### Abstract

Substitution in the calculus is a subtle operation. In a formal description, Barendregt's variable convention isassumed to avoid variable capture, but such an assumption is notwell suited for implementation on computers. We introduce graphrepresentation and manipulation of Terms, in which bound andfree variables are encoded by using hyperlinks with differentattributes. A graph type called hlground is generalized to identifythe scope of a term n in substitution m[x:= n], which enablesbound variables and free variables to have suitable behaviorduring the substitution. Our representation of the Terms arereadable and the definition of substitution in this technique isfree from any side conditions on the freeness and freshness of variables.

Original language | English |
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Title of host publication | Proceedings - 10th International Symposium on Theoretical Aspects of Software Engineering, TASE 2016 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 113-116 |

Number of pages | 4 |

ISBN (Electronic) | 9781509017638 |

DOIs | |

Publication status | Published - 2016 Aug 10 |

Event | 10th International Symposium on Theoretical Aspects of Software Engineering, TASE 2016 - Shanghai, China Duration: 2016 Jul 17 → 2016 Jul 19 |

### Other

Other | 10th International Symposium on Theoretical Aspects of Software Engineering, TASE 2016 |
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Country | China |

City | Shanghai |

Period | 16/7/17 → 16/7/19 |

### Fingerprint

### Keywords

- Graph types
- Hypergraphs
- Substitution
- Terms

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Software

### Cite this

*Proceedings - 10th International Symposium on Theoretical Aspects of Software Engineering, TASE 2016*(pp. 113-116). [7541894] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/TASE.2016.25

**Hypergraph Representation of Lambda-Terms.** / Yasen, Alimujiang; Ueda, Kazunori.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings - 10th International Symposium on Theoretical Aspects of Software Engineering, TASE 2016.*, 7541894, Institute of Electrical and Electronics Engineers Inc., pp. 113-116, 10th International Symposium on Theoretical Aspects of Software Engineering, TASE 2016, Shanghai, China, 16/7/17. https://doi.org/10.1109/TASE.2016.25

}

TY - GEN

T1 - Hypergraph Representation of Lambda-Terms

AU - Yasen, Alimujiang

AU - Ueda, Kazunori

PY - 2016/8/10

Y1 - 2016/8/10

N2 - Substitution in the calculus is a subtle operation. In a formal description, Barendregt's variable convention isassumed to avoid variable capture, but such an assumption is notwell suited for implementation on computers. We introduce graphrepresentation and manipulation of Terms, in which bound andfree variables are encoded by using hyperlinks with differentattributes. A graph type called hlground is generalized to identifythe scope of a term n in substitution m[x:= n], which enablesbound variables and free variables to have suitable behaviorduring the substitution. Our representation of the Terms arereadable and the definition of substitution in this technique isfree from any side conditions on the freeness and freshness of variables.

AB - Substitution in the calculus is a subtle operation. In a formal description, Barendregt's variable convention isassumed to avoid variable capture, but such an assumption is notwell suited for implementation on computers. We introduce graphrepresentation and manipulation of Terms, in which bound andfree variables are encoded by using hyperlinks with differentattributes. A graph type called hlground is generalized to identifythe scope of a term n in substitution m[x:= n], which enablesbound variables and free variables to have suitable behaviorduring the substitution. Our representation of the Terms arereadable and the definition of substitution in this technique isfree from any side conditions on the freeness and freshness of variables.

KW - Graph types

KW - Hypergraphs

KW - Substitution

KW - Terms

UR - http://www.scopus.com/inward/record.url?scp=84987958752&partnerID=8YFLogxK

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U2 - 10.1109/TASE.2016.25

DO - 10.1109/TASE.2016.25

M3 - Conference contribution

SP - 113

EP - 116

BT - Proceedings - 10th International Symposium on Theoretical Aspects of Software Engineering, TASE 2016

PB - Institute of Electrical and Electronics Engineers Inc.

ER -