Pure type systems with explicit substitutions
We introduce a new formulation of pure type systems (PTSs) with explicit substitution and de Bruijn indices and formally prove some of its meta-theory. Using techniques based on Normalisation by Evaluation, we prove that untyped conversion can be typed for predicative PTSs. Although this equivalence was settled by Siles and Herbelin for the conventional presentation of PTSs, we strongly conjecture that our proof method can also be applied to PTSs with η.
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| Main Authors: | , |
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| Format: | article biblioteca |
| Language: | eng |
| Subjects: | Predicative PTS, Normalisation by evaluation, Conversion, |
| Online Access: | http://hdl.handle.net/11086/27605 https://doi.org/10.1017/S0956796815000210 https://doi.org/10.1017/S0956796815000210 |
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| Summary: | We introduce a new formulation of pure type systems (PTSs) with explicit substitution and
de Bruijn indices and formally prove some of its meta-theory. Using techniques based on
Normalisation by Evaluation, we prove that untyped conversion can be typed for predicative
PTSs. Although this equivalence was settled by Siles and Herbelin for the conventional
presentation of PTSs, we strongly conjecture that our proof method can also be applied to
PTSs with η. |
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