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Normalization by evaluation for $$\lambda ^{\rightarrow 2}$$. (English) Zbl 1122.68393
Kameyama, Yukiyoshi (ed.) et al., Functional and logic programming. 7th international symposium, FLOPS 2004, Nara, Japan, April 7–9, 2004. Proceedings. Berlin: Springer (ISBN 3-540-21402-X/pbk). Lecture Notes in Computer Science 2998, 260-275 (2004).
Summary: We show that the set-theoretic semantics of $$\lambda ^{\rightarrow 2}$$ – simply typed lambda calculus with a Boolean type but no type variables – is complete by inverting evaluation using decision trees. This leads to an implementation of normalization by evaluation which is witnessed by the source of part of this paper being a literate Haskell script. We show the correctness of our implementation using logical relations.
For the entire collection see [Zbl 1048.68005].
Reviewer: Reviewer (Berlin)

##### MSC:
 68N18 Functional programming and lambda calculus
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