5. HW5: Compiling Full Oat


This project will be time consuming. Start early and contact the lecturer or the TA with any questions. If you find yourself stuck or writing tons and tons of code, please ask for help on Slack.

5.1. Getting Started

To get started, clone the template repository following the link provided on Canvas and make sure you can compile main.native. The files from the repository are briefly described below. Those marked with * are the only ones you should need to modify while completing this assignment:

README.md           - help about the main test harness
Makefile            - basic make support for invoking dune

util/assert.ml(i)   - the assertion framework

  range.ml(i)       - range datatype for error messages
  platform.ml       - platform-specific compilation support
  driver.ml         - utilities for invoking the compiler

  ll.ml             - the abstract syntax for LLVMlite
  llutil.ml         - name generation and pretty-printing for LLVMlite
  lllexer.mll       - lexer for LLVMlite syntax
  llparser.mly      - parser generator for LLVMlite syntax
  llinterp.ml       - reference interpreter for the LLVMlite semantics

  x86.ml            - the X86lite language used as a target

  backend.ml        - sample solution to HW3
  astlib.ml         - pretty printing
  lexer.mll         - oat lexer
  parser.mly        - oat parser

  main.ml           - main test harness

hw4programs/*.oat   - example hw4 programs used in testing
hw5programs/*.oat   - example hw5 programs used in testing

runtime.c           - oat runtime library

studenttests.ml     - where your own test cases should go
gradedtests.ml      - graded test cases that we provide

Most important for this project:

  ast.ml              - oat abstract syntax
  *frontend.ml        - oat frontend  [including most of a solution to HW4]
  *typechecker.ml     - oat typechecker
  tctxt.ml            - typechecking context data structure

5.2. Overview

Implement a compiler typechecker for an extended version of Oat that has boolean, int, string, array, struct and function pointer types as well as “possibly null” and “definitely not null” references. Your compiler will now accept source files of the form:

struct Color {
  int red;
  int green;
  int blue;
  (Color) -> Color f

Color rot(Color c1) {
  var c2 = new Color{ red = c1.green; green = c1.blue; blue = c1.red; f = c1.f };
  return c2;

global c = new Color { red = 10; green = 20; blue = 30 ; f = rot};

int program (int argc, string[] argv) {
  return c.f(c).red;

and will produce an executable (by default named a.out) that, when linked against runtime.c and then executed produces the resulting output:



For examples of Oat v2 code, see the files in hw5programs.

5.3. The Oat Language

This version of Oat supports all of the features from HW4 but, in addition, support structs and function pointers, and a type system that makes a distinction between “possibly null” and “definitely not null” references. It is the intention that this language is type safe, meaning that any well-typed program will not crash in certain ways. In particular, well-typed Oat v2 programs cannot exhibit null pointer dereference failures (though it may fail with an “array bounds check” failure).

Oat supports multiple base-types of data: int, bool, and string, as well as arrays of such data. The Oat language is large enough that it is simpler to give the specification of its type system using inference rules than to use English prose. The Oat language specification contains a definition of the language syntax and a collection of inference rules that define Oat type checking.

See the file ast.ml for the OCaml representation of the abstract syntax – the type typ of types is defined there, along with representations of expressions, statements, blocks, function declarations, etc. You should familiarize yourself with the correspondence between the OCaml representation and the notation used in the specification. The astlib module defines some helper functions for printing Oat programs and abstract syntax.


The abstract syntax now has support for structs, function pointers, and new types. We have already provided the parser for you.

5.4. New Features


Oat struct types are declared by using the struct keyword at the top level. For example the following program declares a new struct type named Color with three fields. (Note: there is no trailing semicolon on the last struct field.):

struct Color {
  int red;
  int green;
  int blue

int program (int argc, string[] argv) {
  var garr = new Color { green = 4; red = 3; blue = 5 };
  garr.red = 17;
  return garr.red + garr.green;

Struct values can be created by using the new keyword followed by the name of the struct type and a record of field initializers. The order of the fields in the initializers does not have to match the order of the fields as declared, but all of the fields must be present and have the correct types.

Struct values are represented internally as pointers to contiguous heap-allocated blocks of memory. This means that structs, like strings and arrays, are reference values for the purposes of compilation.

Struct fields are also mutable. As shown in the sample program above, you can update the value of a struct.

