## Implementing Type-Checking, CSC430, Spring 2021

### 1` `Goal

Extend the interpreter (no mutation) to include a type system.

### 2` `Guidelines

For this and all remaining assignments, every function you develop must come with the following things:

A commented header line that expresses the result of the function in terms of its inputs, written in English. Be as precise as you can within the space of a line or two.

A type declaration (possibly inline), specifying the input and output types.

Test cases. A function without test cases is incomplete. Write the test cases first, please.

For this assignment, you must develop your solutions using the typed/racket language. If you haven’t seen them, you might be interested in these Hints on Using Typed Racket in CPE 430.

Your test cases must use the check-equal?, check-=, or check-exn forms.

Your solution should take the form of a single file.

Hand in your solution using the handin server. For help with the handin server, please see the course web page.

#### 2.1` `Handling Errors

All of your error messages must contain the string "GIYA". Essentially, this allows my test cases to distinguish errors correctly signaled by your implementation from errors in your implementation. To be more specific: any error message that doesn’t contain the string "GIYA" will be considered to be an error in your implementation.

#### 2.2` `Progress Toward Goal comment

Graders are happier when they know what to expect. Your final submission should start with a short one- or two-line comment indicating how far you got through the project. Ideally, this would just be: “Full project implemented.” But if you only implemented, say, squazz and blotz, and didn’t get to frob or dringo, please indicate this in the comment, so that we don’t spend all our time searching for bits that aren’t there.

### 3` `The Assignment

This assignment will build on the same core as the previous assignment: the Assignment 5 interpeter.

### 4` `Syntax of GIYA8

A GIYA8 program consists of a single expression.

The concrete syntax of the GIYA8 expressions with these additional features can be captured with the following EBNFs.

expr | = | num | ||

| | string | |||

| | id | |||

| | {if expr expr expr} | |||

| | {local [id : ty = expr] ... in expr} | |||

| | {{[id : ty] ...} => expr} | |||

| | {rec {{id [id : ty] ...} : ty => expr} expr} | |||

| | {expr expr ...} |

ty | = | num | ||

| | bool | |||

| | str | |||

| | {ty ... -> ty} |

operator | = | + | ||

| | - | |||

| | * | |||

| | / | |||

| | num-eq? | |||

| | str-eq? | |||

| | <= | |||

| | substring |

... where an id is not if, :, =, local, in, rec, =>, or ->.

#### 4.1` `Primitives

procedure

(+ a b) → num

a : num b : num

procedure

(- a b) → num

a : num b : num

procedure

(* a b) → num

a : num b : num

procedure

(/ a b) → num

a : num b : num

procedure

(<= a b) → boolean

a : num b : num

procedure

(num-eq? a b) → boolean

a : num b : num

procedure

(str-eq? a b) → boolean

a : str b : str

procedure

(substring str begin end) → string

str : str begin : num end : num

value

true : boolean

value

false : boolean

#### 4.2` `Type Checking

Implement a type checker for your language. Note that since functions must now come annotated with types for arguments, you will need to have a type parser that parses types. For Heaven’s sake, make a separate function for this. Note that the types of functions are extended to handle multiple arguments. So, for instance, the type {num str -> bool} refers to a function that accepts two arguments, a number and a string, and returns a boolean.

All type rules are standard.

##### 4.2.1` `Binops

Type-checking binops is more or less as you might expect. For instance, a + should receive two numbers, and will produce a number. The <= operator will take two numbers, and return a boolean.

The equal? operator is a bit different. Specifically, we don’t have subtyping, and we treat the equality operator as a function in the environment, so it must have a single type. In order to simplify our lives, we split it into two equality operators; one that only works for numbers, called num-eq?, with type {num num -> bool}, and one that only works for strings, called str-eq?, with type {str str -> bool}.

Also, note that begin is not a primitive in this language. Can you see why?

### 5` `Recursion

This assignment will add recursion, using a rec form. Implement the rec form as described in the book. Note that you will need some kind of mutation in order to create the closure as a cyclic data structure. For this assignment, we’ll keep things simple and just use Typed Racket’s built-in mutation in order to eliminate the need for store-passing style. I recommend designing your (runtime) environment as a mapping from names to boxed values.

Here’s an example of a simple program that defines a recursive function to compute perfect squares in a kind of silly way:

{rec {square-helper [n : num]} : num => {if {<= n 0} 0 {+ n {square-helper {- n 2}}}} {local {[square : {num -> num} = {{[n : num]} => {square-helper {- {* 2 n} 1}}}]} in {square 13}}}

### 6` `Suggested Implementation Strategy

Here are some of the steps that I followed. I wrote test cases for every step before implementing it.

Add a data definition for Types.

Add a parser for the language of types.

Develop a type checker that only works for constants.

Add a definition for Type Environments, mapping symbols to types.

Extend your type checker to handle variables and if expressions.

Extend your type checker to handle applications. (Since you don’t have types for LamC terms yet, your test cases should just use primitive functions.)

Extend your AST nodes for LamC nodes to include types with the parameters.

Extend your type checker to handle LamC terms.

Extend your parser and type checker to handle the modified local and rec terms.

Add your type checker to top-interp. Type checking should happen after parsing and before interpretation.

Update your environment to map names to boxed values.

Fix breakage by adding boxing and unboxing to environment operations.

As in the previous assignment, add code to recreate the top-env on every call to top-interp.

Add the rec form to the set of ExprCs.

Fix breakage temporarily by signaling an error in interp on instances of RecC.

Develop the parser clause for RecC. Test cases first!

Develop the interpreter clause for RecC. Test cases first!

### 7` `Interface

Make sure that you include the following functions, and that they match this interface:

procedure

(parse s) → ExprC

s : Sexp

procedure

(parse-type s) → Ty

s : Sexp

procedure

(type-check e env) → Ty

e : ExprC env : TEnv

value

base-tenv : TEnv

procedure

(interp e env) → Value

e : ExprC env : Environment

procedure

(top-interp s) → string

s : s-expression

### 8` `Minimum Viable Product

Some of you may be thinking about submitting your solution to assignment 5 for this assignment. Good idea! It won’t actually do any type checking, but it will certainly still pass some of the tests.

If you’re thinking of doing this, the most important change you’ll have to make to your code is to handle the presence of types in => and local terms; update your parser to just ignore these extra pieces, and **profit***!