Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Every countable poset is embeddable in the poset of unsolvable terms
Theoretical Computer Science
Morphisms and Partitions of V-sets
Proceedings of the 12th International Workshop on Computer Science Logic
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Applications of infinitary lambda calculus
Information and Computation
Böhm's theorem, church's delta, numeral systems, and ershov morphisms
Processes, Terms and Cycles
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This theoretical pearl is about the closed term model of pure untyped lambda-terms modulo β-convertibility. A consequence of one of the results is that for arbitrary distinct combinators (closed lambda terms) M, M′, N, N′ there is a combinator H such thatdisplay formula hereThe general result, which comes from Statman (1998), is that uniformly r.e. partitions of the combinators, such that each ‘block’ is closed under β-conversion, are of the form {H−1{M}}M∈ΛΦ. This is proved by making use of the idea behind the so-called Plotkin-terms, originally devised to exhibit some global but non-uniform applicative behaviour. For expository reasons we present the proof below. The following consequences are derived: a characterization of morphisms and a counter-example to the perpendicular lines lemma for β-conversion.