Abstract

This paper is part of FOC[3] a project for developing Computer Algebra libraries, certified in Coq [2]. FOC has developed a methodology for programming Computer Algebra libraries, using modules and objects in Ocaml. In order to specify modularity features used by FOC in Ocaml, we are coding in Coq a theory for extensible records with dependent fields. This theory intends to express especially the kind of inheritance with method redefinition and late binding, that FOC uses in its Ocaml programs. The unit of FOC are coded as records. As we want to encode semantic information on units, the fields of our records may be proofs. Thus, our fields may depend on each others. We called them Drecords. Then, we introduce a new datatype, called mixDrec, to represent FOC classes. Actually, mixDrecs are useful for describing a hierarchy of Drecords in a incremental way. In mixDrecs, fields can be only declared or they can be redefined. MixDrecs can be extended by inheritance.

Citations