On Irrelevance and Algorithmic Equality in Predicative Type Theory
Dependently typed programs contain an excessive amount of static terms which are necessary to please the type checker but irrelevant for computation. To separate static and dynamic code, several static analyses and type systems have been put forward. We consider Pfenning's type theory with irre...
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| Vydáno v: | Logical methods in computer science Ročník 8, Issue 1 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Logical Methods in Computer Science e.V
01.01.2012
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| Témata: | |
| ISSN: | 1860-5974, 1860-5974 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | Dependently typed programs contain an excessive amount of static terms which are necessary to please the type checker but irrelevant for computation. To separate static and dynamic code, several static analyses and type systems have been put forward. We consider Pfenning's type theory with irrelevant quantification which is compatible with a type-based notion of equality that respects eta-laws. We extend Pfenning's theory to universes and large eliminations and develop its meta-theory. Subject reduction, normalization and consistency are obtained by a Kripke model over the typed equality judgement. Finally, a type-directed equality algorithm is described whose completeness is proven by a second Kripke model. |
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| ISSN: | 1860-5974 1860-5974 |
| DOI: | 10.2168/LMCS-8(1:29)2012 |