From: Jacques Garrigue <garrigue@math.nagoya-u.ac.jp>
To: Anders Peter Fugmann <anders@fugmann.net>
Cc: OCaML List Mailing <caml-list@inria.fr>
Subject: Re: [Caml-list] Strange Gadt error
Date: Tue, 13 Oct 2015 10:41:59 +0900 [thread overview]
Message-ID: <6E45A23F-36D5-48C9-88FD-858AFEDA48D6@math.nagoya-u.ac.jp> (raw)
In-Reply-To: <561BC1BC.8070602@fugmann.net>
On 2015/10/12 23:20, Anders Peter Fugmann wrote:
>
> Hi Jacques,
>
> Thanks for detailed explanation. I think I understand now why the error occurs and more specifically how to fix it in a consistent way.
>
> (However, changing 'add' to be
> 'add': int -> int -> int = fun n m-> n + m
> does not seem to help in my case)
Interesting.
This appears to be a rare case where it types with -principal, but not without it.
This is bug. I shall investigate it.
Jacques Garrigue
>
> Thanks
> /Anders
>
> On 09/10/15 01:17, Jacques Garrigue wrote:
>> On 2015/10/09 03:46, Anders Peter Fugmann wrote:
>>>
>>> Hi,
>>>
>>> I the following example (boiled down from a real use case):
>>>
>>> type _ elem =
>>> | Int: int elem
>>>
>>> let rec incr: type a. a elem -> a -> int = function
>>> | Int -> fun i -> add i 1
>>> and add n m = n + m
>>>
>>> I get the error (Ocaml 4.02.3):
>>> File "example.ml", line 5, characters 24-25:
>>> Error: This expression has type int but an expression was expected of type
>>> int
>>> This instance of int is ambiguous:
>>> it would escape the scope of its equation
>>
>> Interesting error.
>> I see your confusion in seeing an error on ‘i’.
>>
>> It is not completely wrong as you can indeed fix it by adding a local type
>> annotation changing the type of ‘i’ from ‘a’ to ‘int’.
>>
>>> I can get rid of the error by annotating the type of i in line 5 like this:
>>>
>>> | Int -> fun (i : int) -> add i 1
>>> ^^^
>>
>> However, the real cause is not so much ‘i', whose type is indeed known (but as `a’, not `int’),
>> but rather the absence of type annotation on ‘add'.
>> Changing add in the following way fixes the problem:
>>
>> and add : int -> int -> int = fun n m -> n + m
>>
>>> Or move add above incr like this:
>>>
>>> let rec add n m = n + m
>>> and incr: type a. a elem -> a -> int = function
>>> | Int -> fun i -> add i 1
>>
>> This change of order only works by chance. If you use ocaml -principal, you still get
>> a type error here with this code.
>>
>>> Is there an explanation to why I need to give the type of i in this case? As 'i' _must_ be an int (from the type annotation of incr), annotating the function seems ambiguous.
>>
>>
>> If you look carefully, you will see that the annotation says that ‘i’ has type ‘a’, not ‘int’.
>> In the local scope, those two types are equivalent, but once you leave if they are different.
>> Since we do not know yet the type of add, making a choice between the two seems arbitrary,
>> hence the error message.
>>
>> The only conclusive source on how this works is my paper with Didier Rémy:
>> Ambivalent types for principal type inference with GADTs
>> http://pauillac.inria.fr/~remy/gadts/
>>
>> In a nutshell, ambiguity occurs when a type obtained by unifying two equivalent
>> (but different) types is leaked out of their equivalence scope. What happens here is
>> a bit complicated. First the typer tries to give the type [a -> int -> int] to `add', avoiding
>> ambivalence. However, `a’ is not allowed to leak out of the definition of `incr’, so it
>> gets expanded into `int’. And this is that expansion which triggers the ambiguity
>> error. (An interesting remark is that, since add cannot have type [a -> int -> int] anyway,
>> there seems to be no ambiguity here. However, there is a scope between the
>> definition of `incr’ and the pattern-matching on `Int’ where such ambiguity might exists.)
>> By adding a local annotation on `i’, the problem is avoided, because then we are assuming
>> that `add’ has type [int -> int -> int] from the beginning (the ambivalence on `i’ does not leak).
>> Same thing with adding an annotation on `add’.
>>
>> As specific remark on what happens when you change the order (without -principal):
>> Since add is typed first, and receives type [int -> int -> int], this type is handled as
>> though it was explicitly known when entering the gadt scope. This is done for
>> the type of all external identifiers, except for their non-generalized type variables.
>> As a result, you get the same behavior as adding a type annotation on add.
>>
>> Thank you for this very demonstrative example.
>>
>> Jacques Garrigue
>>
>
prev parent reply other threads:[~2015-10-13 1:42 UTC|newest]
Thread overview: 4+ messages / expand[flat|nested] mbox.gz Atom feed top
2015-10-08 18:46 Anders Peter Fugmann
2015-10-08 23:17 ` Jacques Garrigue
2015-10-12 14:20 ` Anders Peter Fugmann
2015-10-13 1:41 ` Jacques Garrigue [this message]
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