Abstract
The λ-theory H is obtained from β-conversion by identifying all closed unsolvable terms (or, equivalently, terms without head normal form). The range problem for the theory H asks whether a closed term has always (up to equality in H) either an infinite range or a singleton range (that is, it is a constant function). Here we give a solution to a natural version of this problem, giving a positive answer for the theory H restricted to Combinatory Logic. The method of proof applies also to the Lazy λ-Calculus.
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