[racket-dev] A proposal for parametric opaque types in Typed Racket

On Jan 30, 2015, at 3:59 PM, Alexis King <lexi.lambda at gmail.com> wrote:

> No, the typechecker can’t make any assumptions about the results of opaque types. If you explicitly instantiate a Posn with the type Real, the typechecker should only guarantee the result will be Real. Annotate the type as (U 1 2), though, and obviously it would need to ensure that remains invariant.

How about this program:
untyped.rkt:
#lang racket
(provide (all-defined-out))
(define (make-posn x y) (list 3 y)) ; bad
typed.rkt:
#lang typed/racket
; make Posn parametric
(define-type (Posn X Y) (List X Y))
(require/typed "untyped.rkt"
               [make-posn (All (X Y) X Y -> (Posn X Y))])
(: p : (Posn Real Real))
(define p (make-posn 1 2))
This gives this error:
. . make-posn: broke its contract
  promised: X3
  produced: 3
  in: the car of
      the range of
      (parametric->/c
       (X3 Y4)
       (->*
        (X3 Y4)
        ()
        (values (cons/c X3 (cons/c Y4 g6)))))
  contract from: (interface for make-posn)
  blaming: (interface for make-posn)
   (assuming the contract is correct)
  at: …./typed.rkt:5.16

I think it’s a good thing that it checks that it actually gives you the value that you gave it, and not just something like 3 even if it happens to match the type you want.  And I think parametric opaque types should behave in a similar way, and to do that you would need the opaque value to be wrapped in another opaque structure, which would store either the contracts or the set of values that would pass the contracts or something like that.  

