Implementing Type-Checking, CSC430, Spring 2023
1 Goal
2 Guidelines
2.1 Handling Errors
2.2 Progress Toward Goal comment
3 The Assignment
4 Syntax of VVQS8
4.1 Primitives
4.2 Mutation
4.2.1 Order of Evaluation
4.3 Type Checking
4.3.1 Operators
5 Recursion
6 Suggested Implementation Strategy
6.1 Type Checking for Existing Language
6.2 Adding Binding Mutation
6.3 Adding Arrays
6.4 Adding recursion (last part!)
7 Interface
8.9.900

Implementing Type-Checking, CSC430, Spring 2023

1 Goal

Extend the interpreter to include a type system, binding mutation, and a mutable number array data structure.

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.

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 "VVQS". 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 "VVQS" will be considered to be an error in your implementation.

Additionally, your error messages should be actually helpful. Since you are the primary consumer of your own error messages, making these error messages good in the first place should reduce your overall development time. There are two parts to this: first, the error message should include text that actually indicates what the programmer did wrong. Second, include the text of the user’s program, so they (actualy you) can figure out how to fix it. See lab 3 for an example of how to do this. (Apologies in advance if I renumber the labs and fail to update this paragraph....)

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 Assignment 5 interpeter.

4 Syntax of VVQS8

A VVQS8 program consists of a single expression.

The concrete syntax of the VVQS8 expressions with these additional features can be captured with the following EBNFs.

  Expr = Num
  | id
  | String
  | {id <- Expr}
  | {Expr if Expr else Expr}
  | {Expr where {[[id : ty] := Expr] ...}}
  | {letrec {id {[id : ty] ...} : ty => Expr} in Expr}
  | {{[id : ty] ...} => Expr}
  | {begin Expr ...}
  | {makearr Expr ...}
  | {Expr Expr ...}

  ty = num
  | bool
  | str
  | void
  | {ty ... -> ty}
  | numarray

  operator = +
  | -
  | *
  | /
  | num-eq?
  | str-eq?
  | <=
  | substring
  | arr
  | aref
  | aset
  | alen

... where an id is not where, letrec, :=, if, else, <-, :, =>, begin, in, or makearr.

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

procedure

(arr size default)  numarray

  size : num
  default : num
Return a new array of size size whose elements are all initially set to default, which must be a number.

procedure

(aref arr idx)  num

  arr : numarray
  idx : num
Given an array and an index, return the value in the array at the given index.

procedure

(aset arr idx newval)  Void

  arr : numarray
  idx : num
  newval : num
Given an array and an index and a new value, mutate the array at the given index to contain the new value, and return void.

procedure

(alen arr)  num

  arr : numarray
Given an array, return its size.

value

true : boolean

the literal boolean representing true.

value

false : boolean

the literal boolean representing false.

4.2 Mutation

This assignment includes both mutation of variables and mutable number arrays. We’ll be implementing it in a meta-circular way; that is, we’ll be using racket vectors to implement VVQS8 arrays, and to implement mutable variables, we’ll be adding mutation to our environments.

However, we want to be a bit careful in making the environments mutable; it turns out that it’s not a great idea to use mutable hash tables to represent environments. We want the cells to be mutable, but we still want the nice behavior of immutable hash tables (or, equivalently, lists of bindings). The way to have our cake and eat it too is to create an immutable mapping from names to mutable values. If, for instance, you’re using a Binding structure, you’ll probably want to update it to map a name to a boxed value, written (Boxof Value).

To represent arrays of numbers, just use racket’s mutable vector value. To keep things simple, these will be serialized simply as the string "#<array>".

Also, mutation of a variable will return the new void value, which should be serialized as "#<void>".

4.2.1 Order of Evaluation

Now that we have mutation, order of evaluation becomes observable. So, for instance, consider a program with a call {h {f} {g}} where both the function f and the function g mutate the same variable. Which one happens first?

In languages such as Java, Python, and VVQS8, evaluation is left-to-right; that is, the subterms of every expression are evaluated from left to right, except when the form itself demands a different order of evaluation, as e.g. if. So, to be specific, in an application, the function position should be evaluated first, and then the leftmost argument, the second leftmost argument, and so forth.

4.3 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. You should definitely 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.

4.3.1 Operators

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}.

5 Recursion

This assignment will add recursion, using a letrec 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:

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

6 Suggested Implementation Strategy

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

6.1 Type Checking for Existing Language

At this point, you’re in good shape; your assignment should now pass a significant fraction of the test cases.

6.2 Adding Binding Mutation

6.3 Adding Arrays

6.4 Adding recursion (last part!)

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.