### Abstract

First we give a grammatical (or equational) description of the set {M normal form │ Γ ⊢ M : A} for a given basis Γ and a given type A in the simple type system, and give some applications of the description. Then we extend the idea to systems in λ-cube and more generally to normalizing pure type systems. The attempt resulted in derived (or ‘macro’) rules the totality of which is sound and complete for type assignments of normal terms. A feature of the derived rules is that they reflect the syntactic structure of legal terms in normal form, and thus they may give us more global view than the original definition of the systems.

Original language | English |
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Title of host publication | Theoretical Aspects of Computer Software - International Symposium TACS 1994, Proceedings |

Editors | John C. Mitchell, Masami Hagiya |

Publisher | Springer Verlag |

Pages | 465-493 |

Number of pages | 29 |

ISBN (Print) | 9783540578871 |

Publication status | Published - Jan 1 1994 |

Event | 2nd International Symposium on Theoretical Aspects of Computer Software, TACS 1994 - Sendai, Japan Duration: Apr 19 1994 → Apr 22 1994 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 789 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 2nd International Symposium on Theoretical Aspects of Computer Software, TACS 1994 |
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Country | Japan |

City | Sendai |

Period | 4/19/94 → 4/22/94 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Theoretical Aspects of Computer Software - International Symposium TACS 1994, Proceedings*(pp. 465-493). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 789 LNCS). Springer Verlag.

**Normal proofs and their grammar.** / Takahashi, M.; Akama, Y.; Hirokawa, Sachio.

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

*Theoretical Aspects of Computer Software - International Symposium TACS 1994, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 789 LNCS, Springer Verlag, pp. 465-493, 2nd International Symposium on Theoretical Aspects of Computer Software, TACS 1994, Sendai, Japan, 4/19/94.

}

TY - GEN

T1 - Normal proofs and their grammar

AU - Takahashi, M.

AU - Akama, Y.

AU - Hirokawa, Sachio

PY - 1994/1/1

Y1 - 1994/1/1

N2 - First we give a grammatical (or equational) description of the set {M normal form │ Γ ⊢ M : A} for a given basis Γ and a given type A in the simple type system, and give some applications of the description. Then we extend the idea to systems in λ-cube and more generally to normalizing pure type systems. The attempt resulted in derived (or ‘macro’) rules the totality of which is sound and complete for type assignments of normal terms. A feature of the derived rules is that they reflect the syntactic structure of legal terms in normal form, and thus they may give us more global view than the original definition of the systems.

AB - First we give a grammatical (or equational) description of the set {M normal form │ Γ ⊢ M : A} for a given basis Γ and a given type A in the simple type system, and give some applications of the description. Then we extend the idea to systems in λ-cube and more generally to normalizing pure type systems. The attempt resulted in derived (or ‘macro’) rules the totality of which is sound and complete for type assignments of normal terms. A feature of the derived rules is that they reflect the syntactic structure of legal terms in normal form, and thus they may give us more global view than the original definition of the systems.

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M3 - Conference contribution

AN - SCOPUS:21344495885

SN - 9783540578871

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 465

EP - 493

BT - Theoretical Aspects of Computer Software - International Symposium TACS 1994, Proceedings

A2 - Mitchell, John C.

A2 - Hagiya, Masami

PB - Springer Verlag

ER -