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Lambda-calcul, évaluation paresseuse et mise en mémoire. (Lambda calculus, lazy evaluation and storage operators). (French) Zbl 0717.03003
The abstract of the paper seems to be the best way to resume this very nice paper: “In pure $$\lambda$$-calculus, we identify lazy evaluation with leftmost $$\beta$$-reduction. This strategy of reduction has many advantages (in particular, it always gives normal form when there exists one); but it has the following drawback: the argument of a function must be evaluated as many times as it is used. To avoid this defect, we introduce, for each data type (like Booleans, integers, lists...), some terms called “storage operators”. For example, if $$\nu$$ is $$\beta$$- equivalent to an integer, and $$\phi$$ is any term, we replace $$\phi\nu$$ by $$T\nu\phi$$, where T is a storage operator for integers; during lazy evaluation of $$T\nu\phi$$, $$\nu$$ will be evaluated only once.
We give a general definition for the notion of storage operator for a set of $$\lambda$$-calculus terms. We show how to construct such operators, using a system of typed $$\lambda$$-calculus of second order. To this end, we use Gödel’s $$\neg \neg$$-translation, which transforms a proof in classical logic into an intuitionistic proof.”
Reviewer: R.David

##### MSC:
 03B40 Combinatory logic and lambda calculus 68Q60 Specification and verification (program logics, model checking, etc.)
##### Keywords:
$$\lambda$$ -calculus; lazy evaluation; storage operators
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##### References:
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