Hi Benja,
I wrote:
>> By the type expression Integer -> Integer
>> we mean all Haskell functions mapping Integers to Integers.
>> There are only countably many of those.
> ...
>> But that was not the context in this thread. The category
>> Hask that we often mention in discussions about Haskell
>>
Hi Yitz,
On Jan 2, 2008 10:34 AM, Yitzchak Gale <[EMAIL PROTECTED]> wrote:
> 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.
...
> But that was not the context in this thread.
G'day all.
Quoting Yitzchak Gale <[EMAIL PROTECTED]>:
Data types consist only of computable elements. Since there
are only countably many computable functions, every data type
has at most countably many elements. In particular, it is a set.
I still say it "isn't a set" in the same way that a
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 -> Integ
On Jan 1, 2008 3:43 PM, Yitzchak Gale <[EMAIL PROTECTED]> 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.
Except that there are uncountably many (2^Aleph_0)
Andrew Bromage wrote:
>> [*] Theoretical nit: It's not technically a "set".
>>
>> Consider the data type:
>>
>> data Foo = Foo (Foo -> Bool)
>>
>> This declaration states that there's a bijection between the elements of
>> Foo and the elements of 2^Foo, which by Cantor's diagonal theorem canno
Andrew Bromage wrote:
> [*] Theoretical nit: It's not technically a "set".
>
> Consider the data type:
>
> data Foo = Foo (Foo -> Bool)
>
> This declaration states that there's a bijection between the elements of
> Foo and the elements of 2^Foo, which by Cantor's diagonal theorem cannot
> be t
On Dec 31, 2007 7:17 AM, <[EMAIL PROTECTED]> wrote:
> This declaration states that there's a bijection between the elements of
> Foo and the elements of 2^Foo, which by Cantor's diagonal theorem cannot
> be true for any set. That's because we only allow computable functions,
Nit the nit: Or (mor
G'day all.
Quoting David Menendez <[EMAIL PROTECTED]>:
data A = B
means that "B" constructs a value of type "A". The "=" acts more like the
"::=" in a BNF grammar.
And, indeed, that was the syntax for it in Miranda.
It is *not* a claim that A equals B, since A is a
type and B is a data
On Dec 30, 2007 9:24 AM, Joost Behrends <[EMAIL PROTECTED]> wrote:
> A similar point: The tutorials teach, that "=" has a similar meaning than
> "=" in
> mathematics. But there is a big difference: it is not reflexive. The
> the right side is the definition of the left. Thus "x=y" has still some
>
On Dec 30, 2007, at 8:24 AM, Joost Behrends wrote:
For adapting hws (one of the reasons for me to be here, not many
languages have
a native web server) to Windows i must work on time. In System.Time
i found
data ClockTime = TOD Integer Integer
2 questions arise here: Does this define "TOD"
Hello Joost,
Sunday, December 30, 2007, 5:24:59 PM, you wrote:
> data ClockTime = TOD Integer Integer
it declares type with name ClockTime (which you may use on type
signatures, other type declarations and so on) with one constructor
TOD accepting two Integer values. the only way to construct va
Hello,
perhaps i will make a wishlist of topics not dealt in the tutorials. Here is
something i miss in each of them: notes at the semantics of data constructors.
We read
data Pair a b = Pair a b
in YetAnotherHaskellTutorial. And that is all ! If we omit "data" here, this
would be a silly pl
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