> 
>> On Jan 30, 2015, at 12:30, Alexander D. Knauth <alexander at knauth.org> wrote:
>> 
>> 
>> On Jan 30, 2015, at 1:53 PM, Alexis King <lexi.lambda at gmail.com> wrote:
>> 
>>> No, it doesn’t need to be wrapped in an opaque structure. Wrapping it in an opaque structure would add a layer of indirection for absolutely no gain. Remember, the value itself is already, by definition, opaque. The only way typed code can manipulate the value is by passing it to other functions imported via require/typed.
>>> 
>>> This means that contracts only need to be generated wherever those functions are called. This can be done without wrapping or unwrapping anything because all the information required to generate those contracts is known at expansion-time. The typechecker simply needs to insert the relevant contracts at the relevant locations.
>> 
>> Imagine a program like this:
>> #lang typed/racket
>> (require typed/lang/posn)
>> (: p : (Posn Real Real)) ; I’m assuming Posn is parametric over 2 tvars, not 1
>> (define p (posn 1 2))
>> (: x : Real)
>> (define x (posn-x p))
>> As far as the type checker would check, it would check that the result of posn-x is a Real, but I think that the runtime contract it should also check that it returns 1, because posn could have been instantiated as (Posn 1 2).
>> #lang typed/racket
>> (require typed/lang/posn/mutable) ; like typed/lang/posn, but providing mutation too
>> (: p : (Posn Real Real))
>> (define p (posn 1 2))
>> (: x : Real)
>> (define x (posn-x p))
>> (set-posn-x! p 3)
>> (: x2 : Real)
>> (define x2 (posn-x p))
>> Here, even though the type checker only cares that it’s a number, it should check that x2 definition returns either 1 or 3, since both were provided as x values for the posn p.
>> 
>> For it to keep track of these at runtime, (and it would have to be runtime) the contracts would have to be with the actual posn value in an opaque structure, which would have contracts sort of like (new-∀/c) that would check these things, although I don’t think it would have to wrap the inner values, but just record them so that when posn-x is called on one of these things, it checks that it was one of the values that was passed in to either a constructor or setter function.  
>> 
>>>> On Jan 30, 2015, at 07:27, Alexander D. Knauth <alexander at knauth.org> wrote:
>>>>  
>>>> On Thu, Jan 29, 2015, at 09:03 PM, Alexis King wrote:
>>>>> It isn’t wrapped in an opaque structure. That wasn’t a part of my proposal, and while I didn’t think of it until you brought it up, I still think it’s unnecessary and doesn’t add any convenience.
>>>>  
>>>> I think the opaque structures would be necessary for the kind of "sharing wrappers between functions" that you describe just before section 2.1, except that instead of the sub-values being wrapped on the untyped side, the whole thing is wrapped on the typed side, and there is a contract that wraps it and unwraps it when it goes from untyped to typed and back.  
>>>>  
>>>> For parametric types, they have to also work if the type was constrained to the exact set of values that were provided, which means that if you provide two numbers, say 1 and 2, it has to return a posn with not just any two numbers, but values of the type (U 1 2), since A could have been constrained to (U 1 2).  So it has to be wrapped somehow, and I think wrapping it on the typed side makes more sense.  
>>>>  
>>>>> Perhaps I’m not understanding you properly, but your “one-length string” idea sounds like it has little to do with this opaque type problem and more to do with the fact that you want refinement types in Typed Racket. I do, too! But I don’t think hacking the opaque type system is going to help you with that.
>>>>  
>>>> Well, yeah, refinement types would be the "real" solution for this particular example, but if I do want to constrain it to strings of length 1, opaque types are the only option for now, and they actually work fine.  My point was you couldn't do this type of thing with the opaque structures and you would probably get weird errors if you tried.  (See below because there might be a solution?)
>>>>  
>>>>> (Also, as for the box example, I’m actually a little surprised that doesn’t contract error. Seems like a bug to me, but perhaps I’m missing some idiosyncrasies of the type system. Either way, it’s precisely that kind of craziness I was referring to when I compared casting parametric opaque types to casting mutable types.)
>>>>  
>>>> There is a bug report for it here, and the solution proposed by Sam Tobin-Hochstadt would be for cast to generate 2 contracts, one for the original type, one for the new type, but that never got implemented.  
>>>> http://bugs.racket-lang.org/query/?cmd=view&pr=13626
>>>>  
>>>> Actually now that I think about it the two-contract solution might be able to solve the previous problem, since the original contract could unwrap the value before it is passed to the new contract?  I'm not sure though.  The value inside the cast would be from the typed side, then it is passed through the orig contract as if it were going to the typed side,
>> 
>> This was a typo, I meant to say “as if it were going to the untyped side"
>> 
>>>> which would unwrap it, and then that unwrapped value would be passed to the new contract as if it were flowing from the untyped side to the typed side.  
>>>>  
>>>>>  
>>>>>> On Jan 29, 2015, at 20:50, Alexander D. Knauth <alexander at knauth.org> wrote:
>>>>>>  
>>>>>>  
>>>>>> On Jan 29, 2015, at 11:34 PM, Alexis King <lexi.lambda at gmail.com> wrote:
>>>>>>  
>>>>>>>> But the problem is that if it’s an opaque type then it can’t unwrap it once the value is returned from make-posn.
>>>>>>>  
