[Haskell-cafe] dependent types, singleton types....

Richard Eisenberg eir at cis.upenn.edu
Thu Apr 30 15:41:57 UTC 2015

See below.

On Apr 30, 2015, at 9:34 AM, "Nicholls, Mark" <nicholls.mark at vimn.com> wrote:
> but this doesnt.
>> f :: SBTree a -> Integer
>> f (SBranch SZ SLeaf SLeaf) = 1
> but (for me) the important thing to work out is what's actually wrong....i.e. walk before I run and land on my face
> I struggle with Haskell errors.
> it says
> exerviceOnDependentTypes.lhs:42:14:
>    Could not deduce (a1 ~ SNat t0)
>    from the context (a ~ 'Branch a1 b c)
>      bound by a pattern with constructor
>                 SBranch :: forall a (b :: BTree *) (c :: BTree *).
>                            a -> SBTree b -> SBTree c -> SBTree ('Branch a b c),
>               in an equation for 'f'
>      at exerviceOnDependentTypes.lhs:42:6-27
>      'a1' is a rigid type variable bound by
>           a pattern with constructor
>             SBranch :: forall a (b :: BTree *) (c :: BTree *).
>                        a -> SBTree b -> SBTree c -> SBTree ('Branch a b c),
>           in an equation for 'f'
>           at exerviceOnDependentTypes.lhs:42:6
>    In the pattern: SZ
>    In the pattern: SBranch SZ SLeaf SLeaf
>    In an equation for 'f': f (SBranch SZ SLeaf SLeaf) = 1
> so its trying to work out what? 
> "a" is valid in "SBTree a" in the context of the function definition "f (SBranch SZ SLeaf SLeaf) = 1" ?
> so "a" ~ "Branch a1 b c" from the defintion "SBranch :: (a :: *) -> (SBTree (b :: BTree *)) -> (SBTree (c :: BTree *)) -> SBTree ('Branch a b c)"?
> and it wants to deduce that "a1 ~ SNat t0"?
> why?

GHC is trying to type-check the pattern `SBranch SZ SLeaf SLeaf` against the type `SBTree a`. Once GHC sees the constructor `SBranch`, it knows that `a ~ 'Branch a1 b c` for some `a1`, some `b`, and some `c`. Then, it tries to type-check the pattern `SZ` against the type `a1`. For this to type-check, GHC must be convinced that `a1 ~ SNat t0` for some `t0`. But there's no reason for GHC to believe this, so it reports an error.

One may say "Well, GHC should just decide that `a1` must be `SNat t0` and get on with it." But, that is tantamount to arguing that `foo :: a -> a; foo True = False` should type-check, by saying that GHC should decide that `a` is `Bool`. It's the same thing in the `SBTree` case: we just don't know enough to assume that `a1` should be an `SNat`.

> Why does it care? (is this my OO type head getting in the way)

This doesn't look, in particular, like a question from a recovering OO programmer. It's a good question to ask and a hard part to figure out.

I hope this helps!

> Mark Nicholls | Senior Technical Director, Programmes & Development - Viacom International Media Networks
> A: 17-29 Hawley Crescent London NW1 8TT | e: Nicholls.Mark at vimn.com T: +44 (0)203 580 2223
> -----Original Message-----
> From: Richard Eisenberg [mailto:eir at cis.upenn.edu] 
> Sent: 29 April 2015 2:43 PM
> To: Nicholls, Mark
> Cc: haskell-cafe at haskell.org
> Subject: Re: [Haskell-cafe] dependent types, singleton types....
> On Apr 29, 2015, at 8:54 AM, "Nicholls, Mark" <nicholls.mark at vimn.com> wrote:
>> Accchhhh
>> Thats another level of pain
> It is, unfortunately.
>> , i'm not a big haskeller so i'll have to wrestle with it to get all the knobs and dials working, leave it with me for the moment and i'll start wrestling with cabal
> You won't need cabal and such. Just say `data family Sing (a :: k)` in your file and you'll have the definition. There's really nothing more to it than that!
> Richard
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