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.
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.
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.
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)).
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.
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:
(empty : t) makes an empty list whose elements have type t. For instance, (empty : Num) is an empty list of numbers. The type declaration is important to be able to tell what the type of the list is (otherwise this assignment would be much harder).(link x y) appends the element x to the front of the list y; it acts just like Pyret's link. If x has type t and y has type (List t), then (link x y) should have type (List t).(is-empty x) checks to see whether x is an empty list. If x has type (List t), then (is-empty x) has type Bool. (is-empty should produce a type error if its argument is not a list.)(rest x) returns the list x except for its first element. If x has type (List t), then (rest x) has type (List t). (rest should produce a type error if its argument is not a list.)(first x) returns the first element of the list. If x has type (List t), then (first x) has type t. (first should produce a type error if its argument is not a list.)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.
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.
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:
tc-err-bad-arg-to-fun when a function is applied to an argument of the wrong type. func-type is the type of the function being applied, and arg-type is the type of the argument it was applied to.tc-err-if-branches when an if statement has branches that have different types. then-type is the type of the "then" branch, and else-type is the type of the "else" branch.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)
end
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>)
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)
end
data Operator:
| op-plus
| op-num-eq
| op-link
end
data UnaryOperator:
| op-first
| op-rest
| op-is-empty
end
data Type:
| t-num
| t-bool
| t-fun(arg-type :: Type, return-type :: Type)
| t-list(elem-type :: Type)
end
type TEnv = StringDict<Type>
(For reference, feel free to look at the definitions file.)
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 VikingWeb. Call the files "type-checker-tests.arr" and "type-checker-code.arr".