Type Checker For Paret

We don't intend for these assignments to take too long. If you have spent five hours on any part of this assignment please stop and check in with the TAs.

You will be working with string dicts. The documentation is on pyret.org/docs/latest.

In this assignment, you will implement a type checker for Paret, which has been slightly modified as described below.

1. Type Checker

You will write a function fun type-of(e :: Expr) -> Type that takes a Paret program and either returns the type of that program or, if the program is not well-typed, raises an exception.

Similar to how you passed an Env around in the interp assignment that mapped identifiers to values, to type-check you will want to pass around a type environment (TEnv, defined below) that maps identifiers to types.

We have defined a function fun type-check(prog :: String) -> Type that calls parse and then type-of: you can use type-check in your test cases to avoid calling C.parse manually.

2. The Language

Strings have been removed from the language for this assignment. Lists have been added, as have operations empty, link, is-empty, first, and rest for working with them. Type annotations are included on function parameters, as documentated in the grammar. This language does not have syntactic sugar, so it contains let expressions that your type-checker will handle.

2.1 Types

The type of numbers is written Num, and the type of booleans is written Bool. The type of a list is written (List T), a list of elements of type T. For example, (List Num) is the type of a list of numbers. The type of a function is written (Num -> Num), where the type before the arrow is the argument type and the type after the arrow is the result type. Both of these examples are simple, but types can be nested as well, e.g., (List (List Num)).

2.2 Annotations

Function definitions are now annotated with the types of their arguments. For instance, the function that adds one to its argument could be written,

(let (one 1) (lam (x : Num) (+ x one)))

See the grammar for reference.

2.3 List Operations

You will need to type-check the five list operations, empty, link, is-empty, first, and rest. Lists in this language are homogeneous: all of their elements must have the same type. Here are the rules for type-checking the list operations:

If any of the arguments to these functions have the wrong type, your type-checker should raise a tc-err-bad-arg-to-op exception. So for instance, (link 2 3) should raise a tc-err-bad-arg-to-op exception, as should (link 2 (empty : Bool)). If the type of the first argument to link doesn't match the element-type of its second argument, the arg-type of the error should be the type of the first argument.

2.4 If Statements

Your type-checker should require that both branches of an if statement have the same type. So, for instance, (if true 3 "three") will not type-check. See "Type-Checking Exceptions" for the error to raise.

2.6 Type-Checking Exceptions

Most of the exceptions your type-checker can raise are just like interpreter errors from previous assignments, but with a type instead of a value. There are two new kinds of exceptions, though:

You should type-check in the following order: First type check the children of an expression from left to right, then type check the expression (This is called a post-order traversal of the tree). This makes it unambiguous which error to raise if there are multiple errors.

Here is the full list of exceptions:

data TypeCheckingError:
  | tc-err-if-got-non-boolean(cond-type :: Type)
  | tc-err-bad-arg-to-op(op, arg-type :: Type) # op is Operator or UnaryOperator
  | tc-err-unbound-id(name :: String)
  | tc-err-not-a-function(func-type :: Type)

  | tc-err-bad-arg-to-fun(func-type :: Type, arg-type :: Type)
  | tc-err-if-branches(then-type :: Type, else-type :: Type)

3. Grammar

Note: you must put spaces around ":" and "->" for them to parse correctly.

Here is the new grammar:

<expr> ::= <num>
         | <id>
         | true | false
         | (+ <expr> <expr>)
         | (num= <expr> <expr>)
         | (link <expr> <expr>)
         | (if <expr> <expr> <expr>)
         | (lam (<id> : <type>) <expr>)
         | (let (<id> <expr>) <expr>)
         | (<expr> <expr>)
         | (first <expr>)
         | (rest <expr>)
         | (is-empty <expr>)
         | (empty : <type>)

<type> ::= Num
         | Bool
         | (List <type>)
         | (<type> -> <type>)

4. Abstract Syntax

Here are the extended data definitions:

data Expr:
  | e-op(op :: Operator, left :: Expr, right :: Expr)
  | e-un-op(op :: UnaryOperator, expr :: Expr)
  | e-if(cond :: Expr, consq :: Expr, altern :: Expr)
  | e-let(name :: String, expr :: Expr, body :: Expr)
  | e-lam(param :: String, arg-type :: Type, body :: Expr)
  | e-app(func :: Expr, arg :: Expr)
  | e-id(name :: String)
  | e-num(value :: Number)
  | e-bool(value :: Boolean)
  | e-empty(elem-type :: Type)

data Operator:
  | op-plus
  | op-num-eq
  | op-link

data UnaryOperator:
  | op-first
  | op-rest
  | op-is-empty

data Type:
  | t-num
  | t-bool
  | t-fun(arg-type :: Type, return-type :: Type)
  | t-list(elem-type :: Type)

type TEnv = StringDict<Type>

(For reference, feel free to look at the definitions file.)

5. Submission

To get started, open the code stencil and the test stencil

For your final submission, upload a zip file containing both your test and code files to Captain Teach. Call the files "type-checker-tests.arr" and "type-checker-code.arr". Double-check the file names before submitting; for instance they should not be called ".arr.txt".

Submit at this link: