A FORMAL IDENTIFICATION BETWEEN TUPLES AND LISTS WITH AN APPLICATION TO LIST-ARITHMETIC CATEGORIES

We may say with confidence that in many papers about general programmi ng languages either the distinction between n-tuples and lists of leng th n is avoided, or those objects are identified, but only at an intui tive level [7, 8, 13]. That type of identification, considered formall y, leads to non-trivial problems, making difficult the typing of the f unctions used to deal with lists, i.e. hd, tl, cons... In this paper, following computational intuitions, we present a construction of a lis t object as a coproduct. This idea is the key concept that permits us to prove directly some of the presented results about list-arithmetic categories. This is a most useful construction because we construct re cursive objects on the basis of the expected semantics of a list objec t.