Part of the Lecture Notes in Computer Science book series (LNCS, volume 52)
Termination tests inside λ-calculus
Let be associated to each element N of the set of the normal forms of the λ-κ-β calculus and to each integer r > 0 the semi but non - decidable domain D [N,r] \( \subseteq \)r onto which N, considered as partial map ping r→, is total (that is the computation starting from NX1 ... Xr where N ∈ and X1, ..., xr ∈ D [N,r] and evolging through a β -reduction algorithm terminates). The decidability of the relation D [N,r] = r has been proved in a previous paper. In the present paper, for any N and r, an infinite, decidable subdomain C [N,r] \( \subseteq \)D [N,r] is defined in a constructive way. The ensuing sufficient condition for the termination of a computation starting from N X1 ... Xr can be tested in a number of steps negligible with respect to those needed for reaching the n.f., if there is one.
KeywordsNormal Form Composition Operator Free Variable Combinatory Logic Access Path
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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