Let $B$ be a recursive enumerable set and $B = W_n$, where $W_n = \{x \in \mathbb N \mid \Phi(x,n)\downarrow\}$ and $\Phi^{(n)}(x_1, \ldots, x_n, y)$ is the value of the function at the terminal snaphot.
There is a definition that leaves me really confused: $$n \in W_n \Leftrightarrow \Phi(n,n)\downarrow \Leftrightarrow \text{HALT}(n,n)$$
the thing is we know that $\text{HALT}$ is not computable, therefore is is undefined so how is it possible that it is equivalent to $\Phi(n,n)\downarrow$ which is actually a defined function? What am I missing here?