Function Pointers:

This version of Oat supports function pointers as first-class values. This means that the name of a top-level declared function can itself be used as a value. For example, the following program declares a top-level function inc of type (int) -> int and passes it as an argument to another function named call:

int call((int) -> int f, int arg) {
  return f(arg);

int inc(int x) { return x + 1; }

int program(int argc, string[] argv) {
  return call(inc, 3);

Function types are written (t1, .., tn) -> tret and, as illustrated above, function identifiers act as values of the corresponding type. Note that such function identifiers, unlike global variables do not denote storage space, and so cannot be used as the left-hand side of any assignment statement. These function pointers are not true closures (as the function definitions cannot be nested within other functions), since they cannot capture variables from a local scope.

Built-in Functions:

The built-in functions, whose types are given below, can also be passed as function-pointers:

string_of_array : (int[]) -> string   (Assumes each int of the array is the representation of an ASCII character)
array_of_string : (string) -> int[]
print_string : (string) -> unit
print_int : (int) -> unit
print_bool : (bool) -> unit

Similarly to HW04, these built-in operations, along with some internal C-functions used by the Oat runtime are implemented in runtime.c.

Possibly null vs. Definitely Not Null References:

The Oat type system makes a distinction between possibly null reference types r?, which are marked with a question mark and are not statically known to be different from null, and definitely not-null reference types. These features are illustrated in the following code from the ifq3.oat file:

int sum(int[]? arr) {
    var z = 0;
    if? (int[] a = arr) {
      for(var i = 0; i<length(a); i = i + 1;) {
        z = z + a[i];
    return z;

int program (int argc, string[] argv) {
    var x = 0;
    x = x + sum(new int[]{1,2,3});
    x = x + sum(int[] null);
    return x;

Here, the sum function takes a possibly null array reference. Possibly null types, like int[]?, cannot directly be treated as non-null. Instead, the programmer has to insert the appropriate null check using the if? statement, which performs the non-null check and, if it is successful, creates an alias to the checked value for use as a definitely not null pointer. The rule for typechecking if? works for any possibly null reference types.


The variable introduced by if? is still mutable, so the frontend will have to allocate storage space just as for any other local variable introduced by var.

Array Initializers:

Once we decide to have definitely not-null types, we need a convenient way to initialize arrays of definitely-not-null reference types (so that we can ensure that the entries are not null). We thus add support for built-in initializers, that work as shown below:

var matrix = new int[][4]{i -> new int[3]{j -> i * j}}

This code declares a 4x3 matrix represented as an array (of size 4) of int arrays (each initialized to be of size 3). The entry matrix[i][j] is initialized to be i * j.

The initializer array syntax is of the general form: new t[e1]{id -> e2}, where e1 is an integer determining the size of the array, id names the index, and the initializer expression e2 computes the initial value at each index. Notice that t might itself be of an array type, allowing to implement multi-dimensional arrays. This initializer code is semantically equivalent to allocating an array followed by immediatelly initializing each element:

var a = new t[e1];
for(var id = 0; id < length(a); id = id + 1;) {
   a[id] = e2;

Note that e2 can mention the loop index id. See the typechecking rules for the details about scoping and checking types.

Oat v2 retains the implicitly initialized arrays from Oat v1 (which allowed only int and bool such arrays) and allows possibly-null types to have the default initializer null. That means that the following code snippet is legal, and initializes a length-three array of null pointers (each of type int[]?, i.e., a possibly null pointer to an array of integers):

var a = new int[]?[3];

The Oat v2 typechecker will consider the following code to be ill-typed because the inner array type int[] is definitely-not-null and so cannot be default initialized to null:

var a = new int[][3];

5.5. Task I: Typechecking

The main task of this project is to implement a typechecker for the Oat language, which will put enough restrictions on its code to ensure type safety.

The typing rules describing the intended behavior of the typechecker are given in the accompanying Full Oat Language Specification. Use that, and the notes in typechecker.ml to get started. We suggest that you tackle this part of the project in this order:

  • Try to read over the typing rules and get a sense of how the notion of context used there matches up with the implementation in tctxt.ml.

  • Complete the implementations of subtype and typecheck_ty (and their mutually recursive companions), to remind yourself how the typechecking rules line up with the code that implements them. It might be good to write a few unit tests for these functions to confirm your expectations.

