Formal Methods and Social Context in Software Development

In ordinary social interaction, including cooperative work, there are many structures that participants use and represent in a variety of ways, e.g., with verbal descriptions, drawings, tables, graphs, etc. For example, consider sporting events. Figure 1 shows a table from a newspaper representing the order and participants in a boat race, the Henley Regatta, while Figure 2 shows the same information in the form of a tree. This structure could also be conveyed by a table on a scoreboard, or a sequence of phrases in spoken English. Thus there is a precise structure that is independent of how it happens to be represented; i.e., we have an abstract data type, abbreviated ADT. As in [11], we use order sorted initial algebra semantics (see [12]) to formalize this structure. A complete formal specification of the Henley Regatta ADT is given in the appendix, using the specification language OBJ3 [14]. This specification has been executed. (Experience shows it is necessary to test all but the most trivial specifications in order to eliminate bugs.) The Henley Regatta example was inspired by Toulmin [25], although Toulmin only used concrete representations without realizing they were algebras, that different representations give isomorphic algebras, or that there is no unique best representation. Visitors' Cup. Heat 1: Jesus, Cambridge v. Christ Church; Heat 2: Oriel v. New College; ... Heat 8: Lady Margaret v. winner of Heat 1; ... Heat 26: Winner of Heat 23 v. winner of Heat 24; Final: Winner of Heat 25 v. winner of Heat 26. Figure 1: A Draw for the Henley Regatta Several different kinds of entity are involved in a regatta. Some of these can be arranged in a hierarchical classification scheme according to the subsort relation. Sorts correspond to an important class of members' categories, although not every members' category is formalized by a sort; for example, heats are not formalized this way. We will say that boats have sort Boat, completed regattas have sort Reg, possibly not yet specified boats have sort Boat? (a supersort of Boat), and possibly not yet completed regattas have the supersort Reg?; the latter includes all draws. It is convenient to assume that Boat is a subsort of Reg and that Boat? is a subsort of Reg?; these assumptions imply that there are trivial regattas consisting of just one boat, which could even be the unknown boat, denoted "?". Some sorts are built in, in the sense that they are already