Meaning of an upside down A symbol

A place to discuss the science of computers and programs, from algorithms to computability.

Formal proofs preferred.

Moderators: phlip, Moderators General, Prelates

Boxknife
Posts: 10
Joined: Wed Jul 23, 2008 6:44 am UTC

Meaning of an upside down A symbol

I'm reading Hennessy and Patterson's Computer Architecture: A Quantitative Approach, and I've come across a strange upside-down-'A' like symbol in some pseudo-code describing Tomasulo's Algorithm (I can't even find it in my character map). It's followed immediately by an 'x' and an if statement enclosed by parentheses. I'm guessing it's some sort of function?

Here's the context:

<upside-down-A-thing>x( if(RegisterStat[x].Qi=r){Regs[x] <- result; RegisterStat[x].Qi <- 0} );

What does it mean?

ElvetPuff
Posts: 45
Joined: Fri Jul 18, 2008 4:50 pm UTC

Re: Meaning of an upside down A symbol

It's called the universal quanitfier and it means "for all values of x in the domain".

http://en.wikipedia.org/wiki/Universal_quantification

Boxknife
Posts: 10
Joined: Wed Jul 23, 2008 6:44 am UTC

Re: Meaning of an upside down A symbol

Thanks!

Phillip
Posts: 10
Joined: Sat Oct 06, 2007 11:43 pm UTC

Re: Meaning of an upside down A symbol

And for future reference, since you'll surely run across it in the future, a backwards E represents the existential quantifier meaning, "there exists a value x" which fulfills the given statement.

DubioserKerl
Posts: 71
Joined: Sat Jun 07, 2008 8:23 am UTC

Re: Meaning of an upside down A symbol

Yeah.

And keep in mind: The backwards E means there exists at least one x in the domain that fulfills the statement afterwards. So, a statement that fulfills
FORALL x statement(x)
fulfills also
EXISTS x statement(x) as long as there exists one x.

If there are no values in the domain (that can happen if you have nested statements),
FORALL x statement(x)
is also true, but
EXISTS x statement(x)
is obviously not.

DK