[Haskell-cafe] type metaphysics

[Daniel van den Eijkel]

oops, the '$ drop 1000' in the main function should not be there...


Daniel van den Eijkel schrieb:
> I had the same idea, here's my implemention, running on an old Winhugs 
> 2001 (and GHC 6.8).
> regards,  Daniel
>
>
> import System
> import Directory
>
> chars = map chr [32..126]
>
> string 0 = return ""
> string n = do
>  c <- chars
>  s <- string (n-1)
>  return (c:s)
>
> mkfun n = do
>  s <- string n
>  return ("f :: Integer -> Bool; f = " ++ s)
>
> test fundef = do
>  system ("del test.exe")
>  writeFile "test.hs" (fundef ++ "; main = return ()")
>  system ("ghc --make test.hs")
>  b <- doesFileExist "test.exe"
>  if b then putStrLn fundef else return ()
>  
> main = do
>  let fundefs = [0..] >>= mkfun
>  mapM_ test $ drop 1000 fundefs
>
> Lennart Augustsson schrieb:
>> You can enumerate all possible implementations of functions of type
>> (Integer -> Bool).
>> Just enumerate all strings, and give this to a Haskell compiler
>> f :: Integer -> Bool
>> f = <enumerated-string-goes-here>
>> if the compiler is happy you have an implementation.
>>
>> The enumerated functions do not include all mathematical functions of
>> type (Integer -> Bool), but it does include the ones we usually mean
>> by the type (Integer -> Bool) in Haskell.
>>
>>   -- Lennart
>>
>> On Mon, Feb 2, 2009 at 4:47 PM, Martijn van Steenbergen
>> <martijn at van.steenbergen.nl> wrote:
>>   
>>> Lennart Augustsson wrote:
>>>     
>>>> The Haskell function space, A->B, is not uncountable.
>>>> There is only a countable number of Haskell functions you can write,
>>>> so how could there be more elements in the Haskell function space? :)
>>>> The explanation is that the Haskell function space is not the same as
>>>> the functions space in set theory.  Most importantly Haskell functions
>>>> have to be monotonic (in the domain theoretic sense), so that limits
>>>> the number of possible functions.
>>>>       
>>> I was thinking about a fixed function type A -> B having uncountably many
>>> *values* (i.e. implementations). Not about the number of function types of
>>> the form A -> B. Is that what you meant?
>>>
>>> For example, fix the type to Integer -> Bool. I can't enumeratate all
>>> possible implementations of this function. Right?
>>>
>>> Martijn.
>>>
>>>     
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>>
>>   
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