A Faithful and Quantitative Notion of Distant Reduction for the Lambda-Calculus with Generalized Applications
We introduce a call-by-name lambda-calculus $\lambda Jn$ with generalized applications which is equipped with distant reduction. This allows to unblock $\beta$-redexes without resorting to the standard permutative conversions of generalized applications used in the original $\Lambda J$-calculus with...
Uloženo v:
| Vydáno v: | Logical methods in computer science Ročník 20, Issue 3 |
|---|---|
| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Logical Methods in Computer Science e.V
01.01.2024
|
| Témata: | |
| ISSN: | 1860-5974, 1860-5974 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Shrnutí: | We introduce a call-by-name lambda-calculus $\lambda Jn$ with generalized
applications which is equipped with distant reduction. This allows to unblock
$\beta$-redexes without resorting to the standard permutative conversions of
generalized applications used in the original $\Lambda J$-calculus with
generalized applications of Joachimski and Matthes. We show strong
normalization of simply-typed terms, and we then fully characterize strong
normalization by means of a quantitative (i.e. non-idempotent intersection)
typing system. This characterization uses a non-trivial inductive definition of
strong normalization --related to others in the literature--, which is based on
a weak-head normalizing strategy. We also show that our calculus $\lambda Jn$
relates to explicit substitution calculi by means of a faithful translation, in
the sense that it preserves strong normalization. Moreover, our calculus
$\lambda Jn$ and the original $\Lambda J$-calculus determine equivalent notions
of strong normalization. As a consequence, $\lambda J$ inherits a faithful
translation into explicit substitutions, and its strong normalization can also
be characterized by the quantitative typing system designed for $\lambda Jn$,
despite the fact that quantitative subject reduction fails for permutative
conversions. |
|---|---|
| ISSN: | 1860-5974 1860-5974 |
| DOI: | 10.46298/lmcs-20(3:10)2024 |