[Haskell-cafe] Question about ambiguity and defaulting in recursive bindings

[Richard Eisenberg]

Yes, indeed. That is precisely what GHC does!

Well done discovering this. :)

Richard

> On Jan 19, 2022, at 5:34 PM, Benjamin Redelings <benjamin.redelings at gmail.com> wrote:
> 
> 1. Hmm... Perhaps ghc changes the code to
> 
> fgtuple:: (Eq a, Num a) => (Char -> a -> Char, Char -> Char -> Char)
> fgtuple dEq dNum = 
>    let f c i   = if i == 10 then c else g c 'b'
>        g 'a' w = f 'b' 10
>        g z   w = z
>    in (f,g)
> 
> f :: forall a. (Eq a, Num) => Char -> a -> Char
> f dEq dNum = case fgtuple dEq dNum of (f,g) -> f
> 
> g :: Char -> Char -> Char
> g = case fgtuple dEqInt dNumInt (f,g) -> g
> In order words, 
> 
> * the definition of fgtuple is not ambiguous.
> 
> * the defaulting is applied only to the definition of g, not the definition of fgtuple.
> 
> Does that sound right?
> 
> 2. Running ghc -ddump-tc shows:
> 
>   {Exports: [f <= f_a2gf
>                wrap: <>,
>              g <= g_a2gi
>                wrap: <> @ Integer $dEq_a2xJ $dNum_a2xK]
> The "wrap" code looks like the extra arguments that are applied by defaulting.
> 
> -BenRI
> 
> On 1/19/22 11:19 AM, Benjamin Redelings wrote:
> 
>> Hi,
>> 
>> I am trying to understand how GHC treats the following declaration.
>> 
>> f c i   = if i == 10 then c else g c 'b'
>> g 'a' w = f 'b' 10
>> g z   w = z
>> 
>> l = (f 'a' (1::Int), f 'a' (1.0::Double))
>> It seems to me like, after defaulting, f should have the following type:
>> 
>>     Char -> Int -> Char
>> However, looking at -ddump-tc, GHC is deriving the polymorphic type 
>> 
>>     forall a. (Eq a, Num a) => Char -> a -> Char
>> That's much nicer, because its more flexible.  But I'm confused, because it looks like GHC is defaulting 'g', but not 'f', even though they are in the same recursive group.  This seems to contradict "Typing Haskell in Haskell", which is what I am looking at right now.  If that is correct, can anybody point me to a paper or documentation about how this works?
>> 
>> More detail:
>> 
>> 1. If I understand correctly, the definitions of `f` and `g` are mutually recursive, and should be typed together, and the declaration group is not restricted.
>> 
>> 2. It seems like, before generalization, we have
>> 
>>     f :: Char -> a -> Char
>>     g :: Char -> Char -> Char
>>     Predicates include (Eq a, Num a)
>> 3. Looking at the paper "Typing Haskell in Haskell" (THIH), it looks like the predicates (Num a, Eq a) should cause an ambiguity in the definition of g:
>> 
>> * a is present in the definition of f, but not the definition of g
>> 
>> * so the type (Eq a, Num a) => Char -> Char -> Char is ambiguous.
>> 
>> * more generally, it seems like THIH treats any predicates with a type variable that is part of some, but not all, types in the declaration group to be ambiguous.  Does this sound right?
>> 
>> 4. Then, again following THIH, this ambiguous predicate should be defaulted to Int.
>> 
>> I THINK this should lead to
>> 
>> 	f :: Char -> Int -> Char
>> 	g :: Char -> Char -> Char
>> 5. However, I'm still not sure I'm understanding this right, because a few things still don't make sense:
>> 
>> * First, THIH seems to eliminate the defaulted predicates without substituting a -> Int.  But the type for f DOES mention `a`, so how can we avoid substituting?
>> 
>> * Second, GHC accepts the code with no warnings or errors. There is some kind of defaulting going on, because GHC rejects the code if I add "default ()". Is there some way for GHC to default only g, but not f?  
>> 
>> I wonder if this involves a difference between Haskell '98 and Haskell 2010?
>> 
>> I also wonder how much I should rely on THIH?  Maybe the language has moved on since then?
>> 
>> -BenRI
>> 
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