The purpose of this assignment is to help you learn about type systems.
git clone linux.cs.tufts.edu:/comp/105/build-prove-compareYou will need copies of build-prove-compare/bare/tuscheme/tuscheme.sml and build-prove-compare/bare/timpcore/timpcore.sml.
As in the ML homework, use function definition by pattern matching.
In particular, do not use the functions
I recommend that you do Exercise 1 first (with your partner). It will give you more of a feel for monomorphic type systems.
Hint: Exercise 6 is more difficult than it first appears. I encourage you to scrutinize the lecture notes for similar cases, and to remember that you have to be able to type check every expression at compile time.
Here are some things to watch out for:
Exercise 12 on page 290. Do Exercise 12 on page 290 of Ramsey: write exists? and all? in Typed uScheme. Turn in this exercise in file 12.scm.
17. Do Exercise 17 on page 291
extend Typed uScheme with a type constructor for queues
and with primitives that operate on queues.
As it says in the exercise, do not change the
abstract syntax, the values, the
eval function, or the type
If you change any of these parts of the interpreter, your
solution will earn No Credit.
I recommend that you represent each queue as a list.
If you do this, you will be able to use the following primitive
let fun put (x, NIL) = PAIR (x, NIL) | put (x, PAIR (y, ys)) = PAIR (y, put (x, ys)) | put (x, _) = raise BugInTypeChecking "non-queue passed to put" in put end
Turn in the code for this exercise in file tuscheme.sml, which should also include your solution to Exercise 14 below. Please include the answers to parts (a) and(b) in your README file.
Hint: because empty-queue is not a function,
you will have to modify the
initialEnvs function on page 285a.
that page shows two places you will update: the
<primitive functions for Typed μScheme and the
<primitives that aren't functions, for Typed μScheme .
My solution to this problem, including the implementation of
is under 20 lines of ML.
14. Do Exercise 14 on page 290 of Ramsey: write a type checker for Typed uScheme. Turn in this exercise in file tuscheme.sml, which should also include your solution to Exercise 17 above. Don't worry about the quality of your error messages, but do remember that your code must compile without errors or warnings. There is an error on p. 283 of the textbook with respect to the type of typeof. The error is corrected in this handout. The code in
linux.cs.tufts.edu:/comp/105/build-prove-compare/tuscheme/tuscheme.smlhas been corrected. If you have a copy where the type of typeof doesn't match the type in the handout, you should update your sources.
T. Create three test cases for Typed uScheme type checkers. In file type-tests.scm, please put three val bindings to names e1, e2, and e3. (A val-rec binding is also acceptable.) After each binding, put in a comment the words "type is" followed by the type you expect the name to have. If you expect a type error, instead put a comment saying "type error". Here is an example (with more than three bindings):
(val e1 cons) ; type is (forall ('a) ('a (list 'a) -> (list 'a))) (NEW NOTATION) (val e2 (@ car int)) ; tyep is ((list int) -> int) (NEW NOTATION) (val e3 (type-lambda ('a) (lambda (('a x)) x))) ; type is (forall ('a) ('a -> 'a)) (NEW NOTATION) (val e4 (+ 1 #t)) ; extra example ; type error (val e5 (lambda ((int x)) (cons x x))) ; another extra example ; type errorIf you submit more than three bindings, we will use the first three.
The only really viable strategy for building the type checker is one piece at a time. Writing the whole type checker before running any of it will make you miserable. Instead, start with small pieces similar to what we'll do in class:
It's OK to write out a complete case analysis of the syntax, but have every case raise the LeftAsExercise exception. This trick will start to get you a useful scaffolding, in which you can gradually replace each exception with real code. And of course you'll test each time.
You can begin by type-checking literal numbers and Booleans.
Add IF-expressions as done in class.
Implement the VAL rule for definitions, and maybe also the EXP rule. Now you can test a few IF-expressions with different types, but you'll need to disable the initial basis as shown below.
Implement the rule for function application. You should be able to test all the arithmetic and comparisons from class.
Implement LET binding. The Scheme version is slightly more general than we covered in class. Be careful with your contexts. Implement VAR.
Once you've got LET working, LAMBDA should be quite similar.
To create a function type, use the
funtype function in
Knock off SET, WHILE, BEGIN.
Because of the representation of types, function application is a bit tricky.
funtype function and make sure you
understand how to pattern match against its representation.
There are a couple of different ways to handle LET-STAR. As usual, the simplest way is to treat it as syntactic sugar for nested LETs.
Knock off the definition forms VALREC and DEFINE. (Remember that DEFINE is syntactic sugar for VALREC.)
Save TYAPPLY and TYLAMBDA for after the last class lecture on the topic. (Those are the only parts that have to wait until the last lecture; you can have your entire type checker, except for those two constructs, finished before the last class.)
Let me suggest that you replace the line in the source code
val basis = (* ML representation of initial basis *)with
val basis_included = false val basis = if not basis_included then  elseWith luck this will enable you to test things.
Before submitting, turn the basis back on.
cdrto the empty list. Don't do this! It can be done, but by the standards of COMP 105, such type systems are insanely complicated. As in ML, taking
cdrof the empty list should be a well-typed term that causes an error at run time.
ledit ./timpcoreJust plain timpcore will get the system version.
eqTypefunction to see if two types are equal. If you use built-in equality, you will get wrong answers.
val-recform requires an extra side condition; in
(val-rec x e)it is necessary to be sure that
ecan be evaluated without evaluating
x. Many students forget this side condition, which can be implemented very easily with the help of the function
appearsUnprotectedIn, which should be listed in the ``code index'' of your book.
ListPair.foldlwhen what was really meant was
Exercise 12, writing exists? and all? in Typed μScheme, requires that you really understand instantiation of polymorphic values. Once you get that, the problem is not at all difficult, but the type checker is very, very persnickety. A little of this kind of programming goes a long way.
Exercise 1, type-checking arrays in Typed Impcore, is probably the easiest exercise on this homework. You need to be able to duplicate the kind of reasoning and programming that we did in class for the language of expressions with LET and VAR.
Exercise 17, adding queues to Typed μScheme, requires you to understand how primitive type constructors and values are added to the initial basis. And it requires you to write ML code that manipulates μScheme representations. Study the way the existing primitives are implemented!
Exercise 14, the full type checker for Typed µScheme, presents two kinds of difficulty:
type-tests.scm. In addition to your code, please provide a short
READMEfile which describes, at a high level, the design and implementation of your solutions.
READMEfile containing the following information:
11.scm. All files are mandatory.