`). Similar to types and functions, the exporting module needs to also provide the size, alignment and name of `variableType` to any importing modules, which is handled by compile-time reflection (see Types section for details).

*If the variable is actually a polymorphic type (see Function section for details), I'm actually not sure how this works. The layout function can only be called at runtime, but you need the information in order to allocate the appropriate amount of space in the `.data` section. More analysis is needed here.*

### How importing modules use symbols

The previous section notes compile-time reflection as the solution to many of our challenges with modules. Here we will explain how symbol names are resolved to the correct modules, helping us define how our compile-time reflection crawls through modules. See Formalism section for a more rigorous proof of correctness.

#### Gathering symbols

First, we scan the top-level declarations of a module, gathering a list of imported modules and top-level symbol names defined within the module.

```
// module data/graph/node
module;
import edge;
import ../minheap;
import stdlib;
const int maxEdges = 10;
export struct Node {
    int id;
    int value;
    struct Edge edges[maxEdges];
    struct MinHeap someField;
};
// Shadows imported MinHeap
struct MinHeap {int capacity; int size; int *data;};
struct MinHeap initHeap(int capacity) {
    // Assumes malloc doesn't return error code
    return {capacity, 0, (int*)malloc(sizeof(int) * capacity)};
}
void destroyHeap(struct MinHeap* h) {
    free(h->data);
    h.capacity = 0;
    h.size = 0;
}
```

We first look for the import relative to the current directory - if that fails we look at libraries. So our set of imports here are: `data/graph/edge`, `data/minheap` and `stdlib` (library module).

The top-level symbol names are: `maxEdges`, `Node`, `MinHeap`, `initHeap` and `destroyHeap`.

#### Crawling other modules

Continuing with our example, we do the same top-level analysis with the imported modules.

If `data/minheap` has `export import minheap/functions;` defined, then would be as if `data/graph/node` has `import ../minheap/functions;` defined. This can keep going - if `data/minheap/functions` has `export import`, it is also added to `data/graph/node`. After we run out of `export import` statements to resolve, we can look at the top-level declarations of every imported module in order to determine what symbols are visible to `data/graph/node`.

After gathering the symbols in the imported modules, we can proceed to bind each symbol within `data/graph/node` to the correct module. The details of how multiple symbols are disambiguated are described in the Resolving symbols section.

In addition to name disambiguation, some symbols need additional information in order to be useable by importers. For example, size/alignment information of types, function bodies for inline functions, and trait information for polymorphic functions. This information is obtained by resolving the symbols on any imported module, and so on, as necessary.

This task is recursive, which raises the problem of circular imports: What if we recurse back to `data/graph/node` (or any module that creates a cycle)? Since we reason at the level of symbol definitions, as long as we are analyzing different symbols inside the circularly imported module, we don't actually have a cycle. This leaves us with handling the problem where we circle back to the same symbol. For size/alignment analysis, coming back to the same type means that said type contains itself, which for our purposes is not resolvable (emit error and stop). If an inline function calls other inline function that mutually recurses with itself, we produce a forward declaration of the inline function within the underlying C code (Cforall compiles down to C). For trait information, a trait works like a collection of conditions, which means it includes itself, which means we can safely ignore circular references (we may want to emit a warning though). Since we can handle all of our circular problems, our system is well-defined here.

#### Resolving symbols

A key aspect about our modules is that imported symbols are used in the same way as they are defined - no namespacing needed (eg. `struct Edge` in the provided example). While this raises the potential for name collisions, we argue that the potential benefits outweigh the limitations (and many of the limitations can be mitigated with additional features).

*To provide additional context, a core feature of Cforall is its advanced overloading system (eg. allowing multiple variables with the same name but different types to coexist). Adding namespaces would limit our ability to research and take advantage of this feature.*

When resolving symbols, symbols defined within our module have precedence over imported symbols. If we want to resolve to a specific imported symbol, we use the `::` operator (eg. `struct a::S` or `struct "a"::S`). The module name on the left side of the `::` operator is looked up using the same mechanism as import statements (note that the module being looked up must have been imported, either directly or through `export import`).

