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Solution of a Problem of Barendregt on Sensible lambda-Theories

Benedetto Intrigila ; Richard Statman.

<i>H</i> is the theory extending &#946;-conversion by identifying all closed unsolvables. <i>H</i>&#969; is the closure of this theory under the &#969;-rule (and &#946;-conversion). A long-standing conjecture of H. Barendregt states that the provable equations of <i>H</i>&#969; form&nbsp;[&hellip;]

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Degrees of extensionality in the theory of B\"ohm trees and Sall\'e's conjecture

Benedetto Intrigila ; Giulio Manzonetto ; Andrew Polonsky.

The main observational equivalences of the untyped lambda-calculus have been characterized in terms of extensional equalities between B\"ohm trees. It is well known that the lambda-theory H*, arising by taking as observables the head normal forms, equates two lambda-terms whenever their B\"ohm trees&nbsp;[&hellip;]

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