  • Think about the intended behavior of the typechecker for expressions and work out a few of the easier cases. We have given you helper functions for typechecking the primitive operations (see builtins).

  • Next tackle the context-building functions (e.g., typecheck_stmt), which create the correct typing context for later typechecking.

  • Take an initial stab at typecheck_fdecl. We suggest that you introduce a helper function called typecheck_block, which will be used for function declarations (and elsewhere).

  • Working backwards through the file, work on typechecking statements, which will rely heavily on typechecking expressions. Make sure you understand how the expected return type information and the behavior type of the statement are propagated through this part of the code.

5.6. Task II: Frontend Compilation

We have provided a mostly complete sample implementation of the frontend of the compiler (corresponding to our solution to HW4). Your task for this part of the project is to add support for structures and function pointers.

Functions Pointers: Due to presence of function pointer values, you might want to familiarize yourself with the cmp_function_ctxt and the way we implement the Ast.Id id case for the expression compilation. There is nothing for you to do do here.

Arrays: There are only a few places where the code must be modified, each of which is marked as a ARRAY TASK in the comments. You’ll need to add code to handle the length expression (for which you might want to recall the array representation from the HW4 instructions). You’ll also have to implement the array initializers.

Structs: There are only a few places where the code must be modified, each of which is marked as a STRUCT TASK in the comments. Struct compilation is (broadly) similar to how we handle arrays. The main difference is that you need to use the structure type information to look up the field index for the struct representation (rather than computing an integer directly). Follow the STRUCT TASK breadcrumbs left in the frontend and the comments there.

Checked Cast: To implement the if? statement, you’ll need to generate code that does a null-pointer check. Since this construct introduces a variable into scope (for the ‘not-null’ branch), you’ll have to handle the context and allocate storage space.

5.7. Test Cases

As part of this project, you must post three test cases for the compiler to the GitHub team forum.

Two of your test cases must be small “unit tests” for a specific inference rule used in the type system. Here’s how it works: Choose a typechecking judgment and write one small, self-contained “positive” test case that succeeds because the inference rules for that judgment permit a particular derivation. Then, write a second, small, self-contained “negative” test case that succeeds because the inference rules for that judgment do not permit a particular derivation.

For example, you could pick the “subtype” inference rule and have the positive test case be testing that indeed, H |- string? <: string? and the negative test case could assert that it is not possible to derive H |- string? <: string. The OCaml code for these two tests would be given by:

let unit_tests = [
   (fun () ->
       if Typechecker.subtype Tctxt.empty (TNullRef RString) (TNullRef RString) then ()
       else failwith "should not fail")
; ("no_subtype_stringQ_string",
   (fun () ->
       if Typechecker.subtype Tctxt.empty (TNullRef RString) (TRef RString) then
         failwith "should not succeed" else ())

You might find the typecheck_error and typecheck_correct functions in the gradedtests.ml file useful for writing these unit tests.

Your third test case must take the form of a .oat file along with expected input arguments and outputs (as found in the “hard tests” of gradedtests.ml). Your test should be an Oat program about the size of those in the hard test cases categories. This case must exercise some of the new features of this version of Oat: structs, function pointers, non-null vs. null references, or, ideally, some combination of these. Oat is now quite a full-fledged language, so this can be pretty fun. Ideas include: linked-list algorithms (will definitely need null), object-encodings like the color example above, trees, etc. How handy is it to have notation for array initialization? How intrusive do you think the not-null pointer requirement is?

Please, also add this file to the root of your project with some descriptive name .oat and the test harness to studenttests.ml.


The test cases you post on GitHub will not count if they are too similar to previously-posted tests! Your test should be distinct from prior test cases. (Note that this policy encourages you to submit test cases early!)

We will validate these tests against our own implementation of the compiler (and clang). A second component of your grade will be determined by how your compiler fares against the test cases submitted by the other groups in the class.

5.8. Grading

Projects that do not compile will receive no credit!

Your team’s grade for this project will be based on:

  • 80 Points: the various automated tests that we provide. (Some reserved for online grading)

  • 10 Points: only awarded if your solution passes all automated tests.

  • 5 Points for posting an interesting test case to GitHub. (Graded manually)

  • 5 Points divided among the test cases created by other groups. (Graded manually)