On Computational Paths and the Fundamental Groupoid of a Type
The main objective of this work is to study mathematical properties of computational paths. Originally proposed by de Queiroz \& Gabbay (1994) as `sequences of rewrites', computational paths can be seen as the grounds on which the propositional equality between two computational objects sta...
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| creator | Ramos, Arthur F de Queiroz, Ruy J. G. B de Oliveira, Anjolina |
| description | The main objective of this work is to study mathematical properties of
computational paths. Originally proposed by de Queiroz \& Gabbay (1994) as
`sequences of rewrites', computational paths can be seen as the grounds on
which the propositional equality between two computational objects stand. Using
computational paths and categorical semantics, we take any type $A$ of type
theory and construct a groupoid for this type. We call this groupoid the
fundamental groupoid of a type $A$, since it is similar to the one obtained
using the homotopical interpretation of the identity type. The main difference
is that instead of being just a semantical interpretation, computational paths
are entities of the syntax of type theory. We also expand our results, using
computational paths to construct fundamental groupoids of higher levels. |
| doi_str_mv | 10.48550/arxiv.1509.06429 |
| format | Article |
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computational paths. Originally proposed by de Queiroz \& Gabbay (1994) as
`sequences of rewrites', computational paths can be seen as the grounds on
which the propositional equality between two computational objects stand. Using
computational paths and categorical semantics, we take any type $A$ of type
theory and construct a groupoid for this type. We call this groupoid the
fundamental groupoid of a type $A$, since it is similar to the one obtained
using the homotopical interpretation of the identity type. The main difference
is that instead of being just a semantical interpretation, computational paths
are entities of the syntax of type theory. We also expand our results, using
computational paths to construct fundamental groupoids of higher levels.</description><identifier>DOI: 10.48550/arxiv.1509.06429</identifier><language>eng</language><subject>Computer Science - Logic in Computer Science</subject><creationdate>2015-09</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1509.06429$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1509.06429$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Ramos, Arthur F</creatorcontrib><creatorcontrib>de Queiroz, Ruy J. G. B</creatorcontrib><creatorcontrib>de Oliveira, Anjolina</creatorcontrib><title>On Computational Paths and the Fundamental Groupoid of a Type</title><description>The main objective of this work is to study mathematical properties of
computational paths. Originally proposed by de Queiroz \& Gabbay (1994) as
`sequences of rewrites', computational paths can be seen as the grounds on
which the propositional equality between two computational objects stand. Using
computational paths and categorical semantics, we take any type $A$ of type
theory and construct a groupoid for this type. We call this groupoid the
fundamental groupoid of a type $A$, since it is similar to the one obtained
using the homotopical interpretation of the identity type. The main difference
is that instead of being just a semantical interpretation, computational paths
are entities of the syntax of type theory. We also expand our results, using
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computational paths. Originally proposed by de Queiroz \& Gabbay (1994) as
`sequences of rewrites', computational paths can be seen as the grounds on
which the propositional equality between two computational objects stand. Using
computational paths and categorical semantics, we take any type $A$ of type
theory and construct a groupoid for this type. We call this groupoid the
fundamental groupoid of a type $A$, since it is similar to the one obtained
using the homotopical interpretation of the identity type. The main difference
is that instead of being just a semantical interpretation, computational paths
are entities of the syntax of type theory. We also expand our results, using
computational paths to construct fundamental groupoids of higher levels.</abstract><doi>10.48550/arxiv.1509.06429</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Logic in Computer Science |
| title | On Computational Paths and the Fundamental Groupoid of a Type |
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