A characterization of the Taylor expansion of λ-terms∗
نویسندگان
چکیده
The Taylor expansion of λ-terms, as introduced by Ehrhard and Regnier, expresses a λ-term as a series of multi-linear terms, called simple terms, which capture bounded computations. Normal forms of Taylor expansions give a notion of infinitary normal forms, refining the notion of Böhm trees in a quantitative setting. We give the algebraic conditions over a set of normal simple terms which characterize the property of being the normal form of the Taylor expansion of a λ-term. From this full completeness result, we give further conditions which semantically describe normalizable and total λ-terms. 1998 ACM Subject Classification F.4.1 Lambda calculus and related systems, F.3.2 Denotational semantics
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