[Haskell-cafe] Re: [Haskell] Recursive definition of fibonacci with Data.Vector

[Don Stewart]

ajs:
> 
> On Mar 7, 2010, at 12:56 PM, Don Stewart wrote:
> 
> 
>     In fact, infinite vectors make no sense, as far as I can tell -- these
>     are fundamentally bounded structures.
> 
> 
> Fourier analysis?  Functional analysis?  Hamel bases in Real analysis?  There
> are lots of infinite dimensional vector spaces out there.

Sorry for the overloading, I mean 'vector' in the sense of Data.Vector.
Being strict in the length, its unclear  to me that you can do much with
infinite ones :-)

Of course, all the nice optimizations will also work for lazy
structures, like lists, but that's a different library.

>     GHC even optimizes it to:
> 
>        fib = fib
> 
> Sounds like an implementation bug, not an infinite dimensional vector space
> bug.  My guess is that strictness is getting in the way, and forcing what would
> be a lazy call to fib in the corresponding list code -- fib = 0 : 1 : (zipWith
> (+) fib (tail fib)) -- into a strict one.
> 
> In fact, I'm pretty sure that's what the problem is:
> 
> 
> data Vector a = Vector {-# UNPACK #-} !Int
>                        {-# UNPACK #-} !Int
>                        {-# UNPACK #-} !(Array a)
> 
> 
> The !'s mean "strict" right?

That's precisely the right semantics for strict-in-the-length arrays.
And it is brilliant that GHC reduces it all down to the minimal possible
program that has the same semantics as a non-terminating strict-length
infinite array.

-- Don