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| Content Provider | Springer Nature Link |
|---|---|
| Author | Aspinall, David Denney, Ewen Lüth, Christoph |
| Copyright Year | 2010 |
| Abstract | There is something of a discontinuity at the heart of popular tactical theorem provers. Low-level, fully-checked mechanical proofs are large trees consisting of primitive logical inferences. Meanwhile, high-level human inputs are lexically structured formal texts which include tactics describing search procedures. The proof checking process maps from the high-level to low-level, but after that, explicit connections are usually lost. The lack of connection can make it difficult to understand the proof trees produced by successful tactic proofs, and difficult to debug faulty tactic proofs. We propose the use of hierarchical proofs, also known as hiproofs, to help bridge these levels. Hiproofs superimpose a labelled hierarchical nesting on an ordinary proof tree, abstracting from the underlying logic. The labels and nesting are used to describe the organisation of the proof, typically relating to its construction process. In this paper we introduce a foundational tactic language Hitac which constructs hiproofs in a generic setting. Hitac programs can be evaluated using a big-step or a small-step operational semantics. The big-step semantics captures the intended meaning, whereas the small-step semantics is closer to possible implementations and provides a unified notion of proof state. We prove that the semantics are equivalent and construct valid proofs. We also explain how to detect terms which are stuck in the small-step semantics, and how these suggest interaction points with debugging tools. Finally we show some typical examples of tactics, constructed using tactical combinators, in our language. |
| Starting Page | 309 |
| Ending Page | 330 |
| Page Count | 22 |
| File Format | |
| ISSN | 16618270 |
| Journal | Mathematics in Computer Science |
| Volume Number | 3 |
| Issue Number | 3 |
| e-ISSN | 16618289 |
| Language | English |
| Publisher | Birkhäuser-Verlag |
| Publisher Date | 2010-03-10 |
| Publisher Place | Basel |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Hierarchical proof Hiproof Tactical theorem proving Mathematics Computer Science |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Computational Theory and Mathematics Computational Mathematics |
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