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Computing with Böhm tress

David R.

Fundamenta Informaticae

2001

Vol. 45, nr 1,2

53-77

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 theorem of Hyland and Wadsworth : two l-terms that have the same Böhm trees, up to (possibly infinite) h-equivalence, are operationally equivalent. It is also used to prove a conjecture of R. Kerth : Every unsolvable l-term has a decoration. This syntactical result is motivated by (and gives the solution to) a semantical problem.