Abstract

Inλ-calculus, the strategy of leftmost reduction (“call-by-name”) is known to have good mathematical properties; in particular, it always terminates when applied to a normalizable term. On the other hand, with this strategy, the argument of a function is re-evaluated at each time it is used.To avoid this drawback, we define the notion of “storage operator”, for each data type. IfT is a storage operator for integers, for example, let us replace the evaluation, by leftmost reduction, ofϕτ (whereτ is an integer, andϕ anyλ-term) by the evaluation oftτϕ. Then, this computation is the same as the following: first computeτ up to some reduced formτ 0, and then applyϕ toτ 0. So, we have simulated “call-by-value” evaluation within the strategy of leftmost reduction.The main theorem of the paper (Corollary of Theorem 4.1) shows that, in a second orderλ-calculus, using Gödel's translation of classical intuitionistic logic, we can find a very simple type (or specification) for storage operators. Thus, it gives a way to get such operators, which is to prove this type in second order intuitionistic predicate calculus