Specifying implementations

Abstract

III t.his papor t.he aua.lysis of t.lie data struct,ures uwd in 21 software systcn1 for SyIuhOlic Clomput.at,ioI1 in Algrlxdc T0l>010g~, ~IIOWU i1S EAT (Ejfedi~~~ Al,~~ehic T'o~o~o~TJ), is undertalwn. Having tho11ght. Of t.lIe rolr: Of fIIIIct.ional IJ~O-grauming in this particular prograru, we 11ilVC come to a generitl rlcfinit,ion of an operation on .\lJstract

Modelling algebraic structures and morphisms in ACL2

“…5. Moreover, the representation of a set in a computer needs the encoding of the equality of such a set (this was deeply studied in [45]), and setoids can be used with this aim.…”

Object oriented institutions to specify symbolic computation systems

“…In particular, first we studied one of the most important aspects of EAT, that is, its data structures. In that study [21,22] we found that there are two different layers of data structures in EAT. In the first layer, one finds the usual data structures.…”

“…Then, a Σ imp -algebra defines a family of Σ-algebras (the carrier set for the distinguished sort acts as an index for this family). Besides, working with implementations in [21] we were able to prove that EAT (second-layer) data structures are as general as possible, in the sense that they are ingredients of final objects in certain categories of ADT implementations. Later on, led by this characterization of EAT data structures, in [22] we reinterpreted our results in terms of hidden algebras [15] and coalgebras [27], technologies that have been presented in the literature as related to the object-oriented paradigm [14,18,27].…”

“…For these structures, behaviour and observation are more important than storage and traversing aspects. The way chosen by Sergeraert to develop EAT was based in an intensively functional programming use (see [21,25]). In this program, an element of the second layer is encoded by means of a record of common lisp functions which has a field for each operation of the algebraic structure which is been represented.…”

“…We first realized that in a system such as EAT we are not only implementing an abstract data type, or, shortly, an ADT (as a group, for instance), but also dealing with implementations of ADTs (several hundreds of implementations of the ADT group would populate the program memory). In [21] a construction, which is called imp operation, was defined. This construction models the skip from a kind of structures to families of these structures.…”