Computing with Bohm trees

This paper develops a general technique to analyze the head reduction of a term in a context. This technique is used to give a direct proof of the the orem of Hyland and Wadsworth : two lambda -terms that have the same Bohm tr ees, up to (possibly infinite) eta -equivalence, are operationally equivale nt. It is also used to prove a conjecture of R. Kerth : Every unsolvable la mbda -term has a decoration. This syntactical result is motivated by (and g ives the solution to) a semantical problem.