# [Haskell-cafe] need help with understanding expression

damodar kulkarni kdamodar2000 at gmail.com
Sat Nov 17 08:19:27 CET 2012

```Let's see tthis:
Prelude> :t 3 "a"
3 "a" :: (Num ([Char] -> t)) => t

No complaint from GHC; but now see this:

Prelude> :t  "a" 3

<interactive>:1:0:
Couldn't match expected type `t1 -> t'
against inferred type `[Char]'
In the expression: "a" 3

Why does it not fail for  (:t 3 "a") but does fail for (:t  "a" 3)?

In the second case, why the GHC doesn't give something like?
([Char] (a -> t), Num a) => t

In other words, how the first one does make "sense" (however strange the
"sense" may seem) to GHC while the second one doesn't?

Now let's consider the evaluation scenario:

Prelude>  3 2

<interactive>:1:0:
No instance for (Num (t -> t1))
arising from the literal `3' at <interactive>:1:0-2
Possible fix: add an instance declaration for (Num (t -> t1))
In the expression: 3 2
In the definition of `it': it = 3 2

Note, how the GHC suggests us this "strange constraint" as a *possible
fix*BUT see this:
Prelude>  "a" 2

<interactive>:1:0:
Couldn't match expected type `t1 -> t'
against inferred type `[Char]'
In the expression: "a" 2
In the definition of `it': it = "a" 2

In this case the GHC doesn't even allow us to add any "possible fix".

-Damodar

On Fri, Nov 16, 2012 at 2:27 PM, Sean Leather <leather at cs.uu.nl> wrote:

> Hi Daryoush,
>
>
> Prelude> :t 3 2
>> 3 2 :: (Num a, Num (a -> t)) => t
>>
>> What does the type mean in plain english?
>>
>
> It's important to remember that numeric literals are polymorphic. That is,
> 3 :: Num a => a. They do not have monomorphic types such as Int or Integer.
>
> In the above, GHCi is inferring the principal type of 3 applied to 2.
> Since 3 is in the position of function application, it should have a
> function type, e.g. a -> t. And 2 is the argument to 3, so it has the type
> 'a'. But there must be Num constraints on these types, and that's what the
> context (Num a, Num (a -> t)) is telling you. Num (a -> t) is a strange
> constraint but so is applying 3 to 2. Whenever you see a Num constraint on
> a function type, it probably means you're doing something wrong.
>
> You might find the (brief) description of typing numeric literals in the
>
>
>
> Also, in response to your initial query...
>
> I am having hard time understanding how removing the  outer parenthesis in
>> (max.(+1)) 2 2
>> to
>> max.(+1) 2 2
>
>
> Keep in mind the precedence of the function composition operator (.) here:
>
> Prelude> :i (.)
> (.) :: (b -> c) -> (a -> b) -> a -> c -- Defined in GHC.Base
> infixr 9 .
>
> Function application is infixl 10, so even though max . (+1) :: (Num b,
> Ord b) => b -> b -> b, when you do max . (+1) 2, the application of (+1) to
> 2 binds more tightly than (.).
>
> A common idiom for removing parentheses with a sequence of compositions is
> to use (\$):
>
> Prelude> :i (\$)
> (\$) :: (a -> b) -> a -> b -- Defined in GHC.Base
> infixr 0 \$
>
> Note that it has the lowest possible precedence. So, you often see the
> composition of functions as f . g . h \$ arg. But this doesn't work well
> for (curried) functions with 2 arguments. So, in your case, I'd guess the
> parentheses is simplest idiomatic solution. Though, I think I'd prefer max
> (succ 2) 2.
>
> Regards,
> Sean
>
> _______________________________________________
>
>

--
Thanks and regards,
-Damodar Kulkarni
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