*In Cforall, the addition of the overload system means that symbols defined within our module system only have preference over imported symbols, instead of completely shadowing them. Here, our module system provides a list of candidates for each symbol to the overload resolution system. This will require refactoring the overload resolution algorithm to hold the full name of a symbol (symbol name + module name), and favour symbols defined within the given module (eg. `struct MinHeap` in the provided example).*

## Formalism

Taking the Walkthrough section a step further, we will provide a rough sketch of a formal argument that our module system is well-defined.

We'll first describe the layout of our module system by providing a rough description of the file structure and grammar we are working with. Then we describe what we can grab from each module file separately. By combining this information with those from other modules, we can resolve which module's symbol is being used in each exported declaration. Note that for some symbols to be properly used by importers, additional information such as size/alignment information will be necessary, which we will show is possible to obtain. Finally, we can resolve every symbol within a function body or expression, thereby completing the compilation process.

### Layout of the codebase

In order to provide a formal argument that our module system is sound, we need to first describe the format of the codebase we are trying to analyze. We restrict the syntax of our module files significantly in order to simplify our proof.

The file system is set up so that imports are relative to the current directory, or found in a library. For example, a module file `data/graph.cfa` trying to access `data/graph/node.cfa` would write `import graph/node;`. If such a file doesn't exist, we will look for `graph/node` within the provided libraries (starting from the root directory of each library).

Module files have `module;` as their first statement. Import statements are written as `import filePath;`, where the file path can be escaped with double-quotes if necessary. Only top-level statements can be exported, done by having `export` as the first keyword (eg. `export const int i = 3;`). The available top-level statements are:
* Imports: Format is `import path/to/file;` or `import "path to/file";` (double quotes for escaping characters).
* Types: `struct` and `typedef` statements. Only one `struct`/`typedef` can be defined per top-level statement (eg. no `typedef struct {int i;} MyStruct;`). If we parameterize an array with an integer, it must either be a constant or a single variable.
* Functions: Format is `returnType name(parameterType ...numberOfParameters) {...functionBody}`.
* Variables: Format is `variableType name = initializerExpression;`. Initializer may be omitted. Only one variable can be declared per top-level statement (eg. no `int a, b;`).

The syntax of function bodies and initializer expressions can mostly remain unrestricted, as the module system provides name matches to them, rather than the module system being affected by anything within. One notable change is the `::` operator, which allows us to disambiguate which module a symbol belongs to. For example, if `struct S` is exported from module `a` and `b` and we import from both, we can write `struct a::S` or `struct "a"::S` to disambiguate.

### Individual module information

For every module file, we can collect the import list and the top-level symbols, without needing to consult any other files. The top-level symbols include types, functions and variables.

Top-level statements, at least the way we have it set up here, avoid any context-sensitive sections (eg. `MyType * a;` could be interpreted as an expression, but we don't allow those as a top-level statement). This means we have no issues parsing all symbols at the top-level (function bodies and initializer expressions are context-sensitive, but at this stage we don't need to look inside them). This means that for each module file, we can grab an import list, a type list, a function list and a (global) variable list, as well as determine which are exported.

### Resolving names of exported declarations

Now we wish to resolve every symbol in any module's top-level declaration (this does not include the function bodies or initializer expressions). We achieve this with the following steps:
1. Collect a module's full import list
2. Use the full import list to collect all imported symbols
3. Use all imported symbols to resolve our symbols

In order to determine a module's full import list, we look at the individual module information of each imported module. To find the imported module file, we initially look for it relative to the current directory of the module that the import statement is in - if the module file does not exist, we look starting at the root directory of any provided libraries (if we can't find the module, we error out). If any imported module has `export import moduleName;` (or a name other than `moduleName`), then we recursively examine those too. If we end up importing any modules we have already imported (or the module we are getting the full import list of), we can ignore those. Since there are a finite number of modules in a codebase (plus any provided libraries) and we don't analyze a module twice, this search will terminate with a full import list.

