Haskell List of List Type Error

Question

In GHCi, i type

let xs = [1, 'a']

it complains the error immediately:

<interactive>:28:11:
No instance for (Num Char) arising from the literal ‘1’
In the expression: 1
In the expression: [1, 'a']
In an equation for ‘xs’: xs = [1, 'a']

However, when I type

let xs = [1, [1, 1]]

It just passed. And it complains when I try to print xs:

<interactive>:5:1:
No instance for (Num [t0]) arising from a use of ‘it’
In a stmt of an interactive GHCi command: print it

I think Haskell is a static type language so any type error should be caught in compile time. I am wondering why the above 2 errors are caught at different time?

Daniel Wagner · Accepted Answer · 2015-06-05 00:10:43Z

8

1 is a polymorphic value of type Num a => a. So in [1, [2, 3]], we have [2, 3] :: Num a => [a]; since all list elements must have the same type, we conclude that we must have 1 :: Num a => [a]. That's a bit weird -- it's odd to think of 1 as having a list type -- but can be perfectly valid if somebody creates a sufficiently weird instance of Num. Checking whether an instance exists is pushed off until you try to use the instance; this gives you a chance to define the instance after you've defined the value using the instance. So it doesn't complain until you try to actually do something with the list [1, [2, 3]].

Just to illustrate what I mean, one may write:

instance Num a => Num [a] where
    fromInteger n = pure (fromInteger n)
    (+) = liftA2 (+)
    (-) = liftA2 (-)
    (*) = liftA2 (*)
    abs    = liftA abs
    signum = liftA signum

(Indeed, this instance works for any Applicative, and is occasionally even useful.) Then, in ghci:

> let xs = [1, [1, 1]]
> xs
[[1],[1,1]]

See ma, no errors!

edited Jun 5, 2015 at 0:10

answered Jun 4, 2015 at 23:50

Daniel Wagner

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5 Comments

Reid Barton Over a year ago

Why doesn't the same reasoning apply to a potential Num Char instance though?

Daniel Wagner Over a year ago

@ReidBarton Good question! I'm actually not sure about that. I would guess that during instance resolution, GHC refuses to delay finding evidence for monomorphic constraints; but that's just a guess.

Jeremy List Over a year ago

You could define a Num Char instance based on the Enum Char instance. The same reasoning would apply, but the instance just isn't included here.

Reid Barton Over a year ago

@DanielWagner, sounds plausible, and I guess the reason why it does not eagerly solve the constraint in the polymorphic case is not because you might define an instance Num [a] later (same is true for Num Char), but because (with FlexibleInstances) there might be some specific instances like Num [Double], and then you could use xs at type [[Double]]. In other words, GHC doesn't know what constraint to try to solve yet.

Cherish Over a year ago

This is kind of toooo deep for me, I am just a beginner in FP....takes time to digest your answer. Anyway, thanks a billion....

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