Name
Title | ||
|---|---|---|
A Complete Realisability Semantics for Intersection Types and Arbitrary Expansion Variables |
Abstract | ||
|---|---|---|
Expansionwas introduced at the end of the 1970s for calculating principal typingsfor 驴-terms in intersection type systems. Expansion variables(E-variables) were introduced at the end of the 1990s to simplify and help mechanise expansion. Recently, E-variables have been further simplified and generalised to also allow calculating other type operators than just intersection. There has been much work on semantics for intersection type systems, but only one such work on intersection type systems with E-variables. That work established that building a semantics for E-variables is very challenging. Because it is unclear how to devise a space of meanings for E-variables, that work developed instead a space of meanings for types that is hierarchical in the sense of having many degrees (denoted by indexes). However, although the indexed calculus helped identify the serious problems of giving a semantics for expansion variables, the sound realisability semantics was only complete when one single E-variable is used and furthermore, the universal type 驴was not allowed. In this paper, we are able to overcome these challenges. We develop a realisability semantics where we allow an arbitrary (possibly infinite) number of expansion variables and where 驴is present. We show the soundness and completeness of our proposed semantics. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1007/978-3-540-85762-4_12 | ICTAC |
Keywords | Field | DocType |
expansion variable,proposed semantics,type operator,principal typingsfor,complete realisability semantics,serious problem,intersection types,realisability semantics,sound realisability semantics,universal type,mechanise expansion,arbitrary expansion variables,intersection type system,indexation | Discrete mathematics,Operational semantics,Algebra,Gödel's completeness theorem,Computer science,Binary relation,Intersection,Operator (computer programming),Soundness,Completeness (statistics),Semantics | Conference |
Volume | ISSN | Citations |
5160 | 0302-9743 | 2 |
PageRank | References | Authors |
0.43 | 9 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Fairouz Kamareddine | 1 | 328 | 47.92 |
| Karim Nour | 2 | 65 | 15.07 |
| Vincent Rahli | 3 | 43 | 9.21 |
| J. B. Wells | 4 | 4 | 0.80 |