人工知能学会誌（1986～2013, Print ISSN:0912-8085）
A Canonical Translation from Higher Order Logic to Typed Lambda Calculus
1990 年 5 巻 6 号 p. 796-807
詳細
1990 年 5 巻 6 号 p. 796-807
The relationship between higher order intuitionistic many sorted predicate logic (denoted by L) and the type systemλPK2 (Coquand-Huet's Calculus of Constructions) is investigated using the formulae-as-types notion. As a necessary consequence, the type system λKF which is a restricted version ofλPK2 is obtained to interpret just L. The λKF has made it possible to arrive at an inverse interpretation to L. The interpretation is more constructive than the existing one in the sense that it may also be applied to a proof figure to get a judgment constructively. The soundness and completeness results are given. In this sense, the whole logical system can be translated into the type system, and hence proofs in L are treated formally in λKF.
