A little bit more of intelligence can be given with

    \begingroup\lccode`\~=`\:\lowercase{\endgroup
      \unexpanded\def~}{\futurelet\tmptoken\docolon}
    
\unexpanded\def\docolon{\ifx=\tmptoken\mathrel{\mathop{\mathchar`\:}}\else\colon\fi}
    \mathcode`\:="8000 %

That lets you do $f: A \to B$ and $f(x) := x^2$
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