| Abstract | .... 2 | |
| 1 | Introduction | .... 2 |
| 2 | Preliminaries | .... 2 |
| 3 | Flat Guarded Horn Clauses | .... 3 |
| 3.1 | Syntax of FGHC | .... 3 |
| 3.2 | Operational Semantics of Flat GHC | .... 3 |
| 4 | Fix Approach to the Semantics | .... 4 |
| 4.1 | Atom Reaction | .... 14 |
| 4.2 | Fixpoint Semantics | .... 5 |
| 5 | Relation between Operational Semantics and Fixpoint Semantics | .... 7 |
| 6 | General Framework for Abstract Interpretation | .... 7 |
| 6.1 | Concrete Fixpoint Semantics | .... 7 |
| 6.2 | Abstract Fixpoint Semantics | .... 7 |
| 7 | Applications for Analysis of FGHC Programs | .... 8 |
| 7.1 | Moded type Gragh | .... 8 |
| 7.2 | An Example of Detecting Multiple Writers | .... 9 |
| 8 | Discussions | .... 10 |
| 9 | Conclusion | .... 11 |
| Acknowledgements | .... 11 | |
| References | .... 11 |
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