# [Haskell-beginners] question on types

Brandon Allbery allbery.b at gmail.com
Fri Jul 29 02:23:11 CEST 2011

```On Thu, Jul 28, 2011 at 19:42, Jake Penton <djp at arqux.com> wrote:

> h:: a
> h = 'a'
>
> to which ghci replies:
>
>     Couldn't match type `a' with `Char'
>       `a' is a rigid type variable bound by
>           the type signature for c :: a
>           at /Users/David/Project/EoP/ch04/weak.hs:114:1
>     In the expression: 'a'
>     In an equation for `c': c = 'a'
>
> This last example is probably the most basic one which I need to
> understand. But, why is the problem apparently a different one than in the
> definition of "f" above?
>

The other one was complicated by polymorphism:  a numeric literal is
compiled into a call to fromIntegral, whose result type is Num a => a.

The problem is that, when you say something's type is "a", you are not
saying "pick an appropriate type for me"; you are saying "whoever invokes
this can ask for any type it wants" (equivalently:  "I promise to be able to
produce *any possible* type").  But then you give the value as Num a => a in
the first example and Char in the second example, neither of which is "any
possible type".

An explicit type is a complete contract; having contracted to produce an "a"
(any type), you can't then offer only a Char or a Num a => a.  You have to
satisfy the contract which says "any type", otherwise you're doing the type
checking equivalent of a bait-and-switch.

You can't express "pick a type for me" in a type signature; types are
concrete, and a type variable in a signature is a concrete "anything",
meaning the caller can request whatever it wants and you must produce it.
The type must be *completely* described by the signature; what it says is
what you're committed to, and you can't then offer something else.  If you
need a partial type signature, there are some tricks you can use which let
you force types in the implementation without specifying a concrete