Tau Meta Language and the notion of Fixed Point
Tau Meta Language is very unique in how it works. Each TML program is described as a loop without an arbitrary stopping condition. This is the case because the states of computation are finite. So a TML program merely defines what happens within a single iteration or "instance".
The loop continues until
S ∨ F
A) Two consequetive iterations return the same result (this means success)
i+(1).. i++(1).. S
B) Two non-consequetive iterations return the same result (this means fail)
i+(1).. i++(x).. i+++(1).. F
There can only ever be two possibilities so in essence this is boolean, an either or situation. A represents a Fixed Point which indicates the result is final because the state of the computation has not changed after two consequentive iterations.
To put it more precisely, if a loop ever has a length greater than 1 then it is a fail.
Partial fixed point requires ORDERED structures such as an ordered set. This allows for P-SPACE complexity to be recovered.
nice post reminding me of my university days. will you please check my post?
@dana-edwards - Wow. I remember the tightly bound structures of the C and C++ language programs I wrote during my Master's degree. Though object oriented, the if..then kind of structures were so restrictive and required us to list of every eventuality. This is so simple and logical.
I must read up more. Thanks for the heads up.
Upvoted full through Steemfollower.
Regards,
@vm2904
thanks gan, post very useful and helpful, do not forget vote my post also yes.
Informative post Dana. Regards Nainaz.
this is an excellent mini manual that will be useful to those who decided to deal with the concept of a fixed point. On the principle of nothing complicated here, but I took some of the nuances for myself from your post.
Thank you
Thank you very much :)
Thank your for this article.