No solvable lambda-value term left behind
In the lambda calculus a term is solvable iff it is operationally relevant. Solvable terms are a superset of the terms that convert to a final result called normal form. Unsolvable terms are operationally irrelevant and can be equated without loss of consistency. There is a definition of solvability...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Logical Methods in Computer Science e.V.
2016-06-01
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| Series: | Logical Methods in Computer Science |
| Subjects: | |
| Online Access: | https://lmcs.episciences.org/1644/pdf |
| _version_ | 1797268605176381440 |
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| author | Á. García-Pérez P. Nogueira |
| author_facet | Á. García-Pérez P. Nogueira |
| author_sort | Á. García-Pérez |
| collection | DOAJ |
| description | In the lambda calculus a term is solvable iff it is operationally relevant.
Solvable terms are a superset of the terms that convert to a final result
called normal form. Unsolvable terms are operationally irrelevant and can be
equated without loss of consistency. There is a definition of solvability for
the lambda-value calculus, called v-solvability, but it is not synonymous with
operational relevance, some lambda-value normal forms are unsolvable, and
unsolvables cannot be consistently equated. We provide a definition of
solvability for the lambda-value calculus that does capture operational
relevance and such that a consistent proof-theory can be constructed where
unsolvables are equated attending to the number of arguments they take (their
"order" in the jargon). The intuition is that in lambda-value the different
sequentialisations of a computation can be distinguished operationally. We
prove a version of the Genericity Lemma stating that unsolvable terms are
generic and can be replaced by arbitrary terms of equal or greater order. |
| first_indexed | 2024-04-25T01:35:08Z |
| format | Article |
| id | doaj.art-03cf75037c5849eaa8dbe2dadc92caa2 |
| institution | Directory Open Access Journal |
| issn | 1860-5974 |
| language | English |
| last_indexed | 2024-04-25T01:35:08Z |
| publishDate | 2016-06-01 |
| publisher | Logical Methods in Computer Science e.V. |
| record_format | Article |
| series | Logical Methods in Computer Science |
| spelling | doaj.art-03cf75037c5849eaa8dbe2dadc92caa22024-03-08T09:43:59ZengLogical Methods in Computer Science e.V.Logical Methods in Computer Science1860-59742016-06-01Volume 12, Issue 210.2168/LMCS-12(2:12)20161644No solvable lambda-value term left behindÁ. García-PérezP. NogueiraIn the lambda calculus a term is solvable iff it is operationally relevant. Solvable terms are a superset of the terms that convert to a final result called normal form. Unsolvable terms are operationally irrelevant and can be equated without loss of consistency. There is a definition of solvability for the lambda-value calculus, called v-solvability, but it is not synonymous with operational relevance, some lambda-value normal forms are unsolvable, and unsolvables cannot be consistently equated. We provide a definition of solvability for the lambda-value calculus that does capture operational relevance and such that a consistent proof-theory can be constructed where unsolvables are equated attending to the number of arguments they take (their "order" in the jargon). The intuition is that in lambda-value the different sequentialisations of a computation can be distinguished operationally. We prove a version of the Genericity Lemma stating that unsolvable terms are generic and can be replaced by arbitrary terms of equal or greater order.https://lmcs.episciences.org/1644/pdfcomputer science - logic in computer sciencef.4.1 |
| spellingShingle | Á. García-Pérez P. Nogueira No solvable lambda-value term left behind Logical Methods in Computer Science computer science - logic in computer science f.4.1 |
| title | No solvable lambda-value term left behind |
| title_full | No solvable lambda-value term left behind |
| title_fullStr | No solvable lambda-value term left behind |
| title_full_unstemmed | No solvable lambda-value term left behind |
| title_short | No solvable lambda-value term left behind |
| title_sort | no solvable lambda value term left behind |
| topic | computer science - logic in computer science f.4.1 |
| url | https://lmcs.episciences.org/1644/pdf |
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