Combinatory interpretation of lambda calculus
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31-10-2019 - |
문제
According to Peter Selinger, The Lambda Calculus is Algebraic (PDF). Early in this article he says:
The combinatory interpretation of the lambda calculus is known to be imperfect, because it does not satisfy the $ξ$-rule: under the interpretation, $M = N$ does not imply $\lambda x.M = \lambda x.N$ (Barendregt, 1984).
Questions:
- What kind of equivalence is meant here?
- Given this definition of equivalence, what is a counter-example of the implication?
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