Math Forum Discussions

Graham Cooper

Posts: 4,045
Registered: 5/20/10

Re: The MYTH of UNCOMPUTABLE FUNCTIONS
Posted: Jan 14, 2013 12:59 AM

Plain Text

On Jan 14, 2:16 pm, Rupert <rupertmccal...@yahoo.com> wrote:
> On Sunday, January 13, 2013 10:57:26 PM UTC+1, Graham Cooper wrote:
> > On Jan 14, 7:09 am, Rupert <rupertmccal...@yahoo.com> wrote:
>
> > > On Sunday, January 13, 2013 9:37:46 PM UTC+1, Graham Cooper wrote:
>
> > > > On Jan 14, 6:13 am, Rupert <rupertmccal...@yahoo.com> wrote:
>
> > > > > On Sunday, January 13, 2013 9:04:31 PM UTC+1, Graham Cooper wrote:
>
> > > > > > On Jan 13, 7:30 pm, Rupert <rupertmccal...@yahoo.com> wrote:
>
> > > > > > > On Saturday, January 12, 2013 10:48:43 PM UTC+1, Graham Cooper wrote:
>
> > > > > > > > Turing's Halt Proof clearly proves that
>
> > > > > > > > HALT( program, input ) --> [yes/no]
>
> > > > > > > > is not a PURE FUNCTION!
>
> > > > > > > How do you define "pure function"?
>
> > > > > > the output is determined by the input alone
>
> > > > > > Here is a function that imports CAMGIRLS Sales data to the AFFILIATE
>
> > > > > > PROGRAM
>
> > > > > > function($result)
>
> > > > > > {
>
> > > > > > $myxml = simplexml_load_string($response);
>
> > > > > > $qid = $myxml->SignupData['QueryId'];
>
> > > > > > if ($qid == 'camgirls-com') {
>
> > > > > > $host="mysql.camaffiliate.com"; // Host name
>
> > > > > > $username="camaff"; // Mysql username
>
> > > > > > $password="*********"; // Mysql password
>
> > > > > > $db_name="afftrail"; // Database name
>
> > > > > > $tbl_name="pa_transactions"; // Table name
>
> > > > > > // Connect to server and select database.
>
> > > > > > mysql_connect("$host", "$username", "$password")or die("cannot connect
>
> > > > > > to server ");
>
> > > > > > mysql_select_db("$db_name")or die("cannot select DB");
>
> > > > > > $assets = $myxml->SignupData;
>
> > > > > > $html = '<ul>'."\n";
>
> > > > > > foreach ($assets->Data as $asset) {
>
> > > > > > $html .= '<li>' . $asset['SignupTime'] . ' ' .
>
> > > > > > $asset['TrackingID'] . ' ' . $asset['UserID'] . '</li>' . "\n";
>
> > > > > > $sut = $asset['SignupTime'];
>
> > > > > > $tid = $asset['TrackingID'];
>
> > > > > > $uid = $asset['UserID'];
>
> > > > > > $sql="SELECT * FROM $tbl_name WHERE transid=" . $uid;
>
> > > > > > $result=mysql_query($sql);
>
> > > > > > $rows=mysql_fetch_array($result);
>
> > > > > > $userthere=$rows['transid'];
>
> > > > > > // if table has no UserID value
>
> > > > > > if(empty($userthere)){
>
> > > > > > $sql1="INSERT INTO $tbl_name(transid, dateinserted, totalcost,
>
> > > > > > affiliateid) VALUES('$uid','$sut',80,'$tid')";
>
> > > > > > $result1=mysql_query($sql1);
>
> > > > > > }
>
> > > > > > }//end foreach
>
> > > > > > $html .= '</ul>'."\n";
>
> > > > > > // echo $html;
>
> > > > > > mysql_close();
>
> > > > > > }
>
> > > > > > But the results of the function are not determined only by the input
>
> > > > > > If a new client has already been added... then it is not added a 2nd
>
> > > > > > time!
>
> > > > > > // if table has no UserID value
>
> > > > > > if(empty($userthere)){
>
> > > > > > *********************************
>
> > > > > > You can CHANGE a function with global variables and side effects into
>
> > > > > > a PURE FUNCTION
>
> > > > > > by adding more parameters into the parameter list.
>
> > > > > > Herc
>
> > > > > Are you talking about a mathematical function or a function that can be computed by a computer?
>
> > > > Can you state the difference?
>
> > > > Herc
>
> > > A function from a set A to a set B is an arbitrary rule, which, given a member of A, gives you a unique member of B. There does not need to be an algorithm which will compute the outcome of the rule.
>
> > you just substituted the word computer with algorithm
>
> > Herc
>
> You want me to define "algorithm"? Why don't you read a textbook on recursion theory?
>

Because "Recursion Theory" whatever theory that may be

is just a bunch of idiots putting the word "Recursive" before 20
different other idiotic maths terms about phantom bullshit

when the Authors and their Sap Students couldn't even program a FOR
LOOP yet alone a recursive program.

Here is a RECURSIVE 5TH GENERATION LANGUAGE construct for SUBSET
capable of implementing the FORALL QUANTIFIER that is executable via
reverse Modus Ponens to any Axiomatic base.

PROLOG+ A CONCEPT DATABASE MANAGEMENT LANGUAGE (DBML)

We add simple breadth first extensions to PROLOG CLAUSES.

Y> next record
Y< prev record
Y>> last record
Y<< 1st record

AXIOM OF FINITE SUBSETS
-----------------------

subs(A,X,Y) <- e(A>>,X) ^ e(A,Y).

subs(A,X,Y) <- e(A,Y) ^ e(A>,X) ^ subs(A,X,Y).

ss(X,Y) <- e(A<<,X) ^ subs(A,X,Y).

AXIOM OF FINITE SET EQUALITY
----------------------------

equals(X,Y) <- ss(X,Y) ^ ss(Y,X).

e.g.

?- ss(rower,male).
YES

?- equals(rower,male).
NO

*****************

Considering you are incapable of spotting the RECUSION
in this tiny bit of code, yet alone the FOR LOOP
it emulates, processing through each record

subs(A,X,Y) <- e(A>>,X) ^ e(A,Y).
subs(A,X,Y) <- e(A,Y) ^ e(A>,X) ^ subs(A,X,Y).
ss(X,Y) <- e(A<<,X) ^ subs(A,X,Y).

and the term 'pure function' eludes you

maybe it is you who should sit back and do some reading?

Herc
--
www.microPROLOG.com