To collect all the imported symbols, we take every module in the full import list and we grab all of the top-level statements that have `export` as their first keyword. This gives us an imported type list, an imported function list and an imported variable list.

Now that we have a list of imported symbols as well as the module's own, we can start resolving symbols in the top-level declarations. Since we are not considering function bodies or initializer expressions (and our top-level statements are simple), we do not have ambiguity on whether a type, function or variable is needed. To resolve names, we first check to see if it uses the `::` operator - if so, then we use the same strategy as when resolving import statements (also, we error out if the module isn't in the full import list). Otherwise we look in the module's own top-level symbols to see if we have a match (this means a module's symbols shadow its imported symbols). If we don't find a match, then we look in the list of imported symbols. If the list of imported symbols has more than one match, we error out due to ambiguity (print diagnostic telling user the options and suggesting the use of `::`).

Something to note about this setup is that forward declarations are neither necessary nor allowed, because all visible symbols are known before attempting to resolve names.

### Providing additional information for importers

Unfortunately, in order to use some of these top-level symbols, the importer sometimes needs more than the names within top-level declarations (ie. not including function bodies or initializer expressions) in order for the compiler to process it. For example, if a function returns a `struct`, we need to know the size/alignment of the `struct` in order to use it.

Type names are found within the definitions of other types, the return and parameters of a function, and the type of a variable. In order to use a type, we must know the size/alignment of its fields. Similar problem with functions and their return and parameter types. With variables, size/alignment information is technically not needed, but to keep its semantics consistent with everything else, we require it (eg. `struct Unimported x = s.f1; struct Unimported x1 = importedVariable;`).

In order to figure out size/alignment of types, we first resolve its name. Pointers, references and built-in types have a defined size/alignment, and don't need to be analyzed further. However, an array type needs its element type analyzed further, as well as its integer parameter (our formalism only allows a simple number, but we could extend this in the future). That leaves `struct` or `typedef`, which is determined by looking at the types of its fields or aliased type. This process keeps recursing until we resolve everything or find a cycle (if we have a cycle, we error out). This terminates because there are a finite number of symbols. This means we can obtain the size/alignment of any well-formed type.

While the importing module doesn't change its behaviour whether a function is inline or not, the compiler/optimizer must see the function body. This means the module system must resolve all symbols that the inline function body can access. For example, if we import a module that contains an inline function, we need to resolve all symbols that that module can see. And if any of its imported symbols are inline functions, then we need to keep recursing. If we find a mututally recursive inline function, we would emit a forward declaration (eg. `inline float a();`). Note that the module that owns the inline function must use `extern` when compiling it (eg. `extern inline float a() {return 5;}`), to ensure a definition is emitted in the assembly. This terminates because there are a finite number of modules.

*While the technique used for importing inline functions is sound, it can be optimized (we can resolve symbols within the inline function body first, instead of immediately expanding every import). Here, a single imported inline function forces the containing module to expose its contents to the optimizer. It's as if every import statement within the containing module was converted into `export import`. While our module system ensures these `export import` changes are not visible to the module importing the inline function, it is visible to the optimizer. My major question is: if I add an unused exported inline function to any module, will the additional information provided to the optimizer affect code performance significantly? My intuition says no, since none of it should be accessed by the module that imported the inline function, though I would need to double check.*

*Cforall introduces the `forall` keyword, which allows creating polymorphic functions and types. The polymorphic functions are currently implemented using a technique called "dictionary passing", similar to Haskell or Ocaml. This means there is only one instance of the polymorphic function, and callers need to pass any trait information as additional (hidden) parameters to it. This means that we need to provide the trait information of each polymorphic argument to the importer. In order to obtain this trait information, we could follow a similar technique to obtaining the size/alignment of types, except that we're working to define a trait rather than a type. As such, if a trait mutually includes another trait, we can ignore the circular reference. I have also heard that there are "layout functions" that need to be provided for polymorphic types (since they can be of different sizes/alignments), so we would need to find those functions too.*

### Resolving names for compilation

Now that all symbols visible to a module have been collected, we can proceed to resolve all symbols within function bodies or initializer expressions. Technically, the additional information needed to use them isn't required, though it simplifies our proof and implementation.

