Intersection Types and Related Systems
We present a new approach to the following meta-problem: given a quantitative property of trees, design a type system such that the desired property for the tree generated by an infinitary ground lambda-term corresponds to some property of a derivation of a type for this lambda-term, in this type sy...
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| Format: | Article |
| Language: | English |
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Open Publishing Association
2017-02-01
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| Series: | Electronic Proceedings in Theoretical Computer Science |
| Online Access: | http://arxiv.org/pdf/1702.02278v1 |
| _version_ | 1811254095649964032 |
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| author | Paweł Parys |
| author_facet | Paweł Parys |
| author_sort | Paweł Parys |
| collection | DOAJ |
| description | We present a new approach to the following meta-problem: given a quantitative property of trees, design a type system such that the desired property for the tree generated by an infinitary ground lambda-term corresponds to some property of a derivation of a type for this lambda-term, in this type system.
Our approach is presented in the particular case of the language finiteness problem for nondeterministic higher-order recursion schemes (HORSes): given a nondeterministic HORS, decide whether the set of all finite trees generated by this HORS is finite. We give a type system such that the HORS can generate a tree of an arbitrarily large finite size if and only if in the type system we can obtain derivations that are arbitrarily large, in an appropriate sense; the latter condition can be easily decided. |
| first_indexed | 2024-04-12T17:02:00Z |
| format | Article |
| id | doaj.art-01cbaeb8e96f40619e312efa7da178b2 |
| institution | Directory Open Access Journal |
| issn | 2075-2180 |
| language | English |
| last_indexed | 2024-04-12T17:02:00Z |
| publishDate | 2017-02-01 |
| publisher | Open Publishing Association |
| record_format | Article |
| series | Electronic Proceedings in Theoretical Computer Science |
| spelling | doaj.art-01cbaeb8e96f40619e312efa7da178b22022-12-22T03:24:03ZengOpen Publishing AssociationElectronic Proceedings in Theoretical Computer Science2075-21802017-02-01242Proc. ITRS 2016486310.4204/EPTCS.242.6:3Intersection Types and Related SystemsPaweł Parys0 University of Warsaw We present a new approach to the following meta-problem: given a quantitative property of trees, design a type system such that the desired property for the tree generated by an infinitary ground lambda-term corresponds to some property of a derivation of a type for this lambda-term, in this type system. Our approach is presented in the particular case of the language finiteness problem for nondeterministic higher-order recursion schemes (HORSes): given a nondeterministic HORS, decide whether the set of all finite trees generated by this HORS is finite. We give a type system such that the HORS can generate a tree of an arbitrarily large finite size if and only if in the type system we can obtain derivations that are arbitrarily large, in an appropriate sense; the latter condition can be easily decided.http://arxiv.org/pdf/1702.02278v1 |
| spellingShingle | Paweł Parys Intersection Types and Related Systems Electronic Proceedings in Theoretical Computer Science |
| title | Intersection Types and Related Systems |
| title_full | Intersection Types and Related Systems |
| title_fullStr | Intersection Types and Related Systems |
| title_full_unstemmed | Intersection Types and Related Systems |
| title_short | Intersection Types and Related Systems |
| title_sort | intersection types and related systems |
| url | http://arxiv.org/pdf/1702.02278v1 |
| work_keys_str_mv | AT pawełparys intersectiontypesandrelatedsystems |