This paper presents a method to define a set of mutuaJly recursive inductive types, and develops a higherorder unilication algorithm for Anz extended with inductive types. The algorithm is an extension of Eiliott'...This paper presents a method to define a set of mutuaJly recursive inductive types, and develops a higherorder unilication algorithm for Anz extended with inductive types. The algorithm is an extension of Eiliott's algoritbJn for λ∑.The notation of normal forms plays a vital role in higher-order unification.The weak head normal forms in the extended troe theory is defined to reveal the ultimate 'top level structures' of the fully normalized terms and types. Unification transformation rules are designed to deal with inductive types, a recursive operator and its reduction rule. The algoritlun can construct recuxsive functions automatically.展开更多
The unrestricted use of comprehension principle leads the set theory,λ-conversion,combmatory logic and logical predicate calculus to fall into inconsistency.Therefore,it is usually necessary to set some limit on the ...The unrestricted use of comprehension principle leads the set theory,λ-conversion,combmatory logic and logical predicate calculus to fall into inconsistency.Therefore,it is usually necessary to set some limit on the principle.But with the principle restricted,all the theories become ad hoc,unnatural and very complicated.It is indicated in this paper that the comprehension procedure may be replaced in all aspects by the substitution operation and the comprehension principle itself may be completely abolished.Once the principle is abandoned there will be neither functions nor operators newly generated,and Loaseuuently the deduction procedures will become very simple and free from any ad hoc provisos.Thus we get a nice and complete logical predicate calculus,which may serve as the very foundation for the whole mathematics.展开更多
文摘This paper presents a method to define a set of mutuaJly recursive inductive types, and develops a higherorder unilication algorithm for Anz extended with inductive types. The algorithm is an extension of Eiliott's algoritbJn for λ∑.The notation of normal forms plays a vital role in higher-order unification.The weak head normal forms in the extended troe theory is defined to reveal the ultimate 'top level structures' of the fully normalized terms and types. Unification transformation rules are designed to deal with inductive types, a recursive operator and its reduction rule. The algoritlun can construct recuxsive functions automatically.
基金ProJect supported by the National Natural Science Foundation of China
文摘The unrestricted use of comprehension principle leads the set theory,λ-conversion,combmatory logic and logical predicate calculus to fall into inconsistency.Therefore,it is usually necessary to set some limit on the principle.But with the principle restricted,all the theories become ad hoc,unnatural and very complicated.It is indicated in this paper that the comprehension procedure may be replaced in all aspects by the substitution operation and the comprehension principle itself may be completely abolished.Once the principle is abandoned there will be neither functions nor operators newly generated,and Loaseuuently the deduction procedures will become very simple and free from any ad hoc provisos.Thus we get a nice and complete logical predicate calculus,which may serve as the very foundation for the whole mathematics.