We resolve names in the same manner as described in the section Resolving names of exported declarations. This means that symbols in the current module (types and variables/functions are different) shadow those that are imported, though the imported symbols can still be accessed using the `::` operator.

*In Cforall, the addition of the overload system means that symbols defined within our module system only have preference over imported symbols, instead of completely shadowing them. This works by having our module system provide a list of candidates for each symbol to the overload resolution system. The overload resolution algorithm will need to be refactored to hold the full name of a symbol (symbol name + module name), and favour symbols defined within the given module (eg. `struct MinHeap` in the provided example). Whether favour means "break ties" or "always use current module's symbols if possible" is a design choice (I prefer the latter).*

## Concepts

A module is a collection of symbol definitions, which it can export to other modules. In order to define said symbol definitions, it may import other modules' symbols. We consider 3 kinds of symbols: variables, functions and types.

*Cforall introduces other kinds of symbols, such as traits. The C language as well as GCC extensions also support a significantly more complex grammar than what is used in this proposal. I discuss some more about this in Other kinds of symbols section.*

Our proposed module system is one instance within the space of all viable module systems, created from a number of design choices and solutions to challenging problems. We will highlight a number of them, and discuss how our module system handles them. We will also describe a number of functionalities in our system 

### Handling unboxed types

In the example below, we note a problem: in order to use `B::foobar` and `B:bb` in C, we also need to provide the definition of `A::a`. This breaks our principle of decoupled symbol exports!

```
                 Module B
               --------------------------------------
               | module;                            |
      imports  | import A;                          |  exports
A::a --------> | export int b = a;                  | --------> B::b
A::aa          | export struct aa foobar();         |           B::foobar (+ A::aa)
               | export struct bb {struct aa foo;}; |           B::bb (+ A::aa)
               --------------------------------------
```

This problem arises because the importer needs to know how much space to allocate on the stack for the type. Languages that use boxed types (eg. Java, Go) do not have this restriction, since the caller only needs to store a pointer on the stack (eg. when calling `B::foobar`). In contrast, C and other systems programming languages (eg. C++, Rust) require handling unboxed types, since it demands control over pointer indirection (also, there may not be a heap available to support boxed types). This means we need to know the definitions of types in order to use them, even if it's just to allocate enough space on the stack. In C/C++, this is done by including transitive dependencies in headers; in Rust, this is done by compiling an entire crate at a time.

It turns out that the importer need not know the definition of `A::aa`, however. **We only need to provide the size and alignment of a type in order to store it (in addition to the name).** This means that if we knew that `A::aa` is 32 bytes in size, aligned to 8 bytes, the caller of `B::foobar` has enough information to output working assembly. This allows any importer of `B::foobar` to assign the output of `B::foobar` to a variable, then pass it by value into a function. However, the importer cannot access the fields of `B::foobar` or change them unless it imports `A::aa`, giving us exactly the symbol decoupling we want.

An interesting property of this is that, depending on the ABI (Application Binary Interface, determines exactly how things like functions are called in assembly), if `A::a` changes but does not exceed its size or alignment allocations, any module that imports `B::foobar` but not `A::a` does not need to be recompiled! This could lead to libraries where user-facing `struct` types are set to be larger than they currently are, so that even if the `struct` needs its definition changed, the user's code may not even need to be recompiled!

