Abstract
The cartesian closed category (ccc) and topos differ in both descriptive power and executability. The ccc cannot express the concept of subtypes, while it has the executable structure as a model of typed λ-calculus. On the other hand, the topos has strong expressive power of subtypes, although it does not in general have a good correspondence to any computation system. This paper introduces the structure of e-ccc, as an intermediate of the ccc and topos. The e-ccc has the correspondence to the λ-calculus based on an extended abstract data type theory and thus can be considered to be executable. Moreover, relations between e-ccc and ccc or topos are discussed. In particular, the topos is proved to be a specially-structured e-ccc.
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