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
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