### Abstract

A principal type-scheme of a λ-term is the most general type-scheme for the term. The converse principal type-scheme theorem (J.R. Hindley, The principal typescheme of an object in combinatory logic, Trans. Amer. Math. Soc.146 (1969) 29-60) states that every type-scheme of a combinatory term is a principal type-scheme of some combinatory term. This paper shows a simple proof for the theorem in λ-calculus, by constructing an algorithm which transforms a type assignment to a λ-term into a principal type assignment to another λ-term that has the type as its principal type-scheme. The clearness of the algorithm is due to the characterization theorem of principal type-assignment figures. The algorithm is applicable to BCIW-λ-terms as well. Thus a uniform proof is presented for the converse principal type-scheme theorem for general λ-terms and BCIW-λ-terms.

Original language | English |
---|---|

Pages (from-to) | 83-95 |

Number of pages | 13 |

Journal | Studia Logica |

Volume | 51 |

Issue number | 1 |

DOIs | |

Publication status | Published - Mar 1 1992 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Logic
- History and Philosophy of Science

### Cite this

**The converse principal type-scheme theorem in lambda calculus.** / Hirokawa, Sachio.

Research output: Contribution to journal › Article

*Studia Logica*, vol. 51, no. 1, pp. 83-95. https://doi.org/10.1007/BF00370332

}

TY - JOUR

T1 - The converse principal type-scheme theorem in lambda calculus

AU - Hirokawa, Sachio

PY - 1992/3/1

Y1 - 1992/3/1

N2 - A principal type-scheme of a λ-term is the most general type-scheme for the term. The converse principal type-scheme theorem (J.R. Hindley, The principal typescheme of an object in combinatory logic, Trans. Amer. Math. Soc.146 (1969) 29-60) states that every type-scheme of a combinatory term is a principal type-scheme of some combinatory term. This paper shows a simple proof for the theorem in λ-calculus, by constructing an algorithm which transforms a type assignment to a λ-term into a principal type assignment to another λ-term that has the type as its principal type-scheme. The clearness of the algorithm is due to the characterization theorem of principal type-assignment figures. The algorithm is applicable to BCIW-λ-terms as well. Thus a uniform proof is presented for the converse principal type-scheme theorem for general λ-terms and BCIW-λ-terms.

AB - A principal type-scheme of a λ-term is the most general type-scheme for the term. The converse principal type-scheme theorem (J.R. Hindley, The principal typescheme of an object in combinatory logic, Trans. Amer. Math. Soc.146 (1969) 29-60) states that every type-scheme of a combinatory term is a principal type-scheme of some combinatory term. This paper shows a simple proof for the theorem in λ-calculus, by constructing an algorithm which transforms a type assignment to a λ-term into a principal type assignment to another λ-term that has the type as its principal type-scheme. The clearness of the algorithm is due to the characterization theorem of principal type-assignment figures. The algorithm is applicable to BCIW-λ-terms as well. Thus a uniform proof is presented for the converse principal type-scheme theorem for general λ-terms and BCIW-λ-terms.

UR - http://www.scopus.com/inward/record.url?scp=0346873117&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0346873117&partnerID=8YFLogxK

U2 - 10.1007/BF00370332

DO - 10.1007/BF00370332

M3 - Article

AN - SCOPUS:0346873117

VL - 51

SP - 83

EP - 95

JO - Studia Logica

JF - Studia Logica

SN - 0039-3215

IS - 1

ER -