[Haskell] Re: Implicit type of numeric constants

[Robert Stroud]

On 20 Sep 2006, at 17:28, Christian Sievers wrote:

>>> However, if I type an apparently equivalent let expression into Hugs
>>> directly, then I get the value 4 as expected
>>>
>>> let k = 2 ; f :: Int -> Int -> Int ; f x y = x * y in f k k
>>>
>>> Why is there a difference in behaviour?
>>
>> Here, there is no defaulting, 'k' has the polymorphic type you  
>> expect, and
>> the use of 'k' as an argument to the monomorphically typed 'f'  
>> chooses the
>> right instance of 'Num'.
>
> Well, there is no defaulting at the stage of type checking when k  
> is given
> type Num a => a, the monomorphism restriction applies and this type  
> is not
> generalised to forall a . (Num a) => a, then the use of k forces  
> the type
> variable a to be Int, and then there is no longer any need for  
> defaulting.
>
> So k gets a monotype which is determined by its usage, you cannot  
> do e.g.
>
>   let k = 2 ; f :: Int -> Int -> Int ; f x y = x * y in (f k k, 1/k)
>
> whereas   let k :: Num a => a; k = 2; ...   is possible.

Thanks - that's a helpful example. But why is the following not  
equivalent to the untyped "k = 2" case:

let f :: Int -> Int -> Int ; f x y = x * y in (f 2 2, 1/2)

Does the type of 2 effectively get decided twice, once as an Int, and  
once as a Fractional, and is this the "repeated computation" that the  
monomorphism restriction is intended to prevent?

Otherwise, I would have expected that it wouldn't make any difference  
whether I used a named 2 or an anonymous 2, but imposing the  
monomorphism restriction on the named 2 seems to break referential  
transparency.

Thanks.

Robert