How do we provide the size and alignment of a type, though? A couple strategies come to mind:
1. We provide the entire type definition to the compiler, but anything within the module is not allowed to access its fields unless it is imported. Much simpler to implement, but we might need to crawl the codebase and a lot of additional code needs to be provided to the compiler.
2. We extract size/alignment information into a separate generated module interface, which is used in place of the actual type. This provides much more succinct code to the compiler. We still need to crawl the codebase to get the information, but it is cached afterwards. One way to calculate size/alignment information is to generate a separate program with all the types, compile it, and inspect the result. Another way is to collect the sizes of the built-in types, then calculate the size/alignments of types from the idea that `struct` types take the maximum alignment of their fields.
3. We store all size/alignment information in some central file. This is the same as the previous idea, except that we store all size/alignment in a central file instead of generating a module interface file for every module. This could help reduce file IO cost and simplify updating size/alignment information when types change.

Option 3 sounds like the most ideal option, but option 1 is the easiest to implement, and is the configuration that is used in the Formalism section. There is also another "gotcha" to consider with options 2 and 3: using type-punning to implement them seems to break strict aliasing rules in C99. A common way to avoid type-punning is to use `union` types, but 

*Cforall has the sized trait, which may prove useful for me to use when implementing things (it will likely help with handling polymorphic functions and types). I was also made aware of lifetime operations in Cforall, which I am not that familiar with. I assume they are handled the same way as move/copy constructors - they also need to be provided alongside the size/alignment information.*

### C macros are not exportable

**In our proposal, the C preprocessor runs before the module system.** This allows us to write macros that auto-generate symbols to export, which is likely an important C pattern. However, this makes it very challenging to export C macros.

It is worth pointing out that C++20 modules also do not support exporting C macros. A problem with C macros is that they are too powerful - they can make arbitrary changes to your code, forcing you to reparse, and they operate using a separate language that ignores C code structure. With modern C++ and Cforall features, the need to have modules export C macros is usually not needed outside of porting existing C code.

What if you are dead set on making modules export C macros? You could make the C preprocessor module-aware by using directives such as `#pragma module` and `#pragma export MY_VALUE 3`. Unfortunately, due to having to work within the confines of the C preprocessor, you'd likely be stuck with having to settle with a simple module system. A better alternative would be to have the C preprocessor to output all C macros that it encountered while preprocessing a file, then collect all import statements within the file. We could then reparse the file using all of the C macros from the other files. This configuration is still somewhat unideal, but it does satisfy some common use-cases, and could be used as a starting point. Note that if you're really, really dead set on having the exact same behaviour, just use precompiled headers - they're an optimization that ensure the same behaviour.

The other problem with supporting C macros is that they introduce a kind of ordering on `#include` statements, which we are trying to avoid with imports. We also don't wish to promote the use of C macros when other modern language features are often a much better fit. As such, we elect not to support exporting C macros out of modules.

But what about porting existing C code? With our current formulation, we don't provide a way to use C headers within our modules. This problem is complex enough that we will pull it out into a dedicated section (see Porting existing code section).

### Import ordering does not matter

A key problem with `#include` is that textual inclusion is order-dependent - including `a.h` before `b.h` may result in different behaviour than `b.h` before `a.h`. Not only does this cause confusion among developers, it also affects compilation speed - while headers can be precompiled, they must always account for the possibility of a C macro changing the meaning of the header file.

Since our module system runs after the C preprocessor, our generated module interfaces can be optimized for maximum compiler efficiency. The potential gains are significant: when the standard library became available to import in C++23 (ie. `import std;`), the time to compile a "Hello World" program essentially halved. This significant reduction in build times likely translates to faster iterations and more productive developers.

In terms of developer clarity, it's worth noting that in most programming patterns, this ability for `a.h` to influence `b.h` is undesirable. so when a user imports our modules, they receive the same symbols regardless of import order.

