We show that adequate semantics can be provided for imperative {\em higher
order concurrent} languages simply using {\em syntactical final} coalgebras.
In particular we investigate and compare various behavioural equivalences 
on higher order processes defined by finality using {\em hypersets} and  
{\em c.m.s.'s}. Correspondingly, we derive various coinduction and mixed 
induction-coinduction proof principles for establishing these equivalences. 
\\ {\bf Keywords}: second order assignment, $F$-coalgebra, $F$-bisimulation,
final semantics,  operational semantics, hyperset, complete metric space, 
coinduction, mixed induction-coinduction.