Extending Homotopy Type Theory with Strict Equality
- Submitting institution
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University of Nottingham, The
- Unit of assessment
- 11 - Computer Science and Informatics
- Output identifier
- 1324197
- Type
- E - Conference contribution
- DOI
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10.4230/LIPIcs.CSL.2016.21
- Title of conference / published proceedings
- 25th EACSL Annual Conference on Computer Science Logic
- First page
- 21:1
- Volume
- 2016-Aug
- Issue
- -
- ISSN
- -
- Open access status
- -
- Month of publication
- August
- Year of publication
- 2016
- URL
-
-
- Supplementary information
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-
- Request cross-referral to
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- Output has been delayed by COVID-19
- No
- COVID-19 affected output statement
- -
- Forensic science
- No
- Criminology
- No
- Interdisciplinary
- No
- Number of additional authors
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2
- Research group(s)
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-
- Citation count
- -
- Proposed double-weighted
- No
- Reserve for an output with double weighting
- No
- Additional information
- Homotopy type theory is a foundation of constructive mathematics and a basis for dependently typed programming languages. This paper introduces an extension, namely two-level type theory, and shows that a long-standing open problem, namely defining semi-simplicial types, can be solved. The solution has been checked with a computer proof assistant. The ideas in this paper have inspired several different research directions, e.g. cubical two-level type theory, internalised specifications of type theory, and the development of internal higher category theory. The paper also led to an extension of the Agda proof assistant.
- Author contribution statement
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- Non-English
- No
- English abstract
- -
