` M 0: A.
|
Abstract:
In this presentation we discuss mappings between extensions for recursion of the classical lambda calculus and a linear lambda calculus. In previous work, we showed that translations suggested by Girard for mapping (minimal) intuitionistic logic into intuitionistic linear logic could be used as the basis for mappings of the lambda calculus into a linear lambda calculus. One of Girard's translations corresponded to call-by-name reduction; the other, to call-by-value reduction. Each translation is sound and complete for mapping corresponding reduction sequences into linear reduction sequences. We refer the reader to the previous work for further details [2]. In the present summary we discuss more recent work: the corresponding results for calculi enriched with a recursion construct. Much of the new material in this summary is in preparation as an extended treatment of the older translation results [3]. The recursive linear lambda calculus. Figure 1 presents the recursive linear lambda calculus lin rec. This system satisfies the subject reduction and confluence properties:
Citations
| 25 | Call-by-name, call-by-value, call-by-need and the linear lambda calculus – Maraist, Odersky, et al. - 1999 |
| 9 | The Girard translation extended with recursion – Brauner - 1994 |
