[variant.visit] Rephrase specification of 'visit' to be more technically correct and precise

Author: tkoeppe

source/utilities.tex

@@ -4838,32 +4838,36 @@
 
 \begin{itemdescr}
 \pnum
-\requires
-The expression in the \effects element shall be a valid expression of the same
- type and value category, for all combinations of alternative types of all
- variants. Otherwise, the program is ill-formed.
-
-\pnum
-\effects
-Let \tcode{is...} be \tcode{vars.index()...}. Returns:
+Let $n$ be \tcode{sizeof...(Variants)}. Let \tcode{m} be a pack of $n$
+values of type \tcode{size_t}. Such a pack is called valid if $0 \leq
+\tcode{m}_i < \tcode{variant_size_v<remove_reference_t<Variants}_i\tcode{>>}$ for
+all $0 \leq i < n$. For each valid pack $\tcode{m}$, let $e(\tcode{m})$
+denote the expression:
 \begin{codeblock}
-@\placeholdernc{INVOKE}@(std::forward<Visitor>(vis), get<is>(std::forward<Variants>(vars))...) // see \ref{func.require}
+@\placeholder{INVOKE}@(std::forward<Visitor>(vis), get<m>(std::forward<Variants>(vars))...) // see \ref{func.require}
 \end{codeblock}
 
 \pnum
-\remarks
-The return type is the common type of all possible \tcode{\placeholder{INVOKE}}
-expressions of the \effects element.
+\requires
+For each valid pack \tcode{m}, $e(\tcode{m})$ shall be a valid expression.
+All such expressions shall be of the same type and value category;
+otherwise, the program is ill-formed.
+
+\pnum
+\returns $e(\tcode{m})$, where \tcode{m} is the pack for which
+$\tcode{m}_i$ is \tcode{vars$_i$.index()} for
+all $0 \leq i < n$. The return type is the type of $e(\tcode{m})$.
 
 \pnum
 \throws
 \tcode{bad_variant_access} if any \tcode{variant} in \tcode{vars} is \tcode{valueless_by_exception()}.
 
 \pnum
 \complexity
-For \tcode{sizeof...(Variants) <= 1}, the invocation of the callable object is
-implemented in constant time, i.e., it does not depend on \tcode{sizeof...(Types).}
-For \tcode{sizeof...(Variants) > 1}, the invocation of the callable object has
+For $n \leq 1$, the invocation of the callable object is
+implemented in constant time, i.e., for $n = 1$, it does not depend on
+the number of alternative types of $\tcode{Variants}_0$.
+For $n > 1$, the invocation of the callable object has
 no complexity requirements.
 \end{itemdescr}