Part of the inspiration for order-agnostic imports comes from functional programming, with its focus on limiting side effects. But what if you want to pass macros into a module? Here, we can take inspiration from the concept of a Functor from the ML programming language. While not in our current implementation, we can create a special kind of module which takes in a set of macros to be used when parsing the module. Otherwise, we use the same set of macros when parsing every module (eg. `#define ARCH amd64`, which we can define in some module configuration file).

In the future, we can also support imports within functions. This takes some inspiration from Python, except that they are executed at compile-time instead of run time. These behave like a normal import, except they only take effect within the code block that they are imported in, and only for the statements after the import statement.

Another area for future development is to use the generated module interfaces in a language server. The explicit visibility control provided by our module system over regular C allows us to provide cleaner information to AI in order to provide robust code-generation capabilities.

### Forward declarations are unnecessary

Since we scan all top-level declarations while generating module interfaces, forward declarations are unnecessary. In fact, the module system can resolve what would otherwise be incomplete types in C. In the following example, even if we added `struct Other;` after `module;`, `struct Other details;` would still break. However, with our module system, we can resolve this.

```
module;
export struct Node {
    int id;
    struct Other details;
};
struct Other {
    int symbols[max_symbols_supported];
};
const int max_symbols_supported = 100;
```

This property of being able to "look ahead" in a file echoes some parallels with classes in object-oriented languages. In those languages, a method's definition can call a method defined later, but still within the same class definition. In fact, modules and objects share many features (eg. abstraction, encapsulation). The main difference is that a module behaves more like a singleton class (as they are actually sections of code), wheras objects can be instantiated.

A common pattern in C is to have mutually recursive types defined in different files (eg. `node.h` defines `struct Node {struct Edge **edges;};` while `edge.h` defines `struct Edge {struct Node **nodes;};`). In regular C, this pattern is resolved by inserting forward declarations of the other struct before defining the given struct. In order to make this work in our module system, we would import the other module. This highlights a potential limitation with our module system - it doesn't allow us to only export a forward declaration of a type. We argue this problem isn't particularly concerning, but there are ways to extend our system to support this (we can consider reserving certain export tag names, see Generating multiple module interfaces for details).

The key feature that allows this is that our specification allows parsing top-level declarations with a context-free grammar (expressions in C are context-sensitive, but top-level declarations don't require parsing the expression part). As we extend this proposal with additional features (eg. nested types), care should be taken to ensure we don't introduce ambiguities in naming or context-sensitive parts. I am unsure if C++ top-level declarations are context-sensitive or not - if they are, then they would need to be disambiguated in order to apply this proposal to them.

### Explicit transitive module dependencies

A problem with C headers is that including them can cause other headers to be included. This can lead to difficulties refactoring the code to use a different library, as the existing code inadvertently makes use of these implicitly included headers. C's design requires this because types must be completely defined in order to use them, but our system avoids this problem by having symbol exports be decoupled from each other. As such, we can produce much cleaner module interfaces.

However, we do not wish to ban transitive module dependencies, as there are many cases where we want to bundle multiple modules together. Due to this, we allow explicit transitive module dependencies through the use of `export import`. Let's take a look at two possible use-cases:

```
// module std
module;
export import std/vector;
export import std/iostream;

// module wrapper
module;
export import std/map;
export import std/string;
export typedef map[string, string] stringmap;

// module client 
module;
import std;  // this is equivalent to import std/vector;
             //                       import std/iostream;
             //                       import std;
import wrapper;  // this is equivalent to import std/map;
                 //                       import std/string;
                 //                       import wrapper;
```

To recap, if a module imports a module that contains `export import ABC;`, then it is as if the importing module had `import ABC;` as one of its import statements.

In the above case, `std` allows developers to import a common set of functionality without having to remember the names of its constituent modules. `wrapper` handles a special case with exporting `typedef`: Since `wrapper` does not own `map` or `string`, we should `export import std/map; export import std/string;` if `client` expects to use the fields of `map[string, string]` (otherwise, we would only know that `stringmap` is a `map[string, string]`).

