Combining Testing and Proving in Dependent Type Theory (2003)
| Venue: | 16th International Conference on Theorem Proving in Higher Order Logics (TPHOLs 2003 |
| Citations: | 12 - 1 self |
BibTeX
@INPROCEEDINGS{Dybjer03combiningtesting,
author = {Peter Dybjer and Qiao Haiyan and and Makoto Takeyama and Makoto Takeyama},
title = {Combining Testing and Proving in Dependent Type Theory},
booktitle = {16th International Conference on Theorem Proving in Higher Order Logics (TPHOLs 2003},
year = {2003},
pages = {188--203},
publisher = {SpringerVerlag}
}
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Abstract
We extend the proof assistant Agda/Alfa for dependent type theory with a modi ed version of Claessen and Hughes' tool QuickCheck for random testing of functional programs. In this way we combine testing and proving in one system. Testing is used for debugging programs and speci cations before a proof is attempted. Furthermore, we demonstrate by example how testing can be used repeatedly during proof for testing suitable subgoals. Our tool uses testdata generators which are de ned inside Agda/Alfa. We can therefore use the type system to prove properties about them, in particular surjectivity stating that all possible test cases can indeed be generated.
