| Abstract | .... 2 | |
| 1 | Introduction | .... 2 |
| 2 | Preliminary | .... 3 |
| 3 | Constraint Language | .... 4 |
| 3.1 | Constraint Language L | .... 4 |
| 3.2 | Support | .... 6 |
| 3.3 | Bounded Hereditary Finite Set | .... 6 |
| 4 | Unification over Non-Well Founded Sets | .... 7 |
| 4.1 | Solving Equations with Unequations(=,) | .... 12 |
| 5 | Coinductive Semantics of Horn Clauses | .... 14 |
| 5.1 | Horn Clauses with Constraint | .... 14 |
| 5.2 | Computation Tree | .... 14 |
| 5.3 | Solution Tree | .... 16 |
| 5.4 | Soundness and Completeness | .... 18 |
| 6 | Towards Application to Term and Record | .... 20 |
| 6.1 | Term | .... 21 |
| 6.2 | Record as Hereditary Function | .... 21 |
| 6.3 | Unification over Terms and Records(=,) | .... 21 |
| 6.4 | UNION-FIND Based Unification | .... 22 |
| 6.5 | Boolean Constraint | .... 23 |
| 7 | Concluding Remark | .... 24 |
| Acknowledgments | .... 24 | |
| References | .... 24 | |
| End | .... 25 |
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