### Exporting inline functions

Inline functions require the definition of a function to be available to the compiler/optimizer. However, we want the importing module to behave the same way, whether an imported function is inline or not. Let's look at an example:

```
// module inlined
module;
import supporting;
export inline int power(int a, int b) {
    int ret = 1;
    for (int i=0; i<b; ++i) ret = multiply(ret, a);
    return ret;
}
// module supporting
module;
import deeper;
export int multiply(int a, int b) {
    int ret = 0;
    for (int i=0; i<b; ++i) ret = add(ret, a);
    return ret;
}
// module deeper
module;
export int add (int a, int b) {return a + b;}
// module client
module;
export int foobar() {return power(10, 5);}
```

In this scenario, to compile `client`, the compiler needs the exported symbols of `inlined` and `supporting`. Note that the compiler does not need `deeper` because `multiply()` is not an inline function. However, `client` cannot access symbols from `supporting` unless it imports it directly.

If `inlined` has not generated its module interfaces by the time `client` is being compiled, then the presence of a single inlined function would cause all modules imported by `inlined` to need to be traversed, since the module system cannot ascertain which module contains `multiply()`. After the module interfaces are generated (and the modules have not been edited in the meantime), we can use those instead of traversing imports.

There are some optimizations that can be made here: if `supporting` has an inline function that is not used by `inlined`, then it does not need to be processed. In order to support this, we would need to handle partially defined module interfaces (as we would avoid parsing the body of the inline function in `supporting` while the module system processes `client`). There are also optimizations to be made in terms of how to store the body of an inline function in a module interface so that updates don't require reanalyzing the entire function body.

### Generating multiple module interfaces

A common problem with encapsulation is that certain modules may need certain functionalities from others that should otherwise be private. In object-oriented languages, this is accomplished by designating "friend classes", which get full access to a class' internals. However, this "all or nothing" approach lacks fine-grained control. Another alternative is to present multiple interfaces for importers to choose from, facilitated by the fact that we already generate module interfaces.

```
// module multiple
module;
export int public_function() {return 100;}
export(internal) int internal_function() {return 10;}
int private_function() {return 1;}
// module kernel
module;
import multiple(internal);  // can use public_function, internal_function
// module client
module;
import multiple;  // can use public_function
```

Here, `internal` is a user-defined tag. We could use `export(aaa)` and `import multiple(aaa)` instead. Additionally, we can attach multiple tags to an export (eg. `export(aaa, internal)`) and import with multiple tags (eg. `import multiple(aaa, internal)`). A symbol that is exported with tags is imported if the import statement includes one of its tags, and a symbol that is exported without a tag is imported as long as the import statement does not have `-` as its first argument (eg. `import multiple(-, internal)` would only make `internal_function` visible).

This can be implemented by producing one module interface for every unique export tag in a module (+ export without a tag). Since symbol exports are decoupled from each other, we would only need to handle idempotent symbol exports (ignore duplicate symbol exports). Additional optimizations can be made to this process, such as storing all module interfaces in one file, processing common tag combinations, and handling updates to the module file.

Note that `private_function()` is technically still accessible by accessing its mangled C name directly. An extension to this module system could be to automatically insert `static` to these functions if a flag is set.

### Modules use `import` instead of `#include`

Symbols defined in modules behave differently to those in regular C. In regular C, the defined symbols can be found in the outputted assembly using the same name that they were defined with. This is what allows forward declarations in C headers to work (eg. `void func();` produces a label `func` in the assembly). Unfortunately, this raises the possibility of having symbol names clash with each other. We avoid this by having every symbol defined within a module essentially have their name prepended with the module's file path. This difference in functionality means we cannot use `#include` to define module interfaces.

Taking inspiration from C++20 modules, we use `import` to make a module's exported symbols be visible to another module. We also take some inspiration from C++20 modules with the use of `module;` as the first statement in a module file. However, contrary to C++20 modules, we do not require modules to be compiled fully in order to refer to any of its symbols, as part of an effort to avoid imposing any architectural constraints that aren't already in regular C.

