Re: [Caml-list] polymorphic variants in match statements

["Milan Stanojević" <milanst@gmail.com>]

A small follow-up question

Polymorphic variant types are not allowed to have non-regular
recursion, i.e. the following type definition gives an error

type 'a t = [ `A of 'a | `B of ('a * 'a) t ]

Error: In the definition of t, type ('a * 'a) t should be 'a t

I guess the reason why this is not allowed has something to do with
our previous discussion, but I'm struggling to connect the dots.

Can you please explain this restriction?




2012/1/24 Milan Stanojević <milanst@gmail.com>:
> Thanks a lot, Jacques!
> This helped my understanding a lot.
>
> I only wonder if maybe this (and other type checking issues) could be
> documented in a better way. For example I couldn't find any links to
> your papers on OCaml website
>
>
> 2012/1/23 Jacques Garrigue <garrigue@math.nagoya-u.ac.jp>:
>> On 2012/01/24, at 9:53, Milan Stanojević wrote:
>>
>>> Hi, we're trying to understand the type inference with polymorphic
>>> variants in match statements. This is a simplification of an actual
>>> case that happened in practice.
>>>
>>> 1)
>>> let f i a =
>>>  match i, a with
>>>  | true, `A -> `B
>>>  | false, x -> x
>>>
>>> fails with
>>> File "foo.ml", line 4, characters 16-17:
>>> Error: This expression has type [< `A ]
>>>       but an expression was expected of type [> `B ]
>>>       The first variant type does not allow tag(s) `B
>>>
>>> 2) changing false to _
>>> let f i a =
>>>  match i, a with
>>>  | true, `A -> `B
>>>  | _, x -> x
>>>
>>> this succeeds with
>>> val f : bool -> ([> `A | `B ] as 'a) -> 'a
>>>
>>> 3) changing x in (1) to _ , and using a on the right side
>>> let f i a =
>>>  match i, a with
>>>  | true, `A -> `B
>>>  | false, _ -> a
>>>
>>> this fails in the same way as (1)
>>>
>>> 4) finally adding another case to match statement
>>> let f i a =
>>>  match i, a with
>>>  | true, `A -> `B
>>>  | false, x -> x
>>>  | true, x -> x
>>>
>>> this succeeds with the same type as (2)
>>>
>>>
>>> So it seems there is some interaction between type inference and
>>> exhaustivnest of the match statements.
>>>
>>> Can someone shed some light on what is going on here?
>>
>> Indeed. The basic idea is to close variant types when leaving them
>> open would make the pattern matching non-exhaustive.
>> Here, if we assume that a has type [`A | `B], then the pattern-matching
>> becomes non-exhaustive, so the type inferred is just [`A]
>> (i.e. the list of all constructors appearing inside the patterns at this position).
>>
>> Actually, the theory is a bit more complicated, and the full details are
>> in the following paper, but you should just expect the above behavior
>> in practice.
>>
>>        Typing deep pattern-matching in presence of polymorphic variants.
>>        http://www.math.nagoya-u.ac.jp/~garrigue/papers/index.html
>>
>> Note that there is also another way to make (1) type, without adding
>> new cases
>>
>>  let f i a =
>>    match i, a with
>>    | true, `A -> `B
>>    | false, (`A as x) -> x;;
>>  val f : bool -> [< `A ] -> [> `A | `B ] = <fun>
>>
>> Here we have removed the connection between a and the output,
>> allowing `A to be combine with `B without changing the type of a.
>>
>> Hope this helps.
>>
>> Jacques Garrigue
>>