New Equations for Neutral Terms: A Sound and Complete Decision Procedure, Formalized
The definitional equality of an intensional type theory is its test of type compatibility. Today's systems rely on ordinary evaluation semantics to compare expressions in types, frustrating users with type errors arising when evaluation fails to identify two `obviously' equal terms. If onl...
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| creator | Allais, Guillaume Boutillier, Pierre McBride, Conor |
| description | The definitional equality of an intensional type theory is its test of type
compatibility. Today's systems rely on ordinary evaluation semantics to compare
expressions in types, frustrating users with type errors arising when
evaluation fails to identify two `obviously' equal terms. If only the machine
could decide a richer theory! We propose a way to decide theories which
supplement evaluation with `$\nu$-rules', rearranging the neutral parts of
normal forms, and report a successful initial experiment.
We study a simple -calculus with primitive fold, map and append operations on
lists and develop in Agda a sound and complete decision procedure for an
equational theory enriched with monoid, functor and fusion laws. |
| doi_str_mv | 10.48550/arxiv.1304.0809 |
| format | Article |
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compatibility. Today's systems rely on ordinary evaluation semantics to compare
expressions in types, frustrating users with type errors arising when
evaluation fails to identify two `obviously' equal terms. If only the machine
could decide a richer theory! We propose a way to decide theories which
supplement evaluation with `$\nu$-rules', rearranging the neutral parts of
normal forms, and report a successful initial experiment.
We study a simple -calculus with primitive fold, map and append operations on
lists and develop in Agda a sound and complete decision procedure for an
equational theory enriched with monoid, functor and fusion laws.</description><identifier>DOI: 10.48550/arxiv.1304.0809</identifier><language>eng</language><subject>Computer Science - Programming Languages</subject><creationdate>2013-04</creationdate><rights>http://creativecommons.org/licenses/by/3.0</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/1304.0809$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1304.0809$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Allais, Guillaume</creatorcontrib><creatorcontrib>Boutillier, Pierre</creatorcontrib><creatorcontrib>McBride, Conor</creatorcontrib><title>New Equations for Neutral Terms: A Sound and Complete Decision Procedure, Formalized</title><description>The definitional equality of an intensional type theory is its test of type
compatibility. Today's systems rely on ordinary evaluation semantics to compare
expressions in types, frustrating users with type errors arising when
evaluation fails to identify two `obviously' equal terms. If only the machine
could decide a richer theory! We propose a way to decide theories which
supplement evaluation with `$\nu$-rules', rearranging the neutral parts of
normal forms, and report a successful initial experiment.
We study a simple -calculus with primitive fold, map and append operations on
lists and develop in Agda a sound and complete decision procedure for an
equational theory enriched with monoid, functor and fusion laws.</description><subject>Computer Science - Programming Languages</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj8tOwzAURL1hgQp7VsgfQIIfsZ2wq0ILSFVBIvvoOr6WLCV1cRJeX08KLEazmTPSIeSKs7wolWK3kD7De84lK3JWsuqcNHv8oJu3GaYQDyP1MdE9zlOCnjaYhvGOrulrnA-OwpI6DsceJ6T32IVxIehLih26OeEN3cY0QB--0V2QMw_9iJf_vSLNdtPUj9nu-eGpXu8y0KrKrGdcdR2rCmEr7rgunRFOOCW0scqhNiiMNgV4Z62XIJdJJVE4D0Jaq-WKXP_d_lq1xxQGSF_tya492ckfrDZKaQ</recordid><startdate>20130402</startdate><enddate>20130402</enddate><creator>Allais, Guillaume</creator><creator>Boutillier, Pierre</creator><creator>McBride, Conor</creator><scope>AKY</scope><scope>GOX</scope></search><sort><creationdate>20130402</creationdate><title>New Equations for Neutral Terms: A Sound and Complete Decision Procedure, Formalized</title><author>Allais, Guillaume ; Boutillier, Pierre ; McBride, Conor</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a659-bf015cc0942b91d168d72d2d5267b5de67e27674afdbbf3a3d1693e2dfa23bb63</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Computer Science - Programming Languages</topic><toplevel>online_resources</toplevel><creatorcontrib>Allais, Guillaume</creatorcontrib><creatorcontrib>Boutillier, Pierre</creatorcontrib><creatorcontrib>McBride, Conor</creatorcontrib><collection>arXiv Computer Science</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Allais, Guillaume</au><au>Boutillier, Pierre</au><au>McBride, Conor</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>New Equations for Neutral Terms: A Sound and Complete Decision Procedure, Formalized</atitle><date>2013-04-02</date><risdate>2013</risdate><abstract>The definitional equality of an intensional type theory is its test of type
compatibility. Today's systems rely on ordinary evaluation semantics to compare
expressions in types, frustrating users with type errors arising when
evaluation fails to identify two `obviously' equal terms. If only the machine
could decide a richer theory! We propose a way to decide theories which
supplement evaluation with `$\nu$-rules', rearranging the neutral parts of
normal forms, and report a successful initial experiment.
We study a simple -calculus with primitive fold, map and append operations on
lists and develop in Agda a sound and complete decision procedure for an
equational theory enriched with monoid, functor and fusion laws.</abstract><doi>10.48550/arxiv.1304.0809</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Programming Languages |
| title | New Equations for Neutral Terms: A Sound and Complete Decision Procedure, Formalized |
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