The categorical abstract machine
Proc. of a conference on Functional programming languages and computer architecture
Symbolic Logic and Mechanical Theorem Proving
Symbolic Logic and Mechanical Theorem Proving
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The cartesian closed category (ccc) and topos differ from each other in both the descriptive power and the executability. A ccc cannot express the rich structure of data types, in particular, the concept of subtypes, while it has an executable structure as a model of typed @l-calculus. On the othe rhand, topos has the strong expressive power of the concept of subtypes, although it does not in general have a good correspondence to any computation system. This article introduces the structure of e-ccc, as an intermediate of the ccc and topos. The e-ccc has the correspondence to @l-calculus based on an extended abstract data type theory and thus can be considered to be executable. This theory can be considered to be between typed @l-calculus(ccc) and higher order intuitionistic type theory(topos). General discussion on data type theory and category theory is also made. Moreover, relations between e-ccc and ccc or topos are discussed. In particular, topos is proved to be a specially-structured e-ccc.