[Haskell-cafe] Basic question concerning data constructors
Yitzchak Gale
gale at sefer.org
Wed Jan 2 04:34:02 EST 2008
I wrote:
>> The classical definition of "general recursive function"
>> refers to functions in Integer -> Integer to begin
>> with, so there can only be countably many values by
>> construction.
Luke Palmer wrote:
> Except that there are uncountably many (2^Aleph_0) functions in
> Integer -> Integer.
No, only countably many. By the type expression Integer -> Integer
we mean all Haskell functions mapping Integers to Integers.
There are only countably many of those.
Of course, you can sometimes use Haskell-like notation
for discussing other mathematical concepts. In that context,
you might mean to include uncomputable functions in
your types. (Hey, there's a fun idea - how would you write
the infinite injury algorithm in Haskell?)
But that was not the context in this thread. The category
Hask that we often mention in discussions about Haskell
the programming language is most certainly a small category.
-Yitz
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