| Abstract | .... 2 | |
| Contents | .... 2 | |
| 1 | Introduction | .... 3 |
| 2 | Preliminaries | .... 3 |
| 2.1 | Polarity of Subformulas | .... 3 |
| 2.2 | S-formulars and Goal Formulas | .... 4 |
| 2.3 | Manipulation of Goal Formulas | .... 4 |
| 3 | Framework of Verification of Prolog Programs | .... 5 |
| 3.1 | Programming Language | .... 5 |
| 3.2 | Specification Language | .... 5 |
| 3.3 | Formulation of Verification | .... 6 |
| 4 | An Extention of Execution | .... 6 |
| 4.1 | Case Spiltting | .... 7 |
| 4.2 | Definite Clause Inference | .... 8 |
| 4.3 | "Negation as Failure" Inferece | .... 8 |
| 4.4 | Simplification | .... 9 |
| 4.5 | Oracle Decision | .... 10 |
| 5 | Examples | .... 10 |
| 5.1 | First Order Inferece by Extended Excution | .... 10 |
| 5.2 | Inductive Proof with Extended Execution | .... 11 |
| 5.3 | An Exsample for Comparison | .... 11 |
| 6 | Discussions | .... 13 |
| 7 | Conclusion | .... 14 |
| Acknowledgements | .... 15 | |
| References | .... 15 |
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