>>>>>>> Yes, that’s precisely the problem. Your point about implementing everything as single-valued structs on the typed side is an interesting one, though I don’t think it ultimately solves any problems. The fact that the typed side knowsnothingabout the contents of the value is what makes this such a tricky problem.
>>>>>>>  
>>>>>>> As for this:
>>>>>>>  
>>>>>>>> But then you couldn’t do any operations on it except those that you use import with require/typed, right?
>>>>>>>  
>>>>>>> That’s completely correct. That’s why it’s “opaque.”
>>>>>>>  
>>>>>>>> And what happens if you use cast on one of these things?
>>>>>>>  
>>>>>>> That’s a little more interesting. Usingcaston an object of this type would never fail (unless, of course, it didn’t actually satisfy the basicposn?predicate), but it would possibly introduce failures in the future since it would affect the contracts generated forposn-xandposn-y, for example.
>>>>>>>  
>>>>>>> To make that more clear, casting a(Posn Real)to a(Posn String)would work fine until you tried to callposn-xon the instance, in which case it would raise a contract error. Note that this isn’t really any different from casting mutable data types.
>>>>>>  
>>>>>> But if it were wrapped in an opaque structure, then that structure wouldn’t satisfy the posn? predicate, unless of course the posn? predicate has a contract that unwraps it.  So all of the operations on it would have to have contracts that would unwrap it.  This might actually make sense if the type is meant to be actually opaque, but if it’s an opaque type that represents a normal non-opaque value, then it will still work as an opaque type, but it won’t be a normal non-opaque value anymore on the typed side.  
>>>>>>  
>>>>>> But the reason I asked about cast was because normally I can use cast with a value that has an opaque type, but it’s wrapped on the typed side in this opaque structure, then the contracts on the cast would see this opaque structure instead of the actual value.  
>>>>>>  
>>>>>> I’m thinking of an opaque typed representing a string with length 1, which I can use as long as I use either (cast x String) or (assert x string?) whenever I pass it to a string operation.  But if it were an opaque type, I don’t think I could do that.  There could be a 1string->string function that could take one of these 1strings and convert it to a string, but that seems like it should be unnecessary, but made necessary by this opaque structure thing.  
>>>>>>  
>>>>>> And for “this isn’t really any different from casting mutable data types,” look at this:
>>>>>> #lang typed/racket
>>>>>> (: b : (Boxof Number))
>>>>>> (define b (box 1))
>>>>>> (set-box! (cast b (Boxof (U Number String))) "I am a string")
>>>>>> (ann (unbox b) Number) ;"I am a string” ; not a contract error
>>>>>>  
>>>>>>  
>>>>>>>  
>>>>>>>> On Jan 29, 2015, at 20:20, Alexander D. Knauth <alexander at knauth.org> wrote:
>>>>>>>>  
>>>>>>>> Furthermore, even if the wrappers were shared between functions, untyped code would recieved wrapped values, which would render them quite useless.
>>>>>>>>  
>>>>>>>> If it’s not an opaque type, but something like a list, then this works, and the untyped code receiving wrapped values isn’t a problem here:
>>>>>>>> #lang typed/racket
>>>>>>>> ; make Posn parametric
>>>>>>>> (define-type (Posn A) (List A A))
>>>>>>>> (provide Posn)
>>>>>>>> (require/typed/provide
>>>>>>>>  "untyped.rkt"
>>>>>>>>  [make-posn (All (A) A A -> (Posn A))]
>>>>>>>>  [posn-x (All (A) (Posn A) -> A)]
>>>>>>>>  [posn-y (All (A) (Posn A) -> A)]
>>>>>>>>  [real-posn? [(Posn Any) -> Boolean]])
>>>>>>>> > (define p (make-posn 1 2))
>>>>>>>> (make-posn #<A6> #<A6>) ; a printf that I put in make-posn from “untyped.rkt"
>>>>>>>> > p
>>>>>>>> - : (Listof Positive-Byte) [more precisely: (List Positive-Byte Positive-Byte)]
>>>>>>>> '(1 2) ; unwrapped
>>>>>>>> > (posn-x p)
>>>>>>>> - : Integer [more precisely: Positive-Byte]
>>>>>>>> 1
>>>>>>>> > (posn-y p)
>>>>>>>> - : Integer [more precisely: Positive-Byte]
>>>>>>>> 2
>>>>>>>> > (real-posn? p)
>>>>>>>> - : Boolean
>>>>>>>> #t
>>>>>>>>  
>>>>>>>> Even though for a short time it's wrapped, it’s unwrapped as soon as make-posn returns, and then after that if it flows into untyped code again it’s not wrapped and functions like real-posn? work fine.  
>>>>>>>>  
>>>>>>>> But the problem is that if it’s an opaque type then it can’t unwrap it once the value is returned from make-posn.
>>>>>>>>  
>>>>>>>> And I don’t think parametric opaque types could solve this unless all posns themselves were wrapped with an opaque struct on the typed side, which I guess does make sense now that I think about it.  But then you couldn’t do any operations on it except those that you use import with require/typed, right?  Or not?  And what happens if you use cast on one of these things?
>>>>>>>>  
>>>>>>>>  
>>>>>>>> On Jan 29, 2015, at 9:25 PM, Alexis King <lexi.lambda at gmail.com> wrote:
>>>>>>>>  
>>>>>>>>> I recently ran into a problem in which opaque types (types imported from untyped code) cannot by parameterized by Typed Racket. I initially encountered this problem in my attempt to port 2htdp/image to TR.
>>>>>>>>>  
>>>>>>>>> After some further consideration, I’m interested in adding support to make something like this possible, which would certainly have additional benefits beyond this specific use-case. I’ve outlined my proposal here:
>>>>>>>>> http://lexi-lambda.github.io/racket-parametric-opaque-types/
>>>>>>>>>  
>>>>>>>>> Any feedback, suggestions, or advice would be appreciated, especially from those who are familiar with Typed Racket’s internals.
>>>>>>>>>  
>>>>>>>>> Thank you,
>>>>>>>>> Alexis
>>>>>>>>> _________________________
>>>>>>>>>  Racket Developers list:
>>>>>>>>> http://lists.racket-lang.org/dev
> 

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