If the set of imported symbols still cause name clashes, we take inspiration from C++ namespaces and use the `::` operator to specify which module we are referring to. This uses the same syntax and semantics as `import` statements when resolving the module name.

More discussion on the details of how modules are implemented is found in section Implementing module namespaces.

[[THE REST OF THIS DOCUMENT IS A WORK IN PROGRESS]]

### Cyclic modules
### Other kinds of symbols
[[union types]]
The forall keyword is an addition to Cforall to support polymorphism, with polymorphic functions using dictionary passing and a single implementation. If a module exports a forall statement, the module owns the polymorphic function implementations, while the polymorphic function declarations are exported (if these were declared inline, the definition could be exported, similar to C++20 modules). Polymorphic types are instantiated from the caller's side, so their definitions are exported. This may present problems, but currently I am not familiar enough with Cforall to judge.

An interesting case is to consider if Cforall could be updated to perform specialization (multiple implementations for a single function) in addition to the single implementation strategy. An example of this being done in a production language is with Rust's `impl` vs `dyn` traits. To support this, the module system would need to be updated, as we would want the multiple implementations to exist within the module that owns the forall statement.
### Implementing module namespaces
A module is defined by having `module;` be the first statement in a source file (somewhat similar to C++20 modules). Internally, modules work like namespaces, implemented by prepending the module name in front of all declared symbols. There are multiple alternatives to determine the module name - we use option 2 for its brevity:
1. Have the user define the module names (eg. `module A;`). This is similar to how Java and C++ require specifying packages and namespaces, respectively. This gives the developer some flexibility on naming, as it is not tied to the file system. However, it raises some questions surrounding how module discovery works (if a module imports `A`, where is `A`?).
2. Have the module names be defined from a "root directory" (eg. `module;` is module `A` because it is located at `src/A.cfa`, and `src/` is defined as the root directory). This creates import paths that look similar to include paths, allowing us to align more closely with existing C programmers. When searching for an appropriate module, a search is conducted first from the current directory, then we look for an appropriate library (similar to the include path in C). A downside is that this precludes adding nested modules (ie. module definitions within a module file), though nested modules are arguably not that important.

Another design choice that was made was to have files with the same name as a folder exist outside their folder. For example, module `graph` exists at `src/graph.cfa`, while module `graph/node` exists at `src/graph/node.cfa`. The alternative is to have module `graph` at `src/graph/mod.cfa` - this may be more familiar to some developers, but this complicates module discovery (eg. if there exists a module at `src/graph.cfa` at the same time, which takes precedence? Does `graph` need to `import ../analysis` in order to import the module at `src/analysis`?). Taking insights from Rust's move from `mod.rs` to files with the same name as the folder, we opt to use the more straightforward strategy.

This prepending of the module name in front of all symbols within a module can result in undesirable behaviour if we use `#include` within a module, as all of its contents will be prepended with the module name. To resolve this, we introduce extern blocks, which escape the module prefixing (eg. `extern { #include <stdio.h> }`, though with a newline after the `>`).

This configuration allows for a special kind of optimization to be performed: since modules prepend their names to their symbols, every symobl can be disambiguated. This allows us to add functionality to perform a "unity build", where the entire codebase can be compiled within a single translation unit, allowing the compiler to inline functions as its discretion. This would allow us to balance a "development configuration" with the benefits of modularization, alongside a "release configuration" with maximum optimizations.
## Porting existing C code
[[See C macros are not exportable]]
[[See forward declarations are not necessary. An interesting idea is to allow naked `#include` within the module file, and try and handle it. It works up until type definitions... so can't work]]
[[So have import statements, just like C++20 imports]]
## Handling initialization order
## Why C++20 modules failed (and why we will succeed)
[[I will die on the hill of cyclic modules]]