Implementing Type-Checking, CSC430, Winter 2021
1 Goal
2 Guidelines
2.1 Handling Errors
2.2 Progress Toward Goal comment
3 The Assignment
4 Syntax of WTUQ8
4.1 Primitives
4.2 Type Checking
4.2.1 Binops
5 Recursion
6 Suggested Implementation Strategy
7 Interface
8.0.0.7

Implementing Type-Checking, CSC430, Winter 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:

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. Solve each problem separately, and make sure that each solution appears in a separate part of the file, with comments separating each problem’s solution.

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 "WTUQ". 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 "WTUQ" 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 WTUQ8

A WTUQ8 program consists of a single expression.

The concrete syntax of the WTUQ8 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}
  | {lam {[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, lam, or ->.

4.1 Primitives

procedure

(+ a b)  num

  a : num
  b : num
Compute a + b.

procedure

(- a b)  num

  a : num
  b : num
Compute a - b

procedure

(* a b)  num

  a : num
  b : num
Compute a * b

procedure

(/ a b)  num

  a : num
  b : num
If b is not zero, compute a/ b.

procedure

(<= a b)  boolean

  a : num
  b : num
Return true if a is less than or equal to b

procedure

(num-eq? a b)  boolean

  a : num
  b : num
Return true if a is equal to b

procedure

(str-eq? a b)  boolean

  a : str
  b : str
Return true if a is equal to b

procedure

(substring str begin end)  string

  str : str
  begin : num
  end : num
Return the substring of the given string beginning at the character in position begin and ending just before the character in position end. Signal an error if begin or end are not integers

value

true : boolean

the literal boolean representing true.

value

false : boolean

the literal boolean representing false.

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}  =
          {lam {[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.

7 Interface

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

procedure

(parse s)  ExprC

  s : Sexp
Parses an expression.

procedure

(parse-type s)  Ty

  s : Sexp
Parse a type.

procedure

(type-check e env)  Ty

  e : ExprC
  env : TEnv
Type-check an expression.

value

base-tenv : TEnv

The base type environment.

procedure

(interp e env)  Value

  e : ExprC
  env : Environment
Interprets an expression, with a given environment.

procedure

(top-interp s)  string

  s : s-expression
Combines parsing, type-checking, interpretation, and serialization.