λ-演算的一种扩充

An Extension of Lambda Calculus

对任一固定的集合ＡＮ（Ｎ表示自然数集），本文定义了λ－演算的一种扩充λＡ－演算．证明了λＡ－演算具有Ｃｈｕｒｃｈ－Ｒｏｓｓｅｒ性质，从而是协调的．并证明了λＡ－可定义全函数与Ａ－递归函数是等价的．

For any fixed set AN(N is the set of natural numbers),we define λA calculus which is an extension of λβ calculus .First,we show that λA calculus has Church Rosserproperty(so it is consistent).Then we prove that the notion of A recursive functions and that of